TSTP Solution File: ALG161+1 by Princess---230619
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Princess---230619
% Problem : ALG161+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm : none
% Format : tptp
% Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Aug 30 16:39:11 EDT 2023
% Result : Unsatisfiable 26.03s 4.28s
% Output : Proof 142.94s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG161+1 : TPTP v8.1.2. Released v2.7.0.
% 0.11/0.13 % Command : princess -inputFormat=tptp +threads -portfolio=casc +printProof -timeoutSec=%d %s
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 28 03:45:55 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.61 ________ _____
% 0.19/0.61 ___ __ \_________(_)________________________________
% 0.19/0.61 __ /_/ /_ ___/_ /__ __ \ ___/ _ \_ ___/_ ___/
% 0.19/0.61 _ ____/_ / _ / _ / / / /__ / __/(__ )_(__ )
% 0.19/0.61 /_/ /_/ /_/ /_/ /_/\___/ \___//____/ /____/
% 0.19/0.61
% 0.19/0.61 A Theorem Prover for First-Order Logic modulo Linear Integer Arithmetic
% 0.19/0.61 (2023-06-19)
% 0.19/0.61
% 0.19/0.61 (c) Philipp Rümmer, 2009-2023
% 0.19/0.61 Contributors: Peter Backeman, Peter Baumgartner, Angelo Brillout, Zafer Esen,
% 0.19/0.61 Amanda Stjerna.
% 0.19/0.61 Free software under BSD-3-Clause.
% 0.19/0.61
% 0.19/0.61 For more information, visit http://www.philipp.ruemmer.org/princess.shtml
% 0.19/0.61
% 0.19/0.61 Loading /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.19/0.63 Running up to 7 provers in parallel.
% 0.19/0.64 Prover 0: Options: +triggersInConjecture +genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1042961893
% 0.19/0.64 Prover 1: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1571432423
% 0.19/0.64 Prover 2: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMinimalAndEmpty -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1065072994
% 0.19/0.64 Prover 3: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=1922548996
% 0.19/0.64 Prover 4: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=1868514696
% 0.19/0.64 Prover 5: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allMaximal -realRatSaturationRounds=1 -ignoreQuantifiers -constructProofs=never -generateTriggers=complete -randomSeed=1259561288
% 0.19/0.64 Prover 6: Options: -triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=none +reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximalOutermost -realRatSaturationRounds=0 -ignoreQuantifiers -constructProofs=never -generateTriggers=all -randomSeed=-1399714365
% 4.15/1.43 Prover 4: Preprocessing ...
% 4.15/1.43 Prover 1: Preprocessing ...
% 5.31/1.46 Prover 0: Preprocessing ...
% 5.31/1.46 Prover 6: Preprocessing ...
% 5.31/1.46 Prover 3: Preprocessing ...
% 5.31/1.46 Prover 5: Preprocessing ...
% 5.31/1.46 Prover 2: Preprocessing ...
% 8.26/1.85 Prover 3: Constructing countermodel ...
% 8.26/1.85 Prover 2: Constructing countermodel ...
% 8.26/1.93 Prover 4: Constructing countermodel ...
% 8.26/1.93 Prover 0: Constructing countermodel ...
% 8.26/1.93 Prover 1: Constructing countermodel ...
% 8.26/1.94 Prover 6: Constructing countermodel ...
% 10.90/2.23 Prover 5: Constructing countermodel ...
% 26.03/4.28 Prover 3: proved (3641ms)
% 26.03/4.28
% 26.03/4.28 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 26.03/4.28
% 26.03/4.28 Prover 6: stopped
% 26.03/4.28 Prover 2: stopped
% 26.03/4.29 Prover 0: stopped
% 26.03/4.29 Prover 5: stopped
% 26.03/4.31 Prover 7: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-236303470
% 26.03/4.31 Prover 8: Options: +triggersInConjecture +genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-200781089
% 26.03/4.31 Prover 10: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=919308125
% 26.03/4.31 Prover 11: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=allUni -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=all -randomSeed=-1509710984
% 26.03/4.31 Prover 13: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=simple -reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=0 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=1138197443
% 27.78/4.50 Prover 7: Preprocessing ...
% 27.78/4.51 Prover 8: Preprocessing ...
% 28.15/4.53 Prover 10: Preprocessing ...
% 28.15/4.58 Prover 11: Preprocessing ...
% 28.15/4.59 Prover 13: Preprocessing ...
% 28.41/4.65 Prover 8: Constructing countermodel ...
% 28.41/4.71 Prover 7: Constructing countermodel ...
% 28.41/4.72 Prover 10: Constructing countermodel ...
% 28.41/4.72 Prover 13: Constructing countermodel ...
% 29.66/4.76 Prover 11: Constructing countermodel ...
% 66.42/9.63 Prover 13: stopped
% 66.42/9.66 Prover 16: Options: +triggersInConjecture -genTotalityAxioms +tightFunctionScopes -clausifier=simple +reverseFunctionalityPropagation +boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=completeFrugal -randomSeed=-2043353683
% 67.07/9.74 Prover 16: Preprocessing ...
% 68.66/9.87 Prover 16: Constructing countermodel ...
% 111.85/15.48 Prover 16: stopped
% 111.85/15.48 Prover 19: Options: +triggersInConjecture -genTotalityAxioms -tightFunctionScopes -clausifier=none -reverseFunctionalityPropagation -boolFunsAsPreds -triggerStrategy=maximal -realRatSaturationRounds=1 +ignoreQuantifiers -constructProofs=always -generateTriggers=complete -randomSeed=-1780594085
% 112.75/15.59 Prover 19: Preprocessing ...
% 113.44/15.68 Prover 19: Constructing countermodel ...
% 115.03/15.98 Prover 1: stopped
% 132.28/18.28 Prover 10: Found proof (size 697290)
% 132.28/18.28 Prover 10: proved (13995ms)
% 132.28/18.28 Prover 8: stopped
% 132.28/18.28 Prover 4: stopped
% 132.28/18.29 Prover 7: stopped
% 132.28/18.29 Prover 19: stopped
% 132.28/18.29 Prover 11: stopped
% 132.28/18.29
% 132.28/18.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 132.28/18.29
% 134.15/18.69 % SZS output start Proof for theBenchmark
% 134.28/18.76 Assumptions after simplification:
% 134.28/18.76 ---------------------------------
% 134.28/18.76
% 134.28/18.76 (ax1)
% 134.40/18.81 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.81 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 134.40/18.81 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 134.40/18.81 $i] : ? [v14: $i] : ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 &
% 134.40/18.81 op(e3, e1) = v13 & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 &
% 134.40/18.81 op(e2, e1) = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 &
% 134.40/18.81 op(e1, e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 134.40/18.81 op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 134.40/18.81 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 134.40/18.81 $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15 = e2 | v15 = e1 | v15 =
% 134.40/18.81 e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14 = e0) & (v13 = e3 | v13 = e2 |
% 134.40/18.81 v13 = e1 | v13 = e0) & (v12 = e3 | v12 = e2 | v12 = e1 | v12 = e0) & (v11
% 134.40/18.81 = e3 | v11 = e2 | v11 = e1 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 |
% 134.40/18.81 v10 = e0) & (v9 = e3 | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 |
% 134.40/18.81 v8 = e1 | v8 = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 |
% 134.40/18.81 v6 = e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 134.40/18.81 (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 = e1 | v3
% 134.40/18.81 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3 | v1 = e2 | v1
% 134.40/18.81 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0 = e0))
% 134.40/18.81
% 134.40/18.81 (ax10)
% 134.40/18.82 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.82 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 134.40/18.82 op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 &
% 134.40/18.82 $i(v1))))
% 134.40/18.82
% 134.40/18.82 (ax11)
% 134.40/18.82 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.82 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 134.40/18.82 op(e0, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 &
% 134.40/18.82 $i(v1))))
% 134.40/18.82
% 134.40/18.82 (ax12)
% 134.40/18.82 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.82 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 134.40/18.82 op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 &
% 134.40/18.82 $i(v1))))
% 134.40/18.82
% 134.40/18.82 (ax13)
% 134.40/18.83 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.83 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 134.40/18.83 op(e1, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 &
% 134.40/18.83 $i(v1))))
% 134.40/18.83
% 134.40/18.83 (ax14)
% 134.40/18.83 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.83 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 134.40/18.83 op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 &
% 134.40/18.83 $i(v1))))
% 134.40/18.83
% 134.40/18.83 (ax15)
% 134.40/18.83 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.83 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 &
% 134.40/18.83 op(e1, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 &
% 134.40/18.83 $i(v1))))
% 134.40/18.83
% 134.40/18.83 (ax16)
% 134.40/18.83 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.83 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 &
% 134.40/18.83 op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 &
% 134.40/18.83 $i(v1))))
% 134.40/18.83
% 134.40/18.83 (ax17)
% 134.40/18.83 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.83 (op(e1, e1) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 &
% 134.40/18.83 op(e1, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 &
% 134.40/18.83 $i(v1))))
% 134.40/18.84
% 134.40/18.84 (ax18)
% 134.40/18.84 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.84 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 134.40/18.84 op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 &
% 134.40/18.84 $i(v1))))
% 134.40/18.84
% 134.40/18.84 (ax19)
% 134.40/18.84 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.40/18.84 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 134.40/18.84 op(e2, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 &
% 134.40/18.84 $i(v1))))
% 134.40/18.84
% 134.40/18.84 (ax2)
% 134.69/18.87 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.87 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 134.69/18.87 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 134.69/18.87 $i] : ? [v14: $i] : ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 =
% 134.69/18.87 e3 & op(e3, e2) = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3,
% 134.69/18.87 e0) = e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 134.69/18.87 e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3)) & ((v15
% 134.69/18.87 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11 = e2 &
% 134.69/18.87 op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 = e2 & op(e3,
% 134.69/18.87 e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 & op(e1, e3) = e2)
% 134.69/18.87 | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 & op(e3, e3) = e1) | (v14 = e1
% 134.69/18.87 & op(e3, e2) = e1) | (v11 = e1 & op(e3, e1) = e1) | (v6 = e1 & op(e3,
% 134.69/18.87 e0) = e1)) & ((v15 = e1 & op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) =
% 134.69/18.87 e1) | (v9 = e1 & op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15
% 134.69/18.87 = e0 & op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 134.69/18.87 op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 & op(e3,
% 134.69/18.87 e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 & op(e1, e3) = e0)
% 134.69/18.87 | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 & op(e3, e2) = e3) | (v12 = e3
% 134.69/18.87 & op(e2, e2) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v2 = e3 & op(e0, e2)
% 134.69/18.87 = e3)) & ((v14 = e2 & op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 134.69/18.87 (v8 = e2 & op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 134.69/18.87 op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 & op(e1, e2)
% 134.69/18.87 = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 & op(e3, e2) = e0) |
% 134.69/18.87 (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v2 = e0 &
% 134.69/18.87 op(e0, e2) = e0)) & ((v13 = e3 & op(e2, e3) = e3) | (v12 = e3 & op(e2,
% 134.69/18.87 e2) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) =
% 134.69/18.87 e3)) & ((v13 = e2 & op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) |
% 134.69/18.87 (v10 = e2 & op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 134.69/18.87 op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 & op(e2, e1)
% 134.69/18.87 = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 & op(e2, e3) = e0) |
% 134.69/18.87 (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v5 = e0 &
% 134.69/18.87 op(e2, e0) = e0)) & ((v11 = e3 & op(e3, e1) = e3) | (v10 = e3 & op(e2,
% 134.69/18.87 e1) = e3) | (v7 = e3 & op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3))
% 134.69/18.87 & ((v11 = e2 & op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 134.69/18.87 op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 & op(e3,
% 134.69/18.87 e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 & op(e1, e1) = e1)
% 134.69/18.87 | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 & op(e3, e1) = e0) | (v10 = e0
% 134.69/18.87 & op(e2, e1) = e0) | (v7 = e0 & op(e1, e1) = e0) | (v1 = e0 & op(e0, e1)
% 134.69/18.87 = e0)) & ((v9 = e3 & op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) |
% 134.69/18.87 (v7 = e3 & op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 134.69/18.87 op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 & op(e1, e1) =
% 134.69/18.87 e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 & op(e1, e3) = e1) | (v8
% 134.69/18.87 = e1 & op(e1, e2) = e1) | (v7 = e1 & op(e1, e1) = e1) | (v4 = e1 &
% 134.69/18.87 op(e1, e0) = e1)) & ((v9 = e0 & op(e1, e3) = e0) | (v8 = e0 & op(e1, e2)
% 134.69/18.87 = e0) | (v7 = e0 & op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) &
% 134.69/18.87 ((v6 = e3 & op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 134.69/18.87 op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 & op(e3, e0)
% 134.69/18.87 = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 & op(e1, e0) = e2) | (v0
% 134.69/18.87 = e2 & op(e0, e0) = e2)) & ((v6 = e1 & op(e3, e0) = e1) | (v5 = e1 &
% 134.69/18.87 op(e2, e0) = e1) | (v4 = e1 & op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) =
% 134.69/18.87 e1)) & ((v3 = e3 & op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1
% 134.69/18.87 = e3 & op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 134.69/18.87 op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 & op(e0, e1) =
% 134.69/18.87 e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 & op(e0, e3) = e1) | (v2
% 134.69/18.87 = e1 & op(e0, e2) = e1) | (v1 = e1 & op(e0, e1) = e1) | (v0 = e1 &
% 134.69/18.87 op(e0, e0) = e1)) & ((v0 = e0 & op(e0, e0) = e0) | (((v6 = e0 & op(e3,
% 134.69/18.87 e0) = e0) | (v5 = e0 & op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) =
% 134.69/18.87 e0)) & ((v3 = e0 & op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) |
% 134.69/18.87 (v1 = e0 & op(e0, e1) = e0)))))
% 134.69/18.87
% 134.69/18.87 (ax20)
% 134.69/18.87 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.87 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 134.69/18.87 op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 &
% 134.69/18.87 $i(v1))))
% 134.69/18.87
% 134.69/18.87 (ax21)
% 134.69/18.87 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.87 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 &
% 134.69/18.87 op(e2, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 &
% 134.69/18.87 $i(v1))))
% 134.69/18.87
% 134.69/18.87 (ax22)
% 134.69/18.87 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.87 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 &
% 134.69/18.87 op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 &
% 134.69/18.87 $i(v1))))
% 134.69/18.87
% 134.69/18.87 (ax23)
% 134.69/18.87 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.87 (op(e2, e2) = v0 & $i(v0) & ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 &
% 134.69/18.87 op(e2, e3) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 &
% 134.69/18.87 $i(v1))))
% 134.69/18.87
% 134.69/18.87 (ax24)
% 134.69/18.88 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.88 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 134.69/18.88 op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 &
% 134.69/18.88 $i(v1))))
% 134.69/18.88
% 134.69/18.88 (ax25)
% 134.69/18.88 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.88 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 134.69/18.88 op(e3, e0) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 &
% 134.69/18.88 $i(v1))))
% 134.69/18.88
% 134.69/18.88 (ax26)
% 134.69/18.88 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.88 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 134.69/18.88 op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 &
% 134.69/18.88 $i(v1))))
% 134.69/18.88
% 134.69/18.88 (ax27)
% 134.69/18.88 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.88 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 &
% 134.69/18.88 op(e3, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 &
% 134.69/18.88 $i(v1))))
% 134.69/18.88
% 134.69/18.88 (ax28)
% 134.69/18.88 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.88 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 &
% 134.69/18.88 op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 &
% 134.69/18.88 $i(v1))))
% 134.69/18.88
% 134.69/18.88 (ax29)
% 134.69/18.88 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.88 (op(e3, e3) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 &
% 134.69/18.88 op(e3, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 &
% 134.69/18.88 $i(v1))))
% 134.69/18.88
% 134.69/18.88 (ax3)
% 134.69/18.89 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.89 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 134.69/18.89 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 134.69/18.89 $i] : ? [v14: $i] : ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~
% 134.69/18.89 (v15 = v12) & ~ (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 =
% 134.69/18.89 v13) & ~ (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) &
% 134.69/18.89 ~ (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12 =
% 134.69/18.89 v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 = v9) & ~
% 134.69/18.89 (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9) & ~ (v10 = v8) &
% 134.69/18.89 ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~ (v9 = v5) & ~ (v9 = v1) &
% 134.69/18.89 ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6) & ~ (v7 = v5) & ~ (v7 = v4) &
% 134.69/18.89 ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6 = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~
% 134.69/18.89 (v5 = v1) & ~ (v4 = v0) & ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~
% 134.69/18.89 (v2 = v1) & ~ (v2 = v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) =
% 134.69/18.89 v11 & op(e3, e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) =
% 134.69/18.89 v10 & op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) = v9
% 134.69/18.89 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0, e2) = v8 &
% 134.69/18.89 op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) & $i(v12) &
% 134.69/18.89 $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) & $i(v5) & $i(v4) &
% 134.69/18.89 $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 134.69/18.89
% 134.69/18.89 (ax4)
% 134.69/18.89 ~ (e3 = e2) & ~ (e3 = e1) & ~ (e3 = e0) & ~ (e2 = e1) & ~ (e2 = e0) & ~
% 134.69/18.89 (e1 = e0) & $i(e3) & $i(e2) & $i(e1) & $i(e0)
% 134.69/18.89
% 134.69/18.89 (ax5)
% 134.69/18.90 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.90 ? [v3: $i] : ? [v4: $i] : ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8:
% 134.69/18.90 $i] : ? [v9: $i] : ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13:
% 134.69/18.90 $i] : ? [v14: $i] : ? [v15: $i] : (((v6 = e2 & v4 = e3 & ~ (v15 = e3) &
% 134.69/18.90 op(e3, e3) = e2 & op(e3, e2) = v15 & op(e2, e2) = e3 & $i(v15)) | (v6 =
% 134.69/18.91 e2 & v4 = e3 & ~ (v12 = e2) & op(e3, e3) = e2 & op(e2, e3) = v12 &
% 134.69/18.91 op(e2, e2) = e3 & $i(v12)) | (v6 = e1 & v2 = e3 & ~ (v14 = e3) & op(e3,
% 134.69/18.91 e3) = e1 & op(e3, e1) = v14 & op(e1, e1) = e3 & $i(v14)) | (v6 = e1 &
% 134.69/18.91 v2 = e3 & ~ (v9 = e1) & op(e3, e3) = e1 & op(e1, e3) = v9 & op(e1, e1)
% 134.69/18.91 = e3 & $i(v9)) | (v6 = e0 & v0 = e3 & ~ (v13 = e3) & op(e3, e3) = e0 &
% 134.69/18.91 op(e3, e0) = v13 & op(e0, e0) = e3 & $i(v13)) | (v4 = e1 & v2 = e2 & ~
% 134.69/18.91 (v11 = e2) & op(e2, e2) = e1 & op(e2, e1) = v11 & op(e1, e1) = e2 &
% 134.69/18.91 $i(v11)) | (v4 = e1 & v2 = e2 & ~ (v8 = e1) & op(e2, e2) = e1 & op(e1,
% 134.69/18.91 e2) = v8 & op(e1, e1) = e2 & $i(v8)) | (v4 = e0 & v0 = e2 & ~ (v10 =
% 134.69/18.91 e2) & op(e2, e2) = e0 & op(e2, e0) = v10 & op(e0, e0) = e2 & $i(v10))
% 134.69/18.91 | (op(e0, e0) = v0 & $i(v0) & ((v6 = e0 & v0 = e3 & ~ (v5 = e0) & op(e3,
% 134.69/18.91 e3) = e0 & op(e0, e3) = v5 & $i(v5)) | (v4 = e0 & v0 = e2 & ~ (v3
% 134.69/18.91 = e0) & op(e2, e2) = e0 & op(e0, e2) = v3 & $i(v3)) | (v2 = e0 &
% 134.69/18.91 v0 = e1 & ~ (v7 = e1) & op(e1, e1) = e0 & op(e1, e0) = v7 & $i(v7))
% 134.69/18.91 | (v2 = e0 & v0 = e1 & ~ (v1 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 134.69/18.91 v1 & $i(v1))))) & ((op(e3, e3) = v6 & $i(v6) & ((v12 = e2 & op(e2,
% 134.69/18.91 e3) = e2) | ( ~ (v4 = e3) & op(e2, e2) = v4 & $i(v4))) & ((v9 = e1
% 134.69/18.91 & op(e1, e3) = e1) | ( ~ (v2 = e3) & op(e1, e1) = v2 & $i(v2))) &
% 134.69/18.91 ((v5 = e0 & op(e0, e3) = e0) | ( ~ (v0 = e3) & op(e0, e0) = v0 &
% 134.69/18.91 $i(v0))) & ((v4 = e3 & op(e2, e2) = e3) | ( ~ (v12 = e2) & op(e2,
% 134.69/18.91 e3) = v12 & $i(v12))) & ((v2 = e3 & op(e1, e1) = e3) | ( ~ (v9 =
% 134.69/18.91 e1) & op(e1, e3) = v9 & $i(v9))) & ((v0 = e3 & op(e0, e0) = e3) |
% 134.69/18.91 ( ~ (v5 = e0) & op(e0, e3) = v5 & $i(v5)))) | (op(e2, e2) = v4 &
% 134.69/18.91 $i(v4) & ((v15 = e3 & op(e3, e2) = e3) | ( ~ (v6 = e2) & op(e3, e3) = v6
% 134.69/18.91 & $i(v6))) & ((v8 = e1 & op(e1, e2) = e1) | ( ~ (v2 = e2) & op(e1,
% 134.69/18.91 e1) = v2 & $i(v2))) & ((v6 = e2 & op(e3, e3) = e2) | ( ~ (v15 =
% 134.69/18.91 e3) & op(e3, e2) = v15 & $i(v15))) & ((v3 = e0 & op(e0, e2) = e0)
% 134.69/18.91 | ( ~ (v0 = e2) & op(e0, e0) = v0 & $i(v0))) & ((v2 = e2 & op(e1, e1)
% 134.69/18.91 = e2) | ( ~ (v8 = e1) & op(e1, e2) = v8 & $i(v8))) & ((v0 = e2 &
% 134.69/18.91 op(e0, e0) = e2) | ( ~ (v3 = e0) & op(e0, e2) = v3 & $i(v3)))) |
% 134.69/18.91 (op(e1, e1) = v2 & $i(v2) & ((v14 = e3 & op(e3, e1) = e3) | ( ~ (v6 = e1)
% 134.69/18.91 & op(e3, e3) = v6 & $i(v6))) & ((v11 = e2 & op(e2, e1) = e2) | ( ~
% 134.69/18.91 (v4 = e1) & op(e2, e2) = v4 & $i(v4))) & ((v6 = e1 & op(e3, e3) =
% 134.69/18.91 e1) | ( ~ (v14 = e3) & op(e3, e1) = v14 & $i(v14))) & ((v4 = e1 &
% 134.69/18.91 op(e2, e2) = e1) | ( ~ (v11 = e2) & op(e2, e1) = v11 & $i(v11))) &
% 134.69/18.91 ((v1 = e0 & op(e0, e1) = e0) | ( ~ (v0 = e1) & op(e0, e0) = v0 &
% 134.69/18.91 $i(v0))) & ((v0 = e1 & op(e0, e0) = e1) | ( ~ (v1 = e0) & op(e0, e1)
% 134.69/18.91 = v1 & $i(v1)))) | (op(e0, e0) = v0 & $i(v0) & ((v13 = e3 & op(e3,
% 134.69/18.91 e0) = e3) | ( ~ (v6 = e0) & op(e3, e3) = v6 & $i(v6))) & ((v10 =
% 134.69/18.91 e2 & op(e2, e0) = e2) | ( ~ (v4 = e0) & op(e2, e2) = v4 & $i(v4))) &
% 134.69/18.91 ((v7 = e1 & op(e1, e0) = e1) | ( ~ (v2 = e0) & op(e1, e1) = v2 &
% 134.69/18.91 $i(v2))) & ((v6 = e0 & op(e3, e3) = e0) | ( ~ (v13 = e3) & op(e3,
% 134.69/18.91 e0) = v13 & $i(v13))) & ((v4 = e0 & op(e2, e2) = e0) | ( ~ (v10 =
% 134.69/18.91 e2) & op(e2, e0) = v10 & $i(v10))) & ((v2 = e0 & op(e1, e1) = e0)
% 134.69/18.91 | ( ~ (v7 = e1) & op(e1, e0) = v7 & $i(v7))))))
% 134.69/18.91
% 134.69/18.91 (ax6)
% 134.69/18.91 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.91 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 &
% 134.69/18.91 op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 &
% 134.69/18.91 $i(v1))))
% 134.69/18.91
% 134.69/18.91 (ax7)
% 134.69/18.91 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.91 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 134.69/18.91 op(e0, e1) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 &
% 134.69/18.91 $i(v1))))
% 134.69/18.91
% 134.69/18.91 (ax8)
% 134.69/18.91 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.91 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 &
% 134.69/18.91 op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 &
% 134.69/18.91 $i(v1))))
% 134.69/18.91
% 134.69/18.91 (ax9)
% 134.69/18.91 $i(e3) & $i(e2) & $i(e1) & $i(e0) & ? [v0: $i] : ? [v1: $i] : ? [v2: $i] :
% 134.69/18.91 (op(e0, e0) = v0 & $i(v0) & ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 &
% 134.69/18.91 op(e0, e2) = v1 & $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 &
% 134.69/18.91 $i(v1))))
% 134.69/18.91
% 134.69/18.91 (function-axioms)
% 134.69/18.91 ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~ (op(v3,
% 134.69/18.91 v2) = v1) | ~ (op(v3, v2) = v0))
% 134.69/18.91
% 134.69/18.91 Those formulas are unsatisfiable:
% 134.69/18.91 ---------------------------------
% 134.69/18.91
% 134.69/18.91 Begin of proof
% 134.69/18.91 |
% 134.69/18.92 | ALPHA: (ax1) implies:
% 134.69/18.92 | (1) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 134.69/18.92 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 134.69/18.92 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 134.69/18.92 | ? [v15: $i] : (op(e3, e3) = v15 & op(e3, e2) = v14 & op(e3, e1) = v13
% 134.69/18.92 | & op(e3, e0) = v12 & op(e2, e3) = v11 & op(e2, e2) = v10 & op(e2, e1)
% 134.69/18.92 | = v9 & op(e2, e0) = v8 & op(e1, e3) = v7 & op(e1, e2) = v6 & op(e1,
% 134.69/18.92 | e1) = v5 & op(e1, e0) = v4 & op(e0, e3) = v3 & op(e0, e2) = v2 &
% 134.69/18.92 | op(e0, e1) = v1 & op(e0, e0) = v0 & $i(v15) & $i(v14) & $i(v13) &
% 134.69/18.92 | $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) & $i(v6) &
% 134.69/18.92 | $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0) & (v15 = e3 | v15
% 134.69/18.92 | = e2 | v15 = e1 | v15 = e0) & (v14 = e3 | v14 = e2 | v14 = e1 | v14
% 134.69/18.92 | = e0) & (v13 = e3 | v13 = e2 | v13 = e1 | v13 = e0) & (v12 = e3 |
% 134.69/18.92 | v12 = e2 | v12 = e1 | v12 = e0) & (v11 = e3 | v11 = e2 | v11 = e1 |
% 134.69/18.92 | v11 = e0) & (v10 = e3 | v10 = e2 | v10 = e1 | v10 = e0) & (v9 = e3
% 134.69/18.92 | | v9 = e2 | v9 = e1 | v9 = e0) & (v8 = e3 | v8 = e2 | v8 = e1 | v8
% 134.69/18.92 | = e0) & (v7 = e3 | v7 = e2 | v7 = e1 | v7 = e0) & (v6 = e3 | v6 =
% 134.69/18.92 | e2 | v6 = e1 | v6 = e0) & (v5 = e3 | v5 = e2 | v5 = e1 | v5 = e0) &
% 134.69/18.92 | (v4 = e3 | v4 = e2 | v4 = e1 | v4 = e0) & (v3 = e3 | v3 = e2 | v3 =
% 134.69/18.92 | e1 | v3 = e0) & (v2 = e3 | v2 = e2 | v2 = e1 | v2 = e0) & (v1 = e3
% 134.69/18.92 | | v1 = e2 | v1 = e1 | v1 = e0) & (v0 = e3 | v0 = e2 | v0 = e1 | v0
% 134.69/18.92 | = e0))
% 134.69/18.92 |
% 134.69/18.92 | ALPHA: (ax2) implies:
% 134.69/18.94 | (2) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 134.69/18.94 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 134.69/18.94 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 134.69/18.94 | ? [v15: $i] : (((v15 = e3 & op(e3, e3) = e3) | (v14 = e3 & op(e3, e2)
% 134.69/18.94 | = e3) | (v11 = e3 & op(e3, e1) = e3) | (v6 = e3 & op(e3, e0) =
% 134.69/18.94 | e3)) & ((v15 = e3 & op(e3, e3) = e3) | (v13 = e3 & op(e2, e3) =
% 134.69/18.94 | e3) | (v9 = e3 & op(e1, e3) = e3) | (v3 = e3 & op(e0, e3) = e3))
% 134.69/18.94 | & ((v15 = e2 & op(e3, e3) = e2) | (v14 = e2 & op(e3, e2) = e2) | (v11
% 134.69/18.94 | = e2 & op(e3, e1) = e2) | (v6 = e2 & op(e3, e0) = e2)) & ((v15 =
% 134.69/18.94 | e2 & op(e3, e3) = e2) | (v13 = e2 & op(e2, e3) = e2) | (v9 = e2 &
% 134.69/18.94 | op(e1, e3) = e2) | (v3 = e2 & op(e0, e3) = e2)) & ((v15 = e1 &
% 134.69/18.94 | op(e3, e3) = e1) | (v14 = e1 & op(e3, e2) = e1) | (v11 = e1 &
% 134.69/18.94 | op(e3, e1) = e1) | (v6 = e1 & op(e3, e0) = e1)) & ((v15 = e1 &
% 134.69/18.94 | op(e3, e3) = e1) | (v13 = e1 & op(e2, e3) = e1) | (v9 = e1 &
% 134.69/18.94 | op(e1, e3) = e1) | (v3 = e1 & op(e0, e3) = e1)) & ((v15 = e0 &
% 134.69/18.94 | op(e3, e3) = e0) | (v14 = e0 & op(e3, e2) = e0) | (v11 = e0 &
% 134.69/18.94 | op(e3, e1) = e0) | (v6 = e0 & op(e3, e0) = e0)) & ((v15 = e0 &
% 134.69/18.94 | op(e3, e3) = e0) | (v13 = e0 & op(e2, e3) = e0) | (v9 = e0 &
% 134.69/18.94 | op(e1, e3) = e0) | (v3 = e0 & op(e0, e3) = e0)) & ((v14 = e3 &
% 134.69/18.94 | op(e3, e2) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v8 = e3 &
% 134.69/18.94 | op(e1, e2) = e3) | (v2 = e3 & op(e0, e2) = e3)) & ((v14 = e2 &
% 134.69/18.94 | op(e3, e2) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v8 = e2 &
% 134.69/18.94 | op(e1, e2) = e2) | (v2 = e2 & op(e0, e2) = e2)) & ((v14 = e1 &
% 134.69/18.94 | op(e3, e2) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v8 = e1 &
% 134.69/18.94 | op(e1, e2) = e1) | (v2 = e1 & op(e0, e2) = e1)) & ((v14 = e0 &
% 134.69/18.94 | op(e3, e2) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v8 = e0 &
% 134.69/18.94 | op(e1, e2) = e0) | (v2 = e0 & op(e0, e2) = e0)) & ((v13 = e3 &
% 134.69/18.94 | op(e2, e3) = e3) | (v12 = e3 & op(e2, e2) = e3) | (v10 = e3 &
% 134.69/18.94 | op(e2, e1) = e3) | (v5 = e3 & op(e2, e0) = e3)) & ((v13 = e2 &
% 134.69/18.94 | op(e2, e3) = e2) | (v12 = e2 & op(e2, e2) = e2) | (v10 = e2 &
% 134.69/18.94 | op(e2, e1) = e2) | (v5 = e2 & op(e2, e0) = e2)) & ((v13 = e1 &
% 134.69/18.94 | op(e2, e3) = e1) | (v12 = e1 & op(e2, e2) = e1) | (v10 = e1 &
% 134.69/18.94 | op(e2, e1) = e1) | (v5 = e1 & op(e2, e0) = e1)) & ((v13 = e0 &
% 134.69/18.94 | op(e2, e3) = e0) | (v12 = e0 & op(e2, e2) = e0) | (v10 = e0 &
% 134.69/18.94 | op(e2, e1) = e0) | (v5 = e0 & op(e2, e0) = e0)) & ((v11 = e3 &
% 134.69/18.94 | op(e3, e1) = e3) | (v10 = e3 & op(e2, e1) = e3) | (v7 = e3 &
% 134.69/18.94 | op(e1, e1) = e3) | (v1 = e3 & op(e0, e1) = e3)) & ((v11 = e2 &
% 134.69/18.94 | op(e3, e1) = e2) | (v10 = e2 & op(e2, e1) = e2) | (v7 = e2 &
% 134.69/18.94 | op(e1, e1) = e2) | (v1 = e2 & op(e0, e1) = e2)) & ((v11 = e1 &
% 134.69/18.94 | op(e3, e1) = e1) | (v10 = e1 & op(e2, e1) = e1) | (v7 = e1 &
% 134.69/18.94 | op(e1, e1) = e1) | (v1 = e1 & op(e0, e1) = e1)) & ((v11 = e0 &
% 134.69/18.94 | op(e3, e1) = e0) | (v10 = e0 & op(e2, e1) = e0) | (v7 = e0 &
% 134.69/18.94 | op(e1, e1) = e0) | (v1 = e0 & op(e0, e1) = e0)) & ((v9 = e3 &
% 134.69/18.94 | op(e1, e3) = e3) | (v8 = e3 & op(e1, e2) = e3) | (v7 = e3 &
% 134.69/18.94 | op(e1, e1) = e3) | (v4 = e3 & op(e1, e0) = e3)) & ((v9 = e2 &
% 134.69/18.94 | op(e1, e3) = e2) | (v8 = e2 & op(e1, e2) = e2) | (v7 = e2 &
% 134.69/18.94 | op(e1, e1) = e2) | (v4 = e2 & op(e1, e0) = e2)) & ((v9 = e1 &
% 134.69/18.94 | op(e1, e3) = e1) | (v8 = e1 & op(e1, e2) = e1) | (v7 = e1 &
% 134.69/18.94 | op(e1, e1) = e1) | (v4 = e1 & op(e1, e0) = e1)) & ((v9 = e0 &
% 134.69/18.94 | op(e1, e3) = e0) | (v8 = e0 & op(e1, e2) = e0) | (v7 = e0 &
% 134.69/18.94 | op(e1, e1) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v6 = e3 &
% 134.69/18.94 | op(e3, e0) = e3) | (v5 = e3 & op(e2, e0) = e3) | (v4 = e3 &
% 134.69/18.94 | op(e1, e0) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v6 = e2 &
% 134.69/18.94 | op(e3, e0) = e2) | (v5 = e2 & op(e2, e0) = e2) | (v4 = e2 &
% 134.69/18.94 | op(e1, e0) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v6 = e1 &
% 134.69/18.94 | op(e3, e0) = e1) | (v5 = e1 & op(e2, e0) = e1) | (v4 = e1 &
% 134.69/18.94 | op(e1, e0) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v3 = e3 &
% 134.69/18.94 | op(e0, e3) = e3) | (v2 = e3 & op(e0, e2) = e3) | (v1 = e3 &
% 134.69/18.94 | op(e0, e1) = e3) | (v0 = e3 & op(e0, e0) = e3)) & ((v3 = e2 &
% 134.69/18.94 | op(e0, e3) = e2) | (v2 = e2 & op(e0, e2) = e2) | (v1 = e2 &
% 134.69/18.94 | op(e0, e1) = e2) | (v0 = e2 & op(e0, e0) = e2)) & ((v3 = e1 &
% 134.69/18.94 | op(e0, e3) = e1) | (v2 = e1 & op(e0, e2) = e1) | (v1 = e1 &
% 134.69/18.94 | op(e0, e1) = e1) | (v0 = e1 & op(e0, e0) = e1)) & ((v0 = e0 &
% 134.69/18.94 | op(e0, e0) = e0) | (((v6 = e0 & op(e3, e0) = e0) | (v5 = e0 &
% 134.69/18.94 | op(e2, e0) = e0) | (v4 = e0 & op(e1, e0) = e0)) & ((v3 = e0 &
% 134.69/18.94 | op(e0, e3) = e0) | (v2 = e0 & op(e0, e2) = e0) | (v1 = e0 &
% 134.69/18.94 | op(e0, e1) = e0)))))
% 134.69/18.94 |
% 134.69/18.94 | ALPHA: (ax3) implies:
% 134.69/18.95 | (3) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 134.69/18.95 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] : ?
% 134.69/18.95 | [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14: $i] :
% 134.69/18.95 | ? [v15: $i] : ( ~ (v15 = v14) & ~ (v15 = v13) & ~ (v15 = v12) & ~
% 134.69/18.95 | (v15 = v11) & ~ (v15 = v7) & ~ (v15 = v3) & ~ (v14 = v13) & ~
% 134.69/18.95 | (v14 = v12) & ~ (v14 = v10) & ~ (v14 = v6) & ~ (v14 = v2) & ~
% 134.69/18.95 | (v13 = v12) & ~ (v13 = v9) & ~ (v13 = v5) & ~ (v13 = v1) & ~ (v12
% 134.69/18.95 | = v8) & ~ (v12 = v4) & ~ (v12 = v0) & ~ (v11 = v10) & ~ (v11 =
% 134.69/18.95 | v9) & ~ (v11 = v8) & ~ (v11 = v7) & ~ (v11 = v3) & ~ (v10 = v9)
% 134.69/18.95 | & ~ (v10 = v8) & ~ (v10 = v6) & ~ (v10 = v2) & ~ (v9 = v8) & ~
% 134.69/18.95 | (v9 = v5) & ~ (v9 = v1) & ~ (v8 = v4) & ~ (v8 = v0) & ~ (v7 = v6)
% 134.69/18.95 | & ~ (v7 = v5) & ~ (v7 = v4) & ~ (v7 = v3) & ~ (v6 = v5) & ~ (v6
% 134.69/18.95 | = v4) & ~ (v6 = v2) & ~ (v5 = v4) & ~ (v5 = v1) & ~ (v4 = v0) &
% 134.69/18.95 | ~ (v3 = v2) & ~ (v3 = v1) & ~ (v3 = v0) & ~ (v2 = v1) & ~ (v2 =
% 134.69/18.95 | v0) & ~ (v1 = v0) & op(e3, e3) = v15 & op(e3, e2) = v11 & op(e3,
% 134.69/18.95 | e1) = v7 & op(e3, e0) = v3 & op(e2, e3) = v14 & op(e2, e2) = v10 &
% 134.69/18.95 | op(e2, e1) = v6 & op(e2, e0) = v2 & op(e1, e3) = v13 & op(e1, e2) =
% 134.69/18.95 | v9 & op(e1, e1) = v5 & op(e1, e0) = v1 & op(e0, e3) = v12 & op(e0,
% 134.69/18.95 | e2) = v8 & op(e0, e1) = v4 & op(e0, e0) = v0 & $i(v15) & $i(v14) &
% 134.69/18.95 | $i(v13) & $i(v12) & $i(v11) & $i(v10) & $i(v9) & $i(v8) & $i(v7) &
% 134.69/18.95 | $i(v6) & $i(v5) & $i(v4) & $i(v3) & $i(v2) & $i(v1) & $i(v0))
% 134.69/18.95 |
% 134.69/18.95 | ALPHA: (ax4) implies:
% 134.69/18.95 | (4) ~ (e1 = e0)
% 134.69/18.95 | (5) ~ (e2 = e0)
% 134.69/18.95 | (6) ~ (e2 = e1)
% 134.69/18.95 | (7) ~ (e3 = e0)
% 134.69/18.95 | (8) ~ (e3 = e1)
% 134.69/18.95 | (9) ~ (e3 = e2)
% 134.69/18.95 |
% 134.69/18.95 | ALPHA: (ax5) implies:
% 134.69/18.96 | (10) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : ? [v3: $i] : ? [v4: $i] :
% 134.69/18.96 | ? [v5: $i] : ? [v6: $i] : ? [v7: $i] : ? [v8: $i] : ? [v9: $i] :
% 134.69/18.96 | ? [v10: $i] : ? [v11: $i] : ? [v12: $i] : ? [v13: $i] : ? [v14:
% 134.69/18.96 | $i] : ? [v15: $i] : (((v6 = e2 & v4 = e3 & ~ (v15 = e3) & op(e3,
% 134.69/18.96 | e3) = e2 & op(e3, e2) = v15 & op(e2, e2) = e3 & $i(v15)) | (v6
% 134.69/18.96 | = e2 & v4 = e3 & ~ (v12 = e2) & op(e3, e3) = e2 & op(e2, e3) =
% 134.69/18.96 | v12 & op(e2, e2) = e3 & $i(v12)) | (v6 = e1 & v2 = e3 & ~ (v14
% 134.69/18.96 | = e3) & op(e3, e3) = e1 & op(e3, e1) = v14 & op(e1, e1) = e3 &
% 134.69/18.96 | $i(v14)) | (v6 = e1 & v2 = e3 & ~ (v9 = e1) & op(e3, e3) = e1 &
% 134.69/18.96 | op(e1, e3) = v9 & op(e1, e1) = e3 & $i(v9)) | (v6 = e0 & v0 = e3
% 134.69/18.96 | & ~ (v13 = e3) & op(e3, e3) = e0 & op(e3, e0) = v13 & op(e0,
% 134.69/18.96 | e0) = e3 & $i(v13)) | (v4 = e1 & v2 = e2 & ~ (v11 = e2) &
% 134.69/18.96 | op(e2, e2) = e1 & op(e2, e1) = v11 & op(e1, e1) = e2 & $i(v11))
% 134.69/18.96 | | (v4 = e1 & v2 = e2 & ~ (v8 = e1) & op(e2, e2) = e1 & op(e1, e2)
% 134.69/18.96 | = v8 & op(e1, e1) = e2 & $i(v8)) | (v4 = e0 & v0 = e2 & ~ (v10
% 134.69/18.96 | = e2) & op(e2, e2) = e0 & op(e2, e0) = v10 & op(e0, e0) = e2 &
% 134.69/18.96 | $i(v10)) | (op(e0, e0) = v0 & $i(v0) & ((v6 = e0 & v0 = e3 & ~
% 134.69/18.96 | (v5 = e0) & op(e3, e3) = e0 & op(e0, e3) = v5 & $i(v5)) |
% 134.69/18.96 | (v4 = e0 & v0 = e2 & ~ (v3 = e0) & op(e2, e2) = e0 & op(e0,
% 134.69/18.96 | e2) = v3 & $i(v3)) | (v2 = e0 & v0 = e1 & ~ (v7 = e1) &
% 134.69/18.96 | op(e1, e1) = e0 & op(e1, e0) = v7 & $i(v7)) | (v2 = e0 & v0
% 134.69/18.96 | = e1 & ~ (v1 = e0) & op(e1, e1) = e0 & op(e0, e1) = v1 &
% 134.69/18.96 | $i(v1))))) & ((op(e3, e3) = v6 & $i(v6) & ((v12 = e2 &
% 134.69/18.96 | op(e2, e3) = e2) | ( ~ (v4 = e3) & op(e2, e2) = v4 &
% 134.69/18.96 | $i(v4))) & ((v9 = e1 & op(e1, e3) = e1) | ( ~ (v2 = e3) &
% 134.69/18.96 | op(e1, e1) = v2 & $i(v2))) & ((v5 = e0 & op(e0, e3) = e0) |
% 134.69/18.96 | ( ~ (v0 = e3) & op(e0, e0) = v0 & $i(v0))) & ((v4 = e3 &
% 134.69/18.96 | op(e2, e2) = e3) | ( ~ (v12 = e2) & op(e2, e3) = v12 &
% 134.69/18.96 | $i(v12))) & ((v2 = e3 & op(e1, e1) = e3) | ( ~ (v9 = e1) &
% 134.69/18.96 | op(e1, e3) = v9 & $i(v9))) & ((v0 = e3 & op(e0, e0) = e3) |
% 134.69/18.96 | ( ~ (v5 = e0) & op(e0, e3) = v5 & $i(v5)))) | (op(e2, e2) = v4
% 134.69/18.96 | & $i(v4) & ((v15 = e3 & op(e3, e2) = e3) | ( ~ (v6 = e2) &
% 134.69/18.96 | op(e3, e3) = v6 & $i(v6))) & ((v8 = e1 & op(e1, e2) = e1) |
% 134.69/18.96 | ( ~ (v2 = e2) & op(e1, e1) = v2 & $i(v2))) & ((v6 = e2 &
% 134.69/18.96 | op(e3, e3) = e2) | ( ~ (v15 = e3) & op(e3, e2) = v15 &
% 134.69/18.96 | $i(v15))) & ((v3 = e0 & op(e0, e2) = e0) | ( ~ (v0 = e2) &
% 134.69/18.96 | op(e0, e0) = v0 & $i(v0))) & ((v2 = e2 & op(e1, e1) = e2) |
% 134.69/18.96 | ( ~ (v8 = e1) & op(e1, e2) = v8 & $i(v8))) & ((v0 = e2 &
% 134.69/18.96 | op(e0, e0) = e2) | ( ~ (v3 = e0) & op(e0, e2) = v3 &
% 134.69/18.96 | $i(v3)))) | (op(e1, e1) = v2 & $i(v2) & ((v14 = e3 & op(e3,
% 134.69/18.96 | e1) = e3) | ( ~ (v6 = e1) & op(e3, e3) = v6 & $i(v6))) &
% 134.69/18.96 | ((v11 = e2 & op(e2, e1) = e2) | ( ~ (v4 = e1) & op(e2, e2) = v4
% 134.69/18.96 | & $i(v4))) & ((v6 = e1 & op(e3, e3) = e1) | ( ~ (v14 = e3) &
% 134.69/18.96 | op(e3, e1) = v14 & $i(v14))) & ((v4 = e1 & op(e2, e2) = e1)
% 134.69/18.96 | | ( ~ (v11 = e2) & op(e2, e1) = v11 & $i(v11))) & ((v1 = e0 &
% 134.69/18.96 | op(e0, e1) = e0) | ( ~ (v0 = e1) & op(e0, e0) = v0 &
% 134.69/18.96 | $i(v0))) & ((v0 = e1 & op(e0, e0) = e1) | ( ~ (v1 = e0) &
% 134.69/18.96 | op(e0, e1) = v1 & $i(v1)))) | (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.96 | ((v13 = e3 & op(e3, e0) = e3) | ( ~ (v6 = e0) & op(e3, e3) = v6
% 134.69/18.96 | & $i(v6))) & ((v10 = e2 & op(e2, e0) = e2) | ( ~ (v4 = e0) &
% 134.69/18.96 | op(e2, e2) = v4 & $i(v4))) & ((v7 = e1 & op(e1, e0) = e1) |
% 134.69/18.96 | ( ~ (v2 = e0) & op(e1, e1) = v2 & $i(v2))) & ((v6 = e0 &
% 134.69/18.96 | op(e3, e3) = e0) | ( ~ (v13 = e3) & op(e3, e0) = v13 &
% 134.69/18.96 | $i(v13))) & ((v4 = e0 & op(e2, e2) = e0) | ( ~ (v10 = e2) &
% 134.69/18.96 | op(e2, e0) = v10 & $i(v10))) & ((v2 = e0 & op(e1, e1) = e0)
% 134.69/18.96 | | ( ~ (v7 = e1) & op(e1, e0) = v7 & $i(v7))))))
% 134.69/18.96 |
% 134.69/18.96 | ALPHA: (ax6) implies:
% 134.69/18.96 | (11) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.96 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 134.69/18.96 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e1) = v1 & $i(v1))))
% 134.69/18.96 |
% 134.69/18.96 | ALPHA: (ax7) implies:
% 134.69/18.96 | (12) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.96 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e1) = v1 &
% 134.69/18.96 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e1) = v1 & $i(v1))))
% 134.69/18.96 |
% 134.69/18.96 | ALPHA: (ax8) implies:
% 134.69/18.96 | (13) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.96 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 134.69/18.96 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e0, e2) = v1 & $i(v1))))
% 134.69/18.96 |
% 134.69/18.96 | ALPHA: (ax9) implies:
% 134.69/18.96 | (14) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.96 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e0) = v2 & op(e0, e2) = v1 &
% 134.69/18.96 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e2) = v1 & $i(v1))))
% 134.69/18.96 |
% 134.69/18.96 | ALPHA: (ax10) implies:
% 134.69/18.96 | (15) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.96 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 134.69/18.96 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e0, e3) = v1 & $i(v1))))
% 134.69/18.96 |
% 134.69/18.96 | ALPHA: (ax11) implies:
% 134.69/18.97 | (16) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e0, e0) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e0) = v2 & op(e0, e3) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e0, e3) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax12) implies:
% 134.69/18.97 | (17) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e0) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax13) implies:
% 134.69/18.97 | (18) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e0) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e0) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax14) implies:
% 134.69/18.97 | (19) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e1, e2) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax15) implies:
% 134.69/18.97 | (20) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e2) | ( ~ (v2 = e3) & op(v1, e1) = v2 & op(e1, e2) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e2) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax16) implies:
% 134.69/18.97 | (21) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e1, e3) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax17) implies:
% 134.69/18.97 | (22) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e1, e1) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e3) | ( ~ (v2 = e2) & op(v1, e1) = v2 & op(e1, e3) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e1, e3) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax18) implies:
% 134.69/18.97 | (23) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e0) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax19) implies:
% 134.69/18.97 | (24) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e0) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e0) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e0) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax20) implies:
% 134.69/18.97 | (25) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e3) & op(e2, e1) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax21) implies:
% 134.69/18.97 | (26) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e1) | ( ~ (v2 = e3) & op(v1, e2) = v2 & op(e2, e1) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e1) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax22) implies:
% 134.69/18.97 | (27) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 134.69/18.97 | ( ~ (v0 = e3) | ( ~ (v2 = e0) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 134.69/18.97 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e2, e3) = v1 & $i(v1))))
% 134.69/18.97 |
% 134.69/18.97 | ALPHA: (ax23) implies:
% 134.69/18.98 | (28) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e2, e2) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e3) | ( ~ (v2 = e1) & op(v1, e2) = v2 & op(e2, e3) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e2, e3) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (ax24) implies:
% 134.69/18.98 | (29) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e0) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e0) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (ax25) implies:
% 134.69/18.98 | (30) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e0) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e0) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e0) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (ax26) implies:
% 134.69/18.98 | (31) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e1) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e2) & op(e3, e1) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (ax27) implies:
% 134.69/18.98 | (32) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e1) | ( ~ (v2 = e2) & op(v1, e3) = v2 & op(e3, e1) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e1) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (ax28) implies:
% 134.69/18.98 | (33) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e2) | ( ~ (v2 = e0) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e1) & op(e3, e2) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (ax29) implies:
% 134.69/18.98 | (34) ? [v0: $i] : ? [v1: $i] : ? [v2: $i] : (op(e3, e3) = v0 & $i(v0) &
% 134.69/18.98 | ( ~ (v0 = e2) | ( ~ (v2 = e1) & op(v1, e3) = v2 & op(e3, e2) = v1 &
% 134.69/18.98 | $i(v2) & $i(v1)) | ( ~ (v1 = e0) & op(e3, e2) = v1 & $i(v1))))
% 134.69/18.98 |
% 134.69/18.98 | DELTA: instantiating (20) with fresh symbols all_4_0, all_4_1, all_4_2 gives:
% 134.69/18.98 | (35) op(e1, e1) = all_4_2 & $i(all_4_2) & ( ~ (all_4_2 = e2) | ( ~ (all_4_0
% 134.69/18.98 | = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 134.69/18.98 | $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) =
% 134.69/18.98 | all_4_1 & $i(all_4_1)))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (35) implies:
% 134.69/18.98 | (36) op(e1, e1) = all_4_2
% 134.69/18.98 | (37) ~ (all_4_2 = e2) | ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 &
% 134.69/18.98 | op(e1, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 =
% 134.69/18.98 | e0) & op(e1, e2) = all_4_1 & $i(all_4_1))
% 134.69/18.98 |
% 134.69/18.98 | DELTA: instantiating (27) with fresh symbols all_6_0, all_6_1, all_6_2 gives:
% 134.69/18.98 | (38) op(e2, e2) = all_6_2 & $i(all_6_2) & ( ~ (all_6_2 = e3) | ( ~ (all_6_0
% 134.69/18.98 | = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 134.69/18.98 | $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) =
% 134.69/18.98 | all_6_1 & $i(all_6_1)))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (38) implies:
% 134.69/18.98 | (39) op(e2, e2) = all_6_2
% 134.69/18.98 | (40) ~ (all_6_2 = e3) | ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 &
% 134.69/18.98 | op(e2, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 134.69/18.98 | e1) & op(e2, e3) = all_6_1 & $i(all_6_1))
% 134.69/18.98 |
% 134.69/18.98 | DELTA: instantiating (21) with fresh symbols all_8_0, all_8_1, all_8_2 gives:
% 134.69/18.98 | (41) op(e1, e1) = all_8_2 & $i(all_8_2) & ( ~ (all_8_2 = e3) | ( ~ (all_8_0
% 134.69/18.98 | = e0) & op(all_8_1, e1) = all_8_0 & op(e1, e3) = all_8_1 &
% 134.69/18.98 | $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e2) & op(e1, e3) =
% 134.69/18.98 | all_8_1 & $i(all_8_1)))
% 134.69/18.98 |
% 134.69/18.98 | ALPHA: (41) implies:
% 134.69/18.98 | (42) op(e1, e1) = all_8_2
% 134.69/18.99 | (43) ~ (all_8_2 = e3) | ( ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 &
% 134.69/18.99 | op(e1, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 =
% 134.69/18.99 | e2) & op(e1, e3) = all_8_1 & $i(all_8_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (11) with fresh symbols all_10_0, all_10_1, all_10_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (44) op(e0, e0) = all_10_2 & $i(all_10_2) & ( ~ (all_10_2 = e1) | ( ~
% 134.69/18.99 | (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0, e1) =
% 134.69/18.99 | all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e3) &
% 134.69/18.99 | op(e0, e1) = all_10_1 & $i(all_10_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (44) implies:
% 134.69/18.99 | (45) op(e0, e0) = all_10_2
% 134.69/18.99 | (46) ~ (all_10_2 = e1) | ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0
% 134.69/18.99 | & op(e0, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 134.69/18.99 | (all_10_1 = e3) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (22) with fresh symbols all_12_0, all_12_1, all_12_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (47) op(e1, e1) = all_12_2 & $i(all_12_2) & ( ~ (all_12_2 = e3) | ( ~
% 134.69/18.99 | (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 & op(e1, e3) =
% 134.69/18.99 | all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e0) &
% 134.69/18.99 | op(e1, e3) = all_12_1 & $i(all_12_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (47) implies:
% 134.69/18.99 | (48) op(e1, e1) = all_12_2
% 134.69/18.99 | (49) ~ (all_12_2 = e3) | ( ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0
% 134.69/18.99 | & op(e1, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~
% 134.69/18.99 | (all_12_1 = e0) & op(e1, e3) = all_12_1 & $i(all_12_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (29) with fresh symbols all_14_0, all_14_1, all_14_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (50) op(e3, e3) = all_14_2 & $i(all_14_2) & ( ~ (all_14_2 = e0) | ( ~
% 134.69/18.99 | (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 134.69/18.99 | all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) &
% 134.69/18.99 | op(e3, e0) = all_14_1 & $i(all_14_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (50) implies:
% 134.69/18.99 | (51) op(e3, e3) = all_14_2
% 134.69/18.99 | (52) ~ (all_14_2 = e0) | ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0
% 134.69/18.99 | & op(e3, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 134.69/18.99 | (all_14_1 = e2) & op(e3, e0) = all_14_1 & $i(all_14_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (23) with fresh symbols all_16_0, all_16_1, all_16_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (53) op(e2, e2) = all_16_2 & $i(all_16_2) & ( ~ (all_16_2 = e0) | ( ~
% 134.69/18.99 | (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 134.69/18.99 | all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) &
% 134.69/18.99 | op(e2, e0) = all_16_1 & $i(all_16_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (53) implies:
% 134.69/18.99 | (54) op(e2, e2) = all_16_2
% 134.69/18.99 | (55) ~ (all_16_2 = e0) | ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0
% 134.69/18.99 | & op(e2, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~
% 134.69/18.99 | (all_16_1 = e3) & op(e2, e0) = all_16_1 & $i(all_16_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (24) with fresh symbols all_18_0, all_18_1, all_18_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (56) op(e2, e2) = all_18_2 & $i(all_18_2) & ( ~ (all_18_2 = e0) | ( ~
% 134.69/18.99 | (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 134.69/18.99 | all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) &
% 134.69/18.99 | op(e2, e0) = all_18_1 & $i(all_18_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (56) implies:
% 134.69/18.99 | (57) op(e2, e2) = all_18_2
% 134.69/18.99 | (58) ~ (all_18_2 = e0) | ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0
% 134.69/18.99 | & op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~
% 134.69/18.99 | (all_18_1 = e1) & op(e2, e0) = all_18_1 & $i(all_18_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (26) with fresh symbols all_20_0, all_20_1, all_20_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (59) op(e2, e2) = all_20_2 & $i(all_20_2) & ( ~ (all_20_2 = e1) | ( ~
% 134.69/18.99 | (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 134.69/18.99 | all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) &
% 134.69/18.99 | op(e2, e1) = all_20_1 & $i(all_20_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (59) implies:
% 134.69/18.99 | (60) op(e2, e2) = all_20_2
% 134.69/18.99 | (61) ~ (all_20_2 = e1) | ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0
% 134.69/18.99 | & op(e2, e1) = all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~
% 134.69/18.99 | (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (31) with fresh symbols all_22_0, all_22_1, all_22_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (62) op(e3, e3) = all_22_2 & $i(all_22_2) & ( ~ (all_22_2 = e1) | ( ~
% 134.69/18.99 | (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 & op(e3, e1) =
% 134.69/18.99 | all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) &
% 134.69/18.99 | op(e3, e1) = all_22_1 & $i(all_22_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (62) implies:
% 134.69/18.99 | (63) op(e3, e3) = all_22_2
% 134.69/18.99 | (64) ~ (all_22_2 = e1) | ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0
% 134.69/18.99 | & op(e3, e1) = all_22_1 & $i(all_22_0) & $i(all_22_1)) | ( ~
% 134.69/18.99 | (all_22_1 = e2) & op(e3, e1) = all_22_1 & $i(all_22_1))
% 134.69/18.99 |
% 134.69/18.99 | DELTA: instantiating (13) with fresh symbols all_24_0, all_24_1, all_24_2
% 134.69/18.99 | gives:
% 134.69/18.99 | (65) op(e0, e0) = all_24_2 & $i(all_24_2) & ( ~ (all_24_2 = e2) | ( ~
% 134.69/18.99 | (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 134.69/18.99 | all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) &
% 134.69/18.99 | op(e0, e2) = all_24_1 & $i(all_24_1)))
% 134.69/18.99 |
% 134.69/18.99 | ALPHA: (65) implies:
% 134.69/18.99 | (66) op(e0, e0) = all_24_2
% 134.69/19.00 | (67) ~ (all_24_2 = e2) | ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0
% 134.69/19.00 | & op(e0, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~
% 134.69/19.00 | (all_24_1 = e3) & op(e0, e2) = all_24_1 & $i(all_24_1))
% 134.69/19.00 |
% 134.69/19.00 | DELTA: instantiating (28) with fresh symbols all_26_0, all_26_1, all_26_2
% 134.69/19.00 | gives:
% 134.69/19.00 | (68) op(e2, e2) = all_26_2 & $i(all_26_2) & ( ~ (all_26_2 = e3) | ( ~
% 134.69/19.00 | (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 134.69/19.00 | all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) &
% 134.69/19.00 | op(e2, e3) = all_26_1 & $i(all_26_1)))
% 134.69/19.00 |
% 134.69/19.00 | ALPHA: (68) implies:
% 134.69/19.00 | (69) op(e2, e2) = all_26_2
% 134.78/19.00 | (70) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0
% 134.78/19.00 | & op(e2, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~
% 134.78/19.00 | (all_26_1 = e0) & op(e2, e3) = all_26_1 & $i(all_26_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (30) with fresh symbols all_28_0, all_28_1, all_28_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (71) op(e3, e3) = all_28_2 & $i(all_28_2) & ( ~ (all_28_2 = e0) | ( ~
% 134.78/19.00 | (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 134.78/19.00 | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) &
% 134.78/19.00 | op(e3, e0) = all_28_1 & $i(all_28_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (71) implies:
% 134.78/19.00 | (72) op(e3, e3) = all_28_2
% 134.78/19.00 | (73) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0
% 134.78/19.00 | & op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~
% 134.78/19.00 | (all_28_1 = e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (12) with fresh symbols all_30_0, all_30_1, all_30_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (74) op(e0, e0) = all_30_2 & $i(all_30_2) & ( ~ (all_30_2 = e1) | ( ~
% 134.78/19.00 | (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 134.78/19.00 | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e2) &
% 134.78/19.00 | op(e0, e1) = all_30_1 & $i(all_30_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (74) implies:
% 134.78/19.00 | (75) op(e0, e0) = all_30_2
% 134.78/19.00 | (76) ~ (all_30_2 = e1) | ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0
% 134.78/19.00 | & op(e0, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~
% 134.78/19.00 | (all_30_1 = e2) & op(e0, e1) = all_30_1 & $i(all_30_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (19) with fresh symbols all_32_0, all_32_1, all_32_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (77) op(e1, e1) = all_32_2 & $i(all_32_2) & ( ~ (all_32_2 = e2) | ( ~
% 134.78/19.00 | (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 134.78/19.00 | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 134.78/19.00 | op(e1, e2) = all_32_1 & $i(all_32_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (77) implies:
% 134.78/19.00 | (78) op(e1, e1) = all_32_2
% 134.78/19.00 | (79) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0
% 134.78/19.00 | & op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~
% 134.78/19.00 | (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (32) with fresh symbols all_34_0, all_34_1, all_34_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (80) op(e3, e3) = all_34_2 & $i(all_34_2) & ( ~ (all_34_2 = e1) | ( ~
% 134.78/19.00 | (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 134.78/19.00 | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e0) &
% 134.78/19.00 | op(e3, e1) = all_34_1 & $i(all_34_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (80) implies:
% 134.78/19.00 | (81) op(e3, e3) = all_34_2
% 134.78/19.00 | (82) ~ (all_34_2 = e1) | ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0
% 134.78/19.00 | & op(e3, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~
% 134.78/19.00 | (all_34_1 = e0) & op(e3, e1) = all_34_1 & $i(all_34_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (33) with fresh symbols all_36_0, all_36_1, all_36_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (83) op(e3, e3) = all_36_2 & $i(all_36_2) & ( ~ (all_36_2 = e2) | ( ~
% 134.78/19.00 | (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 134.78/19.00 | all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) &
% 134.78/19.00 | op(e3, e2) = all_36_1 & $i(all_36_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (83) implies:
% 134.78/19.00 | (84) op(e3, e3) = all_36_2
% 134.78/19.00 | (85) ~ (all_36_2 = e2) | ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 134.78/19.00 | & op(e3, e2) = all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~
% 134.78/19.00 | (all_36_1 = e1) & op(e3, e2) = all_36_1 & $i(all_36_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (25) with fresh symbols all_38_0, all_38_1, all_38_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (86) op(e2, e2) = all_38_2 & $i(all_38_2) & ( ~ (all_38_2 = e1) | ( ~
% 134.78/19.00 | (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 134.78/19.00 | all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) &
% 134.78/19.00 | op(e2, e1) = all_38_1 & $i(all_38_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (86) implies:
% 134.78/19.00 | (87) op(e2, e2) = all_38_2
% 134.78/19.00 | (88) ~ (all_38_2 = e1) | ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0
% 134.78/19.00 | & op(e2, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~
% 134.78/19.00 | (all_38_1 = e3) & op(e2, e1) = all_38_1 & $i(all_38_1))
% 134.78/19.00 |
% 134.78/19.00 | DELTA: instantiating (14) with fresh symbols all_40_0, all_40_1, all_40_2
% 134.78/19.00 | gives:
% 134.78/19.00 | (89) op(e0, e0) = all_40_2 & $i(all_40_2) & ( ~ (all_40_2 = e2) | ( ~
% 134.78/19.00 | (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 134.78/19.00 | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e1) &
% 134.78/19.00 | op(e0, e2) = all_40_1 & $i(all_40_1)))
% 134.78/19.00 |
% 134.78/19.00 | ALPHA: (89) implies:
% 134.78/19.00 | (90) op(e0, e0) = all_40_2
% 134.78/19.01 | (91) ~ (all_40_2 = e2) | ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 134.78/19.01 | & op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~
% 134.78/19.01 | (all_40_1 = e1) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 134.78/19.01 |
% 134.78/19.01 | DELTA: instantiating (15) with fresh symbols all_42_0, all_42_1, all_42_2
% 134.78/19.01 | gives:
% 134.78/19.01 | (92) op(e0, e0) = all_42_2 & $i(all_42_2) & ( ~ (all_42_2 = e3) | ( ~
% 134.78/19.01 | (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 134.78/19.01 | all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e2) &
% 134.78/19.01 | op(e0, e3) = all_42_1 & $i(all_42_1)))
% 134.78/19.01 |
% 134.78/19.01 | ALPHA: (92) implies:
% 134.78/19.01 | (93) op(e0, e0) = all_42_2
% 134.78/19.01 | (94) ~ (all_42_2 = e3) | ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0
% 134.78/19.01 | & op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~
% 134.78/19.01 | (all_42_1 = e2) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 134.78/19.01 |
% 134.78/19.01 | DELTA: instantiating (34) with fresh symbols all_44_0, all_44_1, all_44_2
% 134.78/19.01 | gives:
% 134.78/19.01 | (95) op(e3, e3) = all_44_2 & $i(all_44_2) & ( ~ (all_44_2 = e2) | ( ~
% 134.78/19.01 | (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 134.78/19.01 | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) &
% 134.78/19.01 | op(e3, e2) = all_44_1 & $i(all_44_1)))
% 134.78/19.01 |
% 134.78/19.01 | ALPHA: (95) implies:
% 134.78/19.01 | (96) op(e3, e3) = all_44_2
% 134.78/19.01 | (97) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0
% 134.78/19.01 | & op(e3, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~
% 134.78/19.01 | (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1))
% 134.78/19.01 |
% 134.78/19.01 | DELTA: instantiating (16) with fresh symbols all_46_0, all_46_1, all_46_2
% 134.78/19.01 | gives:
% 134.78/19.01 | (98) op(e0, e0) = all_46_2 & $i(all_46_2) & ( ~ (all_46_2 = e3) | ( ~
% 134.78/19.01 | (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 134.78/19.01 | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e1) &
% 134.78/19.01 | op(e0, e3) = all_46_1 & $i(all_46_1)))
% 134.78/19.01 |
% 134.78/19.01 | ALPHA: (98) implies:
% 134.78/19.01 | (99) op(e0, e0) = all_46_2
% 134.78/19.01 | (100) ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e0) =
% 134.78/19.01 | all_46_0 & op(e0, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | (
% 134.78/19.01 | ~ (all_46_1 = e1) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 134.78/19.01 |
% 134.78/19.01 | DELTA: instantiating (18) with fresh symbols all_48_0, all_48_1, all_48_2
% 134.78/19.01 | gives:
% 134.78/19.01 | (101) op(e1, e1) = all_48_2 & $i(all_48_2) & ( ~ (all_48_2 = e0) | ( ~
% 134.78/19.01 | (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 134.78/19.01 | all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e2) &
% 134.78/19.01 | op(e1, e0) = all_48_1 & $i(all_48_1)))
% 134.78/19.01 |
% 134.78/19.01 | ALPHA: (101) implies:
% 134.78/19.01 | (102) op(e1, e1) = all_48_2
% 134.78/19.01 | (103) ~ (all_48_2 = e0) | ( ~ (all_48_0 = e3) & op(all_48_1, e1) =
% 134.78/19.01 | all_48_0 & op(e1, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | (
% 134.78/19.01 | ~ (all_48_1 = e2) & op(e1, e0) = all_48_1 & $i(all_48_1))
% 134.78/19.01 |
% 134.78/19.01 | DELTA: instantiating (17) with fresh symbols all_50_0, all_50_1, all_50_2
% 134.78/19.01 | gives:
% 134.78/19.01 | (104) op(e1, e1) = all_50_2 & $i(all_50_2) & ( ~ (all_50_2 = e0) | ( ~
% 134.78/19.01 | (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 & op(e1, e0) =
% 134.78/19.01 | all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e3) &
% 134.78/19.01 | op(e1, e0) = all_50_1 & $i(all_50_1)))
% 134.78/19.01 |
% 134.78/19.01 | ALPHA: (104) implies:
% 134.78/19.01 | (105) op(e1, e1) = all_50_2
% 134.78/19.01 | (106) ~ (all_50_2 = e0) | ( ~ (all_50_0 = e2) & op(all_50_1, e1) =
% 134.78/19.01 | all_50_0 & op(e1, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | (
% 134.78/19.01 | ~ (all_50_1 = e3) & op(e1, e0) = all_50_1 & $i(all_50_1))
% 134.78/19.01 |
% 134.78/19.01 | DELTA: instantiating (3) with fresh symbols all_52_0, all_52_1, all_52_2,
% 134.78/19.01 | all_52_3, all_52_4, all_52_5, all_52_6, all_52_7, all_52_8, all_52_9,
% 134.78/19.01 | all_52_10, all_52_11, all_52_12, all_52_13, all_52_14, all_52_15 gives:
% 134.78/19.01 | (107) ~ (all_52_0 = all_52_1) & ~ (all_52_0 = all_52_2) & ~ (all_52_0 =
% 134.78/19.01 | all_52_3) & ~ (all_52_0 = all_52_4) & ~ (all_52_0 = all_52_8) &
% 134.78/19.01 | ~ (all_52_0 = all_52_12) & ~ (all_52_1 = all_52_2) & ~ (all_52_1 =
% 134.78/19.01 | all_52_3) & ~ (all_52_1 = all_52_5) & ~ (all_52_1 = all_52_9) &
% 134.78/19.01 | ~ (all_52_1 = all_52_13) & ~ (all_52_2 = all_52_3) & ~ (all_52_2 =
% 134.78/19.01 | all_52_6) & ~ (all_52_2 = all_52_10) & ~ (all_52_2 = all_52_14) &
% 134.78/19.01 | ~ (all_52_3 = all_52_7) & ~ (all_52_3 = all_52_11) & ~ (all_52_3 =
% 134.78/19.01 | all_52_15) & ~ (all_52_4 = all_52_5) & ~ (all_52_4 = all_52_6) &
% 134.78/19.01 | ~ (all_52_4 = all_52_7) & ~ (all_52_4 = all_52_8) & ~ (all_52_4 =
% 134.78/19.01 | all_52_12) & ~ (all_52_5 = all_52_6) & ~ (all_52_5 = all_52_7) &
% 134.78/19.01 | ~ (all_52_5 = all_52_9) & ~ (all_52_5 = all_52_13) & ~ (all_52_6 =
% 134.78/19.01 | all_52_7) & ~ (all_52_6 = all_52_10) & ~ (all_52_6 = all_52_14) &
% 134.78/19.01 | ~ (all_52_7 = all_52_11) & ~ (all_52_7 = all_52_15) & ~ (all_52_8
% 134.78/19.01 | = all_52_9) & ~ (all_52_8 = all_52_10) & ~ (all_52_8 = all_52_11)
% 134.78/19.01 | & ~ (all_52_8 = all_52_12) & ~ (all_52_9 = all_52_10) & ~
% 134.78/19.01 | (all_52_9 = all_52_11) & ~ (all_52_9 = all_52_13) & ~ (all_52_10 =
% 134.78/19.01 | all_52_11) & ~ (all_52_10 = all_52_14) & ~ (all_52_11 =
% 134.78/19.01 | all_52_15) & ~ (all_52_12 = all_52_13) & ~ (all_52_12 =
% 134.78/19.01 | all_52_14) & ~ (all_52_12 = all_52_15) & ~ (all_52_13 =
% 134.78/19.01 | all_52_14) & ~ (all_52_13 = all_52_15) & ~ (all_52_14 =
% 134.78/19.01 | all_52_15) & op(e3, e3) = all_52_0 & op(e3, e2) = all_52_4 & op(e3,
% 134.78/19.01 | e1) = all_52_8 & op(e3, e0) = all_52_12 & op(e2, e3) = all_52_1 &
% 134.78/19.01 | op(e2, e2) = all_52_5 & op(e2, e1) = all_52_9 & op(e2, e0) =
% 134.78/19.01 | all_52_13 & op(e1, e3) = all_52_2 & op(e1, e2) = all_52_6 & op(e1,
% 134.78/19.01 | e1) = all_52_10 & op(e1, e0) = all_52_14 & op(e0, e3) = all_52_3 &
% 134.78/19.01 | op(e0, e2) = all_52_7 & op(e0, e1) = all_52_11 & op(e0, e0) =
% 134.78/19.01 | all_52_15 & $i(all_52_0) & $i(all_52_1) & $i(all_52_2) & $i(all_52_3)
% 134.78/19.01 | & $i(all_52_4) & $i(all_52_5) & $i(all_52_6) & $i(all_52_7) &
% 134.78/19.01 | $i(all_52_8) & $i(all_52_9) & $i(all_52_10) & $i(all_52_11) &
% 134.78/19.01 | $i(all_52_12) & $i(all_52_13) & $i(all_52_14) & $i(all_52_15)
% 134.78/19.01 |
% 134.78/19.01 | ALPHA: (107) implies:
% 134.78/19.01 | (108) ~ (all_52_14 = all_52_15)
% 134.78/19.01 | (109) ~ (all_52_13 = all_52_15)
% 134.78/19.02 | (110) ~ (all_52_13 = all_52_14)
% 134.78/19.02 | (111) ~ (all_52_12 = all_52_15)
% 134.78/19.02 | (112) ~ (all_52_12 = all_52_14)
% 134.78/19.02 | (113) ~ (all_52_12 = all_52_13)
% 134.78/19.02 | (114) ~ (all_52_11 = all_52_15)
% 134.78/19.02 | (115) ~ (all_52_10 = all_52_14)
% 134.78/19.02 | (116) ~ (all_52_10 = all_52_11)
% 134.78/19.02 | (117) ~ (all_52_9 = all_52_13)
% 134.78/19.02 | (118) ~ (all_52_9 = all_52_11)
% 134.78/19.02 | (119) ~ (all_52_9 = all_52_10)
% 134.78/19.02 | (120) ~ (all_52_8 = all_52_12)
% 134.78/19.02 | (121) ~ (all_52_8 = all_52_11)
% 134.78/19.02 | (122) ~ (all_52_8 = all_52_10)
% 134.78/19.02 | (123) ~ (all_52_8 = all_52_9)
% 134.78/19.02 | (124) ~ (all_52_7 = all_52_15)
% 134.78/19.02 | (125) ~ (all_52_7 = all_52_11)
% 134.78/19.02 | (126) ~ (all_52_6 = all_52_14)
% 134.78/19.02 | (127) ~ (all_52_6 = all_52_10)
% 134.78/19.02 | (128) ~ (all_52_6 = all_52_7)
% 134.78/19.02 | (129) ~ (all_52_5 = all_52_13)
% 134.78/19.02 | (130) ~ (all_52_5 = all_52_9)
% 134.78/19.02 | (131) ~ (all_52_5 = all_52_7)
% 134.78/19.02 | (132) ~ (all_52_5 = all_52_6)
% 134.78/19.02 | (133) ~ (all_52_4 = all_52_12)
% 134.78/19.02 | (134) ~ (all_52_4 = all_52_8)
% 134.78/19.02 | (135) ~ (all_52_4 = all_52_7)
% 134.78/19.02 | (136) ~ (all_52_4 = all_52_6)
% 134.78/19.02 | (137) ~ (all_52_4 = all_52_5)
% 134.78/19.02 | (138) ~ (all_52_3 = all_52_15)
% 134.78/19.02 | (139) ~ (all_52_3 = all_52_11)
% 134.78/19.02 | (140) ~ (all_52_3 = all_52_7)
% 134.78/19.02 | (141) ~ (all_52_2 = all_52_14)
% 134.78/19.02 | (142) ~ (all_52_2 = all_52_10)
% 134.78/19.02 | (143) ~ (all_52_2 = all_52_6)
% 134.78/19.02 | (144) ~ (all_52_2 = all_52_3)
% 134.78/19.02 | (145) ~ (all_52_1 = all_52_13)
% 134.78/19.02 | (146) ~ (all_52_1 = all_52_9)
% 134.78/19.02 | (147) ~ (all_52_1 = all_52_5)
% 134.78/19.02 | (148) ~ (all_52_1 = all_52_3)
% 134.78/19.02 | (149) ~ (all_52_1 = all_52_2)
% 134.78/19.02 | (150) ~ (all_52_0 = all_52_12)
% 134.78/19.02 | (151) ~ (all_52_0 = all_52_8)
% 134.78/19.02 | (152) ~ (all_52_0 = all_52_4)
% 134.78/19.02 | (153) ~ (all_52_0 = all_52_3)
% 134.78/19.02 | (154) ~ (all_52_0 = all_52_2)
% 134.78/19.02 | (155) ~ (all_52_0 = all_52_1)
% 134.78/19.02 | (156) op(e0, e0) = all_52_15
% 134.78/19.02 | (157) op(e0, e1) = all_52_11
% 134.78/19.02 | (158) op(e0, e2) = all_52_7
% 134.78/19.02 | (159) op(e0, e3) = all_52_3
% 134.78/19.02 | (160) op(e1, e0) = all_52_14
% 134.78/19.02 | (161) op(e1, e1) = all_52_10
% 134.78/19.02 | (162) op(e1, e2) = all_52_6
% 134.78/19.02 | (163) op(e1, e3) = all_52_2
% 134.78/19.02 | (164) op(e2, e0) = all_52_13
% 134.78/19.02 | (165) op(e2, e1) = all_52_9
% 134.78/19.02 | (166) op(e2, e2) = all_52_5
% 134.78/19.02 | (167) op(e2, e3) = all_52_1
% 134.78/19.02 | (168) op(e3, e0) = all_52_12
% 134.78/19.02 | (169) op(e3, e1) = all_52_8
% 134.78/19.02 | (170) op(e3, e2) = all_52_4
% 134.78/19.02 | (171) op(e3, e3) = all_52_0
% 134.78/19.02 |
% 134.78/19.02 | DELTA: instantiating (1) with fresh symbols all_54_0, all_54_1, all_54_2,
% 134.78/19.02 | all_54_3, all_54_4, all_54_5, all_54_6, all_54_7, all_54_8, all_54_9,
% 134.78/19.02 | all_54_10, all_54_11, all_54_12, all_54_13, all_54_14, all_54_15 gives:
% 134.78/19.02 | (172) op(e3, e3) = all_54_0 & op(e3, e2) = all_54_1 & op(e3, e1) = all_54_2
% 134.78/19.02 | & op(e3, e0) = all_54_3 & op(e2, e3) = all_54_4 & op(e2, e2) =
% 134.78/19.02 | all_54_5 & op(e2, e1) = all_54_6 & op(e2, e0) = all_54_7 & op(e1, e3)
% 134.78/19.02 | = all_54_8 & op(e1, e2) = all_54_9 & op(e1, e1) = all_54_10 & op(e1,
% 134.78/19.02 | e0) = all_54_11 & op(e0, e3) = all_54_12 & op(e0, e2) = all_54_13 &
% 134.78/19.02 | op(e0, e1) = all_54_14 & op(e0, e0) = all_54_15 & $i(all_54_0) &
% 134.78/19.02 | $i(all_54_1) & $i(all_54_2) & $i(all_54_3) & $i(all_54_4) &
% 134.78/19.02 | $i(all_54_5) & $i(all_54_6) & $i(all_54_7) & $i(all_54_8) &
% 134.78/19.02 | $i(all_54_9) & $i(all_54_10) & $i(all_54_11) & $i(all_54_12) &
% 134.78/19.02 | $i(all_54_13) & $i(all_54_14) & $i(all_54_15) & (all_54_0 = e3 |
% 134.78/19.02 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0) & (all_54_1 = e3 |
% 134.78/19.02 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0) & (all_54_2 = e3 |
% 134.78/19.02 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0) & (all_54_3 = e3 |
% 134.78/19.02 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0) & (all_54_4 = e3 |
% 134.78/19.02 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0) & (all_54_5 = e3 |
% 134.78/19.02 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0) & (all_54_6 = e3 |
% 134.78/19.02 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0) & (all_54_7 = e3 |
% 134.78/19.02 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0) & (all_54_8 = e3 |
% 134.78/19.02 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0) & (all_54_9 = e3 |
% 134.78/19.02 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0) & (all_54_10 = e3 |
% 134.78/19.02 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0) & (all_54_11 = e3
% 134.78/19.02 | | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0) & (all_54_12 =
% 134.78/19.02 | e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0) & (all_54_13
% 134.78/19.02 | = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0) &
% 134.78/19.02 | (all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0) &
% 134.78/19.02 | (all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0)
% 134.78/19.02 |
% 134.78/19.02 | ALPHA: (172) implies:
% 134.78/19.02 | (173) op(e0, e0) = all_54_15
% 134.78/19.02 | (174) op(e0, e1) = all_54_14
% 134.78/19.02 | (175) op(e0, e2) = all_54_13
% 134.78/19.02 | (176) op(e0, e3) = all_54_12
% 134.78/19.02 | (177) op(e1, e0) = all_54_11
% 134.78/19.02 | (178) op(e1, e1) = all_54_10
% 134.78/19.02 | (179) op(e1, e2) = all_54_9
% 134.78/19.02 | (180) op(e1, e3) = all_54_8
% 134.78/19.02 | (181) op(e2, e0) = all_54_7
% 134.78/19.02 | (182) op(e2, e1) = all_54_6
% 134.78/19.03 | (183) op(e2, e2) = all_54_5
% 134.78/19.03 | (184) op(e2, e3) = all_54_4
% 134.78/19.03 | (185) op(e3, e0) = all_54_3
% 134.78/19.03 | (186) op(e3, e1) = all_54_2
% 134.78/19.03 | (187) op(e3, e2) = all_54_1
% 134.78/19.03 | (188) op(e3, e3) = all_54_0
% 134.78/19.03 | (189) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 134.78/19.03 | (190) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 134.78/19.03 | (191) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 134.78/19.03 | (192) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 134.78/19.03 | (193) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 134.78/19.03 | (194) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 134.78/19.03 | (195) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 134.78/19.03 | (196) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 134.78/19.03 | (197) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 134.78/19.03 | (198) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 134.78/19.03 | (199) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 134.78/19.03 | (200) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 134.78/19.03 | (201) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 134.78/19.03 | (202) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 134.78/19.03 | (203) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 134.78/19.03 | (204) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 134.78/19.03 |
% 134.78/19.03 | DELTA: instantiating (10) with fresh symbols all_56_0, all_56_1, all_56_2,
% 134.78/19.03 | all_56_3, all_56_4, all_56_5, all_56_6, all_56_7, all_56_8, all_56_9,
% 134.78/19.03 | all_56_10, all_56_11, all_56_12, all_56_13, all_56_14, all_56_15 gives:
% 134.78/19.03 | (205) ((all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 134.78/19.03 | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 134.78/19.03 | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 134.78/19.03 | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 134.78/19.03 | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 134.78/19.03 | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 134.78/19.03 | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 134.78/19.03 | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) |
% 134.78/19.03 | (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 134.78/19.03 | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 134.78/19.03 | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 134.78/19.03 | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 134.78/19.03 | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 134.78/19.03 | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 134.78/19.03 | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 134.78/19.03 | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 134.78/19.03 | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 134.78/19.03 | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 134.78/19.03 | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 134.78/19.03 | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 134.78/19.03 | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 134.78/19.03 | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 134.78/19.03 | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 134.78/19.03 | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 134.78/19.03 | op(e0, e1) = all_56_14 & $i(all_56_14))))) & ((op(e3, e3) =
% 134.78/19.03 | all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) = e2) | (
% 134.78/19.03 | ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 & $i(all_56_11)))
% 134.78/19.03 | & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) &
% 134.78/19.03 | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 134.78/19.03 | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 134.78/19.04 | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) =
% 134.78/19.04 | e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 134.78/19.04 | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 134.78/19.04 | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 134.78/19.04 | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 134.78/19.04 | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 134.78/19.04 | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) |
% 134.78/19.04 | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 134.78/19.04 | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 134.78/19.04 | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 &
% 134.78/19.04 | op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 134.78/19.04 | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) =
% 134.78/19.04 | e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 134.78/19.04 | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 134.78/19.04 | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 134.78/19.04 | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 134.78/19.04 | op(e0, e2) = all_56_12 & $i(all_56_12)))) | (op(e1, e1) =
% 134.78/19.04 | all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) = e3) |
% 134.78/19.04 | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 134.78/19.04 | ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) &
% 134.78/19.04 | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 &
% 134.78/19.04 | op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 134.78/19.04 | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) =
% 134.78/19.04 | e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 134.78/19.04 | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 134.78/19.04 | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 134.78/19.04 | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 134.78/19.04 | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 134.78/19.04 | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) |
% 134.78/19.04 | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 134.78/19.04 | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 134.78/19.04 | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 &
% 134.78/19.04 | op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 134.78/19.04 | all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) =
% 134.78/19.04 | e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 134.78/19.04 | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 134.78/19.04 | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 134.78/19.04 | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 134.78/19.04 | op(e1, e0) = all_56_8 & $i(all_56_8)))))
% 134.78/19.04 |
% 134.78/19.04 | ALPHA: (205) implies:
% 134.78/19.04 | (206) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 134.78/19.04 | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 134.78/19.04 | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 134.78/19.04 | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 134.78/19.04 | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 134.78/19.04 | e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 134.78/19.04 | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 134.78/19.04 | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 134.78/19.04 | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 134.78/19.04 | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 134.78/19.04 | e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11
% 134.78/19.04 | & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 134.78/19.04 | (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 134.78/19.04 | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 134.78/19.04 | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 134.78/19.04 | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 134.78/19.04 | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 134.78/19.04 | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 134.78/19.04 | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 134.78/19.04 | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 134.78/19.04 | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 134.78/19.04 | $i(all_56_12)))) | (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 134.78/19.04 | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3,
% 134.78/19.04 | e3) = all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 134.78/19.04 | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 134.78/19.04 | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 134.78/19.04 | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 134.78/19.04 | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 134.78/19.04 | e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 134.78/19.04 | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 134.78/19.04 | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 134.78/19.04 | (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 134.78/19.04 | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 134.78/19.04 | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 134.78/19.04 | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 134.78/19.04 | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 134.78/19.04 | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 134.78/19.04 | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 134.78/19.04 | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 134.78/19.04 | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 134.78/19.04 | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 134.78/19.04 | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 134.78/19.04 | e0) = all_56_8 & $i(all_56_8))))
% 134.78/19.04 | (207) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 134.78/19.04 | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 134.78/19.04 | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 134.78/19.04 | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 134.78/19.04 | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 134.78/19.04 | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 134.78/19.04 | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 134.78/19.04 | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) |
% 134.78/19.04 | (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 134.78/19.04 | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 134.78/19.04 | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 134.78/19.04 | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 134.78/19.04 | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 134.78/19.04 | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 134.78/19.04 | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 134.78/19.04 | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 134.78/19.04 | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 134.78/19.04 | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 134.78/19.04 | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 134.78/19.04 | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12
% 134.78/19.04 | & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 134.78/19.04 | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 134.78/19.04 | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 134.78/19.04 | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 134.78/19.04 | $i(all_56_14))))
% 134.78/19.04 |
% 134.78/19.04 | DELTA: instantiating (2) with fresh symbols all_57_0, all_57_1, all_57_2,
% 134.78/19.04 | all_57_3, all_57_4, all_57_5, all_57_6, all_57_7, all_57_8, all_57_9,
% 134.78/19.04 | all_57_10, all_57_11, all_57_12, all_57_13, all_57_14, all_57_15 gives:
% 135.60/19.05 | (208) ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 135.60/19.05 | e3) | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 135.60/19.05 | e0) = e3)) & ((all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 =
% 135.60/19.05 | e3 & op(e2, e3) = e3) | (all_57_6 = e3 & op(e1, e3) = e3) |
% 135.60/19.05 | (all_57_12 = e3 & op(e0, e3) = e3)) & ((all_57_0 = e2 & op(e3, e3)
% 135.60/19.05 | = e2) | (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_4 = e2 &
% 135.60/19.05 | op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)) &
% 135.60/19.05 | ((all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 135.60/19.05 | e2) | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 135.60/19.05 | op(e0, e3) = e2)) & ((all_57_0 = e1 & op(e3, e3) = e1) |
% 135.60/19.05 | (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_4 = e1 & op(e3, e1) =
% 135.60/19.05 | e1) | (all_57_9 = e1 & op(e3, e0) = e1)) & ((all_57_0 = e1 &
% 135.60/19.05 | op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_6
% 135.60/19.05 | = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)) &
% 135.60/19.05 | ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 135.60/19.05 | e0) | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 135.60/19.05 | e0) = e0)) & ((all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 =
% 135.60/19.05 | e0 & op(e2, e3) = e0) | (all_57_6 = e0 & op(e1, e3) = e0) |
% 135.60/19.05 | (all_57_12 = e0 & op(e0, e3) = e0)) & ((all_57_1 = e3 & op(e3, e2)
% 135.60/19.05 | = e3) | (all_57_3 = e3 & op(e2, e2) = e3) | (all_57_7 = e3 &
% 135.60/19.05 | op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)) &
% 135.60/19.05 | ((all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 135.60/19.05 | e2) | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 135.60/19.05 | op(e0, e2) = e2)) & ((all_57_1 = e1 & op(e3, e2) = e1) |
% 135.60/19.05 | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 135.60/19.05 | e1) | (all_57_13 = e1 & op(e0, e2) = e1)) & ((all_57_1 = e0 &
% 135.60/19.05 | op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) | (all_57_7
% 135.60/19.05 | = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)) &
% 135.60/19.05 | ((all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 135.60/19.05 | e3) | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 135.60/19.05 | op(e2, e0) = e3)) & ((all_57_2 = e2 & op(e2, e3) = e2) |
% 135.60/19.05 | (all_57_3 = e2 & op(e2, e2) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 135.60/19.05 | e2) | (all_57_10 = e2 & op(e2, e0) = e2)) & ((all_57_2 = e1 &
% 135.60/19.05 | op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) | (all_57_5
% 135.60/19.05 | = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)) &
% 135.60/19.05 | ((all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 135.60/19.05 | e0) | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 135.60/19.05 | op(e2, e0) = e0)) & ((all_57_4 = e3 & op(e3, e1) = e3) |
% 135.60/19.05 | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_8 = e3 & op(e1, e1) =
% 135.60/19.05 | e3) | (all_57_14 = e3 & op(e0, e1) = e3)) & ((all_57_4 = e2 &
% 135.60/19.05 | op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_8
% 135.60/19.05 | = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)) &
% 135.60/19.05 | ((all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 135.60/19.05 | e1) | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 &
% 135.60/19.05 | op(e0, e1) = e1)) & ((all_57_4 = e0 & op(e3, e1) = e0) |
% 135.60/19.05 | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_8 = e0 & op(e1, e1) =
% 135.60/19.05 | e0) | (all_57_14 = e0 & op(e0, e1) = e0)) & ((all_57_6 = e3 &
% 135.60/19.05 | op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_8
% 135.60/19.05 | = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)) &
% 135.60/19.05 | ((all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 135.60/19.05 | e2) | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 135.60/19.05 | op(e1, e0) = e2)) & ((all_57_6 = e1 & op(e1, e3) = e1) |
% 135.60/19.05 | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_8 = e1 & op(e1, e1) =
% 135.60/19.05 | e1) | (all_57_11 = e1 & op(e1, e0) = e1)) & ((all_57_6 = e0 &
% 135.60/19.05 | op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_8
% 135.60/19.05 | = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 135.60/19.05 | ((all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 135.60/19.05 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 135.60/19.05 | op(e0, e0) = e3)) & ((all_57_9 = e2 & op(e3, e0) = e2) |
% 135.60/19.05 | (all_57_10 = e2 & op(e2, e0) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 135.60/19.05 | e2) | (all_57_15 = e2 & op(e0, e0) = e2)) & ((all_57_9 = e1 &
% 135.60/19.05 | op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 135.60/19.05 | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 135.60/19.05 | e1)) & ((all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 135.60/19.05 | op(e0, e2) = e3) | (all_57_14 = e3 & op(e0, e1) = e3) |
% 135.60/19.05 | (all_57_15 = e3 & op(e0, e0) = e3)) & ((all_57_12 = e2 & op(e0, e3)
% 135.60/19.05 | = e2) | (all_57_13 = e2 & op(e0, e2) = e2) | (all_57_14 = e2 &
% 135.60/19.05 | op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)) &
% 135.60/19.05 | ((all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 135.60/19.05 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 135.60/19.05 | op(e0, e0) = e1)) & ((all_57_15 = e0 & op(e0, e0) = e0) |
% 135.60/19.05 | (((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 135.60/19.05 | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 =
% 135.60/19.05 | e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 135.60/19.05 | (all_57_14 = e0 & op(e0, e1) = e0))))
% 135.60/19.05 |
% 135.60/19.05 | ALPHA: (208) implies:
% 135.60/19.05 | (209) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) =
% 135.60/19.05 | e0) | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 135.60/19.05 | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 135.60/19.05 | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 135.60/19.05 | = e0)))
% 135.60/19.05 | (210) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 135.60/19.05 | e1) | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 135.60/19.05 | e0) = e1)
% 135.60/19.05 | (211) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 135.60/19.05 | e2) | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 135.60/19.05 | e0) = e2)
% 135.60/19.05 | (212) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 135.60/19.05 | e3) | (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 135.60/19.05 | e0) = e3)
% 135.60/19.06 | (213) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 135.60/19.06 | e1) | (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 135.60/19.06 | e0) = e1)
% 135.60/19.06 | (214) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 135.60/19.06 | e2) | (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 135.60/19.06 | e0) = e2)
% 135.60/19.06 | (215) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 135.60/19.06 | e3) | (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 135.60/19.06 | e0) = e3)
% 135.60/19.06 | (216) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 135.60/19.06 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 135.60/19.06 | e0)
% 135.60/19.06 | (217) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 135.60/19.06 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 135.60/19.06 | e1)
% 135.60/19.06 | (218) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 135.60/19.06 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 135.60/19.06 | e2)
% 135.60/19.06 | (219) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 135.60/19.06 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 135.60/19.06 | e3)
% 135.60/19.06 | (220) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 135.60/19.06 | | (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 135.60/19.06 | e0)
% 135.60/19.06 | (221) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1)
% 135.60/19.06 | | (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 135.60/19.06 | e1)
% 135.60/19.06 | (222) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 135.60/19.06 | | (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 135.60/19.06 | e2)
% 135.60/19.06 | (223) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 135.60/19.06 | | (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 135.60/19.06 | e3)
% 135.60/19.06 | (224) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 135.60/19.06 | | (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 135.60/19.06 | e0)
% 135.60/19.06 | (225) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 135.60/19.06 | | (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 135.60/19.06 | e1)
% 135.60/19.06 | (226) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 135.60/19.06 | | (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 135.60/19.06 | e2)
% 135.60/19.06 | (227) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 135.60/19.06 | | (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 135.60/19.06 | e3)
% 135.60/19.06 | (228) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 135.60/19.06 | | (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 135.60/19.06 | e0)
% 135.60/19.06 | (229) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 135.60/19.06 | | (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 135.60/19.06 | e1)
% 135.60/19.06 | (230) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 135.60/19.06 | | (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 135.60/19.06 | e2)
% 135.60/19.06 | (231) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 135.60/19.06 | | (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 135.60/19.06 | e3)
% 135.60/19.06 | (232) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 135.60/19.06 | | (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 135.60/19.06 | e0)
% 135.60/19.06 | (233) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 135.60/19.06 | | (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 135.60/19.06 | e0)
% 135.60/19.06 | (234) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 135.60/19.06 | | (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 135.60/19.06 | e1)
% 135.60/19.06 | (235) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 135.60/19.06 | | (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 135.60/19.06 | e1)
% 135.60/19.06 | (236) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 135.60/19.06 | | (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 135.60/19.06 | e2)
% 135.60/19.06 | (237) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2)
% 135.60/19.06 | | (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 135.60/19.06 | e2)
% 135.60/19.06 | (238) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 135.60/19.06 | | (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 135.60/19.06 | e3)
% 135.60/19.07 | (239) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 135.60/19.07 | | (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 135.60/19.07 | e3)
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_24_2, all_30_2, e0, e0,
% 135.60/19.07 | simplifying with (66), (75) gives:
% 135.60/19.07 | (240) all_30_2 = all_24_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_30_2, all_40_2, e0, e0,
% 135.60/19.07 | simplifying with (75), (90) gives:
% 135.60/19.07 | (241) all_40_2 = all_30_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_40_2, all_42_2, e0, e0,
% 135.60/19.07 | simplifying with (90), (93) gives:
% 135.60/19.07 | (242) all_42_2 = all_40_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_46_2, all_52_15, e0, e0,
% 135.60/19.07 | simplifying with (99), (156) gives:
% 135.60/19.07 | (243) all_52_15 = all_46_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_42_2, all_52_15, e0, e0,
% 135.60/19.07 | simplifying with (93), (156) gives:
% 135.60/19.07 | (244) all_52_15 = all_42_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_15, all_54_15, e0,
% 135.60/19.07 | e0, simplifying with (156), (173) gives:
% 135.60/19.07 | (245) all_54_15 = all_52_15
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_10_2, all_54_15, e0, e0,
% 135.60/19.07 | simplifying with (45), (173) gives:
% 135.60/19.07 | (246) all_54_15 = all_10_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_11, all_54_14, e1,
% 135.60/19.07 | e0, simplifying with (157), (174) gives:
% 135.60/19.07 | (247) all_54_14 = all_52_11
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_7, all_54_13, e2, e0,
% 135.60/19.07 | simplifying with (158), (175) gives:
% 135.60/19.07 | (248) all_54_13 = all_52_7
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_3, all_54_12, e3, e0,
% 135.60/19.07 | simplifying with (159), (176) gives:
% 135.60/19.07 | (249) all_54_12 = all_52_3
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_14, all_54_11, e0,
% 135.60/19.07 | e1, simplifying with (160), (177) gives:
% 135.60/19.07 | (250) all_54_11 = all_52_14
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_8_2, all_12_2, e1, e1,
% 135.60/19.07 | simplifying with (42), (48) gives:
% 135.60/19.07 | (251) all_12_2 = all_8_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_50_2, all_52_10, e1, e1,
% 135.60/19.07 | simplifying with (105), (161) gives:
% 135.60/19.07 | (252) all_52_10 = all_50_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_4_2, all_52_10, e1, e1,
% 135.60/19.07 | simplifying with (36), (161) gives:
% 135.60/19.07 | (253) all_52_10 = all_4_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_10, all_54_10, e1,
% 135.60/19.07 | e1, simplifying with (161), (178) gives:
% 135.60/19.07 | (254) all_54_10 = all_52_10
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_48_2, all_54_10, e1, e1,
% 135.60/19.07 | simplifying with (102), (178) gives:
% 135.60/19.07 | (255) all_54_10 = all_48_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_32_2, all_54_10, e1, e1,
% 135.60/19.07 | simplifying with (78), (178) gives:
% 135.60/19.07 | (256) all_54_10 = all_32_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_12_2, all_54_10, e1, e1,
% 135.60/19.07 | simplifying with (48), (178) gives:
% 135.60/19.07 | (257) all_54_10 = all_12_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_6, all_54_9, e2, e1,
% 135.60/19.07 | simplifying with (162), (179) gives:
% 135.60/19.07 | (258) all_54_9 = all_52_6
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_2, all_54_8, e3, e1,
% 135.60/19.07 | simplifying with (163), (180) gives:
% 135.60/19.07 | (259) all_54_8 = all_52_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_13, all_54_7, e0, e2,
% 135.60/19.07 | simplifying with (164), (181) gives:
% 135.60/19.07 | (260) all_54_7 = all_52_13
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_9, all_54_6, e1, e2,
% 135.60/19.07 | simplifying with (165), (182) gives:
% 135.60/19.07 | (261) all_54_6 = all_52_9
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_26_2, e2, e2,
% 135.60/19.07 | simplifying with (60), (69) gives:
% 135.60/19.07 | (262) all_26_2 = all_20_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_16_2, all_26_2, e2, e2,
% 135.60/19.07 | simplifying with (54), (69) gives:
% 135.60/19.07 | (263) all_26_2 = all_16_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_38_2, all_52_5, e2, e2,
% 135.60/19.07 | simplifying with (87), (166) gives:
% 135.60/19.07 | (264) all_52_5 = all_38_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_26_2, all_52_5, e2, e2,
% 135.60/19.07 | simplifying with (69), (166) gives:
% 135.60/19.07 | (265) all_52_5 = all_26_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_18_2, all_52_5, e2, e2,
% 135.60/19.07 | simplifying with (57), (166) gives:
% 135.60/19.07 | (266) all_52_5 = all_18_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_20_2, all_54_5, e2, e2,
% 135.60/19.07 | simplifying with (60), (183) gives:
% 135.60/19.07 | (267) all_54_5 = all_20_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_6_2, all_54_5, e2, e2,
% 135.60/19.07 | simplifying with (39), (183) gives:
% 135.60/19.07 | (268) all_54_5 = all_6_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_1, all_54_4, e3, e2,
% 135.60/19.07 | simplifying with (167), (184) gives:
% 135.60/19.07 | (269) all_54_4 = all_52_1
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_12, all_54_3, e0, e3,
% 135.60/19.07 | simplifying with (168), (185) gives:
% 135.60/19.07 | (270) all_54_3 = all_52_12
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_8, all_54_2, e1, e3,
% 135.60/19.07 | simplifying with (169), (186) gives:
% 135.60/19.07 | (271) all_54_2 = all_52_8
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_52_4, all_54_1, e2, e3,
% 135.60/19.07 | simplifying with (170), (187) gives:
% 135.60/19.07 | (272) all_54_1 = all_52_4
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_34_2, e3, e3,
% 135.60/19.07 | simplifying with (72), (81) gives:
% 135.60/19.07 | (273) all_34_2 = all_28_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_34_2, all_36_2, e3, e3,
% 135.60/19.07 | simplifying with (81), (84) gives:
% 135.60/19.07 | (274) all_36_2 = all_34_2
% 135.60/19.07 |
% 135.60/19.07 | GROUND_INST: instantiating (function-axioms) with all_36_2, all_44_2, e3, e3,
% 135.60/19.07 | simplifying with (84), (96) gives:
% 135.60/19.07 | (275) all_44_2 = all_36_2
% 135.60/19.07 |
% 135.60/19.08 | GROUND_INST: instantiating (function-axioms) with all_28_2, all_52_0, e3, e3,
% 135.60/19.08 | simplifying with (72), (171) gives:
% 135.60/19.08 | (276) all_52_0 = all_28_2
% 135.60/19.08 |
% 135.60/19.08 | GROUND_INST: instantiating (function-axioms) with all_22_2, all_52_0, e3, e3,
% 135.60/19.08 | simplifying with (63), (171) gives:
% 135.60/19.08 | (277) all_52_0 = all_22_2
% 135.60/19.08 |
% 135.60/19.08 | GROUND_INST: instantiating (function-axioms) with all_44_2, all_54_0, e3, e3,
% 135.60/19.08 | simplifying with (96), (188) gives:
% 135.60/19.08 | (278) all_54_0 = all_44_2
% 135.60/19.08 |
% 135.60/19.08 | GROUND_INST: instantiating (function-axioms) with all_14_2, all_54_0, e3, e3,
% 135.60/19.08 | simplifying with (51), (188) gives:
% 135.60/19.08 | (279) all_54_0 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (278), (279) imply:
% 135.60/19.08 | (280) all_44_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (280) implies:
% 135.60/19.08 | (281) all_44_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (267), (268) imply:
% 135.60/19.08 | (282) all_20_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (282) implies:
% 135.60/19.08 | (283) all_20_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (255), (257) imply:
% 135.60/19.08 | (284) all_48_2 = all_12_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (255), (256) imply:
% 135.60/19.08 | (285) all_48_2 = all_32_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (254), (255) imply:
% 135.60/19.08 | (286) all_52_10 = all_48_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (286) implies:
% 135.60/19.08 | (287) all_52_10 = all_48_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (245), (246) imply:
% 135.60/19.08 | (288) all_52_15 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (288) implies:
% 135.60/19.08 | (289) all_52_15 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (276), (277) imply:
% 135.60/19.08 | (290) all_28_2 = all_22_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (290) implies:
% 135.60/19.08 | (291) all_28_2 = all_22_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (264), (266) imply:
% 135.60/19.08 | (292) all_38_2 = all_18_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (264), (265) imply:
% 135.60/19.08 | (293) all_38_2 = all_26_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (252), (287) imply:
% 135.60/19.08 | (294) all_50_2 = all_48_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (252), (253) imply:
% 135.60/19.08 | (295) all_50_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (243), (244) imply:
% 135.60/19.08 | (296) all_46_2 = all_42_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (243), (289) imply:
% 135.60/19.08 | (297) all_46_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (294), (295) imply:
% 135.60/19.08 | (298) all_48_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (298) implies:
% 135.60/19.08 | (299) all_48_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (284), (285) imply:
% 135.60/19.08 | (300) all_32_2 = all_12_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (285), (299) imply:
% 135.60/19.08 | (301) all_32_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (296), (297) imply:
% 135.60/19.08 | (302) all_42_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (302) implies:
% 135.60/19.08 | (303) all_42_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (275), (281) imply:
% 135.60/19.08 | (304) all_36_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (304) implies:
% 135.60/19.08 | (305) all_36_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (242), (303) imply:
% 135.60/19.08 | (306) all_40_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (306) implies:
% 135.60/19.08 | (307) all_40_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (241), (307) imply:
% 135.60/19.08 | (308) all_30_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (308) implies:
% 135.60/19.08 | (309) all_30_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (292), (293) imply:
% 135.60/19.08 | (310) all_26_2 = all_18_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (310) implies:
% 135.60/19.08 | (311) all_26_2 = all_18_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (274), (305) imply:
% 135.60/19.08 | (312) all_34_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (312) implies:
% 135.60/19.08 | (313) all_34_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (273), (313) imply:
% 135.60/19.08 | (314) all_28_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (314) implies:
% 135.60/19.08 | (315) all_28_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (300), (301) imply:
% 135.60/19.08 | (316) all_12_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (316) implies:
% 135.60/19.08 | (317) all_12_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (240), (309) imply:
% 135.60/19.08 | (318) all_24_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (318) implies:
% 135.60/19.08 | (319) all_24_2 = all_10_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (291), (315) imply:
% 135.60/19.08 | (320) all_22_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (320) implies:
% 135.60/19.08 | (321) all_22_2 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (262), (311) imply:
% 135.60/19.08 | (322) all_20_2 = all_18_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (322) implies:
% 135.60/19.08 | (323) all_20_2 = all_18_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (263), (311) imply:
% 135.60/19.08 | (324) all_18_2 = all_16_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (283), (323) imply:
% 135.60/19.08 | (325) all_18_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (325) implies:
% 135.60/19.08 | (326) all_18_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (324), (326) imply:
% 135.60/19.08 | (327) all_16_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (327) implies:
% 135.60/19.08 | (328) all_16_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (251), (317) imply:
% 135.60/19.08 | (329) all_8_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (329) implies:
% 135.60/19.08 | (330) all_8_2 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (311), (326) imply:
% 135.60/19.08 | (331) all_26_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (292), (326) imply:
% 135.60/19.08 | (332) all_38_2 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (264), (332) imply:
% 135.60/19.08 | (333) all_52_5 = all_6_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (277), (321) imply:
% 135.60/19.08 | (334) all_52_0 = all_14_2
% 135.60/19.08 |
% 135.60/19.08 | COMBINE_EQS: (255), (299) imply:
% 135.60/19.08 | (335) all_54_10 = all_4_2
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (155), (334) imply:
% 135.60/19.08 | (336) ~ (all_52_1 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (336) implies:
% 135.60/19.08 | (337) ~ (all_52_1 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (154), (334) imply:
% 135.60/19.08 | (338) ~ (all_52_2 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (338) implies:
% 135.60/19.08 | (339) ~ (all_52_2 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (153), (334) imply:
% 135.60/19.08 | (340) ~ (all_52_3 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (340) implies:
% 135.60/19.08 | (341) ~ (all_52_3 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (152), (334) imply:
% 135.60/19.08 | (342) ~ (all_52_4 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (342) implies:
% 135.60/19.08 | (343) ~ (all_52_4 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (151), (334) imply:
% 135.60/19.08 | (344) ~ (all_52_8 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (344) implies:
% 135.60/19.08 | (345) ~ (all_52_8 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (150), (334) imply:
% 135.60/19.08 | (346) ~ (all_52_12 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (346) implies:
% 135.60/19.08 | (347) ~ (all_52_12 = all_14_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (147), (333) imply:
% 135.60/19.08 | (348) ~ (all_52_1 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (142), (253) imply:
% 135.60/19.08 | (349) ~ (all_52_2 = all_4_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (138), (289) imply:
% 135.60/19.08 | (350) ~ (all_52_3 = all_10_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (137), (333) imply:
% 135.60/19.08 | (351) ~ (all_52_4 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (132), (333) imply:
% 135.60/19.08 | (352) ~ (all_52_6 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (352) implies:
% 135.60/19.08 | (353) ~ (all_52_6 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (131), (333) imply:
% 135.60/19.08 | (354) ~ (all_52_7 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (354) implies:
% 135.60/19.08 | (355) ~ (all_52_7 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | REDUCE: (130), (333) imply:
% 135.60/19.08 | (356) ~ (all_52_9 = all_6_2)
% 135.60/19.08 |
% 135.60/19.08 | SIMP: (356) implies:
% 135.60/19.08 | (357) ~ (all_52_9 = all_6_2)
% 135.60/19.08 |
% 135.60/19.09 | REDUCE: (129), (333) imply:
% 135.60/19.09 | (358) ~ (all_52_13 = all_6_2)
% 135.60/19.09 |
% 135.60/19.09 | SIMP: (358) implies:
% 135.60/19.09 | (359) ~ (all_52_13 = all_6_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (127), (253) imply:
% 135.60/19.09 | (360) ~ (all_52_6 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (124), (289) imply:
% 135.60/19.09 | (361) ~ (all_52_7 = all_10_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (122), (253) imply:
% 135.60/19.09 | (362) ~ (all_52_8 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (119), (253) imply:
% 135.60/19.09 | (363) ~ (all_52_9 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (116), (253) imply:
% 135.60/19.09 | (364) ~ (all_52_11 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | SIMP: (364) implies:
% 135.60/19.09 | (365) ~ (all_52_11 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (115), (253) imply:
% 135.60/19.09 | (366) ~ (all_52_14 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | SIMP: (366) implies:
% 135.60/19.09 | (367) ~ (all_52_14 = all_4_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (114), (289) imply:
% 135.60/19.09 | (368) ~ (all_52_11 = all_10_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (111), (289) imply:
% 135.60/19.09 | (369) ~ (all_52_12 = all_10_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (109), (289) imply:
% 135.60/19.09 | (370) ~ (all_52_13 = all_10_2)
% 135.60/19.09 |
% 135.60/19.09 | REDUCE: (108), (289) imply:
% 135.60/19.09 | (371) ~ (all_52_14 = all_10_2)
% 135.60/19.09 |
% 135.60/19.09 | BETA: splitting (37) gives:
% 135.60/19.09 |
% 135.60/19.09 | Case 1:
% 135.60/19.09 | |
% 135.60/19.09 | | (372) ~ (all_4_2 = e2)
% 135.60/19.09 | |
% 135.60/19.09 | | BETA: splitting (40) gives:
% 135.60/19.09 | |
% 135.60/19.09 | | Case 1:
% 135.60/19.09 | | |
% 135.60/19.09 | | | (373) ~ (all_6_2 = e3)
% 135.60/19.09 | | |
% 135.60/19.09 | | | BETA: splitting (43) gives:
% 135.60/19.09 | | |
% 135.60/19.09 | | | Case 1:
% 135.60/19.09 | | | |
% 135.60/19.09 | | | | (374) ~ (all_8_2 = e3)
% 135.60/19.09 | | | |
% 135.60/19.09 | | | | REDUCE: (330), (374) imply:
% 135.60/19.09 | | | | (375) ~ (all_4_2 = e3)
% 135.60/19.09 | | | |
% 135.60/19.09 | | | | BETA: splitting (46) gives:
% 135.60/19.09 | | | |
% 135.60/19.09 | | | | Case 1:
% 135.60/19.09 | | | | |
% 135.60/19.09 | | | | | (376) ~ (all_10_2 = e1)
% 135.60/19.09 | | | | |
% 135.60/19.09 | | | | | BETA: splitting (52) gives:
% 135.60/19.09 | | | | |
% 135.60/19.09 | | | | | Case 1:
% 135.60/19.09 | | | | | |
% 135.60/19.09 | | | | | | (377) ~ (all_14_2 = e0)
% 135.60/19.09 | | | | | |
% 135.60/19.09 | | | | | | BETA: splitting (55) gives:
% 135.60/19.09 | | | | | |
% 135.60/19.09 | | | | | | Case 1:
% 135.60/19.09 | | | | | | |
% 135.60/19.09 | | | | | | | (378) ~ (all_16_2 = e0)
% 135.60/19.09 | | | | | | |
% 135.60/19.09 | | | | | | | REDUCE: (328), (378) imply:
% 135.60/19.09 | | | | | | | (379) ~ (all_6_2 = e0)
% 135.60/19.09 | | | | | | |
% 135.78/19.09 | | | | | | | BETA: splitting (207) gives:
% 135.78/19.09 | | | | | | |
% 135.78/19.09 | | | | | | | Case 1:
% 135.78/19.09 | | | | | | | |
% 135.78/19.09 | | | | | | | | (380) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 135.78/19.09 | | | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2)
% 135.78/19.09 | | | | | | | | = e3 & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 =
% 135.78/19.09 | | | | | | | | e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 135.78/19.09 | | | | | | | | e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 135.78/19.09 | | | | | | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) &
% 135.78/19.09 | | | | | | | | op(e3, e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1)
% 135.78/19.09 | | | | | | | | = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13 =
% 135.78/19.09 | | | | | | | | e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 135.78/19.09 | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 135.78/19.09 | | | | | | | |
% 135.78/19.09 | | | | | | | | BETA: splitting (380) gives:
% 135.78/19.09 | | | | | | | |
% 135.78/19.09 | | | | | | | | Case 1:
% 135.78/19.09 | | | | | | | | |
% 135.78/19.09 | | | | | | | | | (381) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3)
% 135.78/19.09 | | | | | | | | | & op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2,
% 135.78/19.09 | | | | | | | | | e2) = e3 & $i(all_56_0)) | (all_56_9 = e2 &
% 135.78/19.09 | | | | | | | | | all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 135.78/19.09 | | | | | | | | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 &
% 135.78/19.09 | | | | | | | | | $i(all_56_3))
% 135.78/19.09 | | | | | | | | |
% 135.78/19.09 | | | | | | | | | REF_CLOSE: (39), (373), (381), (function-axioms) are
% 135.78/19.09 | | | | | | | | | inconsistent by sub-proof #1128.
% 135.78/19.09 | | | | | | | | |
% 135.78/19.09 | | | | | | | | Case 2:
% 135.78/19.09 | | | | | | | | |
% 135.78/19.09 | | | | | | | | | (382) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3)
% 135.78/19.09 | | | | | | | | | & op(e3, e3) = e1 & op(e3, e1) = all_56_1 & op(e1,
% 135.78/19.09 | | | | | | | | | e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 135.78/19.09 | | | | | | | | | all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 135.78/19.09 | | | | | | | | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 &
% 135.78/19.09 | | | | | | | | | $i(all_56_6))
% 135.78/19.09 | | | | | | | | |
% 135.78/19.09 | | | | | | | | | REF_CLOSE: (36), (375), (382), (function-axioms) are
% 135.78/19.09 | | | | | | | | | inconsistent by sub-proof #1126.
% 135.78/19.09 | | | | | | | | |
% 135.78/19.09 | | | | | | | | End of split
% 135.78/19.09 | | | | | | | |
% 135.78/19.09 | | | | | | | Case 2:
% 135.78/19.09 | | | | | | | |
% 135.78/19.10 | | | | | | | | (383) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 135.78/19.10 | | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 135.78/19.10 | | | | | | | | = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 =
% 135.78/19.10 | | | | | | | | e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2,
% 135.78/19.10 | | | | | | | | e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 135.78/19.10 | | | | | | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 135.78/19.10 | | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1)
% 135.78/19.10 | | | | | | | | = e2 & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 =
% 135.78/19.10 | | | | | | | | e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 135.78/19.10 | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 135.78/19.10 | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 135.78/19.10 | | | | | | | | e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 135.78/19.10 | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 135.78/19.10 | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2
% 135.78/19.10 | | | | | | | | & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 135.78/19.10 | | | | | | | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 =
% 135.78/19.10 | | | | | | | | e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 135.78/19.10 | | | | | | | | e1) = e0 & op(e1, e0) = all_56_8 &
% 135.78/19.10 | | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1
% 135.78/19.10 | | | | | | | | & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 135.78/19.10 | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 135.78/19.10 | | | | | | | |
% 135.78/19.10 | | | | | | | | BETA: splitting (383) gives:
% 135.78/19.10 | | | | | | | |
% 135.78/19.10 | | | | | | | | Case 1:
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | | (384) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3)
% 135.78/19.10 | | | | | | | | | & op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0,
% 135.78/19.10 | | | | | | | | | e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 135.78/19.10 | | | | | | | | | all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 135.78/19.10 | | | | | | | | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 135.78/19.10 | | | | | | | | | $i(all_56_4))
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | | REF_CLOSE: (36), (51), (372), (377), (384), (function-axioms)
% 135.78/19.10 | | | | | | | | | are inconsistent by sub-proof #1123.
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | Case 2:
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | | (385) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1)
% 135.78/19.10 | | | | | | | | | & op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1,
% 135.78/19.10 | | | | | | | | | e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 135.78/19.10 | | | | | | | | | all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 135.78/19.10 | | | | | | | | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 135.78/19.10 | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 135.78/19.10 | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 &
% 135.78/19.10 | | | | | | | | | ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0,
% 135.78/19.10 | | | | | | | | | e3) = all_56_10 & $i(all_56_10)) | (all_56_11
% 135.78/19.10 | | | | | | | | | = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 135.78/19.10 | | | | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 135.78/19.10 | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 135.78/19.10 | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 135.78/19.10 | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 135.78/19.10 | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 135.78/19.10 | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 135.78/19.10 | | | | | | | | | all_56_14 & $i(all_56_14))))
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | | BETA: splitting (385) gives:
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | | Case 1:
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | (386) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 135.78/19.10 | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 135.78/19.10 | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | ALPHA: (386) implies:
% 135.78/19.10 | | | | | | | | | | (387) op(e1, e1) = e2
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | REF_CLOSE: (36), (372), (387), (function-axioms) are
% 135.78/19.10 | | | | | | | | | | inconsistent by sub-proof #1124.
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | Case 2:
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | (388) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 135.78/19.10 | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 135.78/19.10 | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 135.78/19.10 | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 135.78/19.10 | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 135.78/19.10 | | | | | | | | | | e3) = e0 & op(e0, e3) = all_56_10 &
% 135.78/19.10 | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 135.78/19.10 | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 135.78/19.10 | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 135.78/19.10 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 135.78/19.10 | | | | | | | | | | = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 135.78/19.10 | | | | | | | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 135.78/19.10 | | | | | | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 135.78/19.10 | | | | | | | | | | e1) = e0 & op(e0, e1) = all_56_14 &
% 135.78/19.10 | | | | | | | | | | $i(all_56_14))))
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | BETA: splitting (388) gives:
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | Case 1:
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | | (389) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 135.78/19.10 | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 135.78/19.10 | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | | ALPHA: (389) implies:
% 135.78/19.10 | | | | | | | | | | | (390) op(e2, e2) = e0
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | | REF_CLOSE: (39), (379), (390), (function-axioms) are
% 135.78/19.10 | | | | | | | | | | | inconsistent by sub-proof #1122.
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | Case 2:
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | | (391) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 135.78/19.10 | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 135.78/19.10 | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 135.78/19.10 | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 135.78/19.10 | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 135.78/19.10 | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 135.78/19.10 | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 135.78/19.10 | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 135.78/19.10 | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 135.78/19.10 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 135.78/19.10 | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 135.78/19.10 | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | | ALPHA: (391) implies:
% 135.78/19.10 | | | | | | | | | | | (392) op(e0, e0) = all_56_15
% 135.78/19.10 | | | | | | | | | | | (393) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 135.78/19.10 | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 135.78/19.10 | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 135.78/19.10 | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 135.78/19.10 | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 135.78/19.10 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 135.78/19.10 | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 135.78/19.10 | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 135.78/19.10 | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 135.78/19.10 | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | | REF_CLOSE: (39), (45), (51), (376), (377), (379), (392),
% 135.78/19.10 | | | | | | | | | | | (393), (function-axioms) are inconsistent by
% 135.78/19.10 | | | | | | | | | | | sub-proof #1120.
% 135.78/19.10 | | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | | End of split
% 135.78/19.10 | | | | | | | | | |
% 135.78/19.10 | | | | | | | | | End of split
% 135.78/19.10 | | | | | | | | |
% 135.78/19.10 | | | | | | | | End of split
% 135.78/19.10 | | | | | | | |
% 135.78/19.10 | | | | | | | End of split
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | Case 2:
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | (394) all_16_2 = e0
% 135.78/19.10 | | | | | | | (395) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 &
% 135.78/19.10 | | | | | | | op(e2, e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)) |
% 135.78/19.10 | | | | | | | ( ~ (all_16_1 = e3) & op(e2, e0) = all_16_1 &
% 135.78/19.10 | | | | | | | $i(all_16_1))
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | COMBINE_EQS: (328), (394) imply:
% 135.78/19.10 | | | | | | | (396) all_6_2 = e0
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | COMBINE_EQS: (326), (396) imply:
% 135.78/19.10 | | | | | | | (397) all_18_2 = e0
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | REDUCE: (348), (396) imply:
% 135.78/19.10 | | | | | | | (398) ~ (all_52_1 = e0)
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | REDUCE: (351), (396) imply:
% 135.78/19.10 | | | | | | | (399) ~ (all_52_4 = e0)
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | REDUCE: (353), (396) imply:
% 135.78/19.10 | | | | | | | (400) ~ (all_52_6 = e0)
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | REDUCE: (355), (396) imply:
% 135.78/19.10 | | | | | | | (401) ~ (all_52_7 = e0)
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | REDUCE: (357), (396) imply:
% 135.78/19.10 | | | | | | | (402) ~ (all_52_9 = e0)
% 135.78/19.10 | | | | | | |
% 135.78/19.10 | | | | | | | REDUCE: (359), (396) imply:
% 135.78/19.10 | | | | | | | (403) ~ (all_52_13 = e0)
% 135.78/19.10 | | | | | | |
% 135.78/19.11 | | | | | | | REDUCE: (373), (396) imply:
% 135.78/19.11 | | | | | | | (404) ~ (e3 = e0)
% 135.78/19.11 | | | | | | |
% 135.78/19.11 | | | | | | | REDUCE: (39), (396) imply:
% 135.78/19.11 | | | | | | | (405) op(e2, e2) = e0
% 135.78/19.11 | | | | | | |
% 135.78/19.11 | | | | | | | BETA: splitting (58) gives:
% 135.78/19.11 | | | | | | |
% 135.78/19.11 | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | | (406) ~ (all_18_2 = e0)
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | | REDUCE: (397), (406) imply:
% 135.78/19.11 | | | | | | | | (407) $false
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | | CLOSE: (407) is inconsistent.
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | Case 2:
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | | (408) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 &
% 135.78/19.11 | | | | | | | | op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1))
% 135.78/19.11 | | | | | | | | | ( ~ (all_18_1 = e1) & op(e2, e0) = all_18_1 &
% 135.78/19.11 | | | | | | | | $i(all_18_1))
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | | BETA: splitting (64) gives:
% 135.78/19.11 | | | | | | | |
% 135.78/19.11 | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | |
% 135.78/19.11 | | | | | | | | | (409) ~ (all_22_2 = e1)
% 135.78/19.11 | | | | | | | | |
% 135.78/19.11 | | | | | | | | | REDUCE: (321), (409) imply:
% 135.78/19.11 | | | | | | | | | (410) ~ (all_14_2 = e1)
% 135.78/19.11 | | | | | | | | |
% 135.78/19.11 | | | | | | | | | BETA: splitting (67) gives:
% 135.78/19.11 | | | | | | | | |
% 135.78/19.11 | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | (411) ~ (all_24_2 = e2)
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | REDUCE: (319), (411) imply:
% 135.78/19.11 | | | | | | | | | | (412) ~ (all_10_2 = e2)
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | REF_CLOSE: (4), (7), (36), (45), (51), (207), (375), (376),
% 135.78/19.11 | | | | | | | | | | (377), (405), (412), (function-axioms) are
% 135.78/19.11 | | | | | | | | | | inconsistent by sub-proof #1113.
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | Case 2:
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | (413) all_24_2 = e2
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | COMBINE_EQS: (319), (413) imply:
% 135.78/19.11 | | | | | | | | | | (414) all_10_2 = e2
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | SIMP: (414) implies:
% 135.78/19.11 | | | | | | | | | | (415) all_10_2 = e2
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | REDUCE: (369), (415) imply:
% 135.78/19.11 | | | | | | | | | | (416) ~ (all_52_12 = e2)
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | REDUCE: (370), (415) imply:
% 135.78/19.11 | | | | | | | | | | (417) ~ (all_52_13 = e2)
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | REDUCE: (371), (415) imply:
% 135.78/19.11 | | | | | | | | | | (418) ~ (all_52_14 = e2)
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | REDUCE: (45), (415) imply:
% 135.78/19.11 | | | | | | | | | | (419) op(e0, e0) = e2
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | BETA: splitting (85) gives:
% 135.78/19.11 | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | (420) ~ (all_36_2 = e2)
% 135.78/19.11 | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | REDUCE: (305), (420) imply:
% 135.78/19.11 | | | | | | | | | | | (421) ~ (all_14_2 = e2)
% 135.78/19.11 | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | BETA: splitting (204) gives:
% 135.78/19.11 | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | (422) all_54_0 = e3
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | COMBINE_EQS: (279), (422) imply:
% 135.78/19.11 | | | | | | | | | | | | (423) all_14_2 = e3
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | SIMP: (423) implies:
% 135.78/19.11 | | | | | | | | | | | | (424) all_14_2 = e3
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | REDUCE: (343), (424) imply:
% 135.78/19.11 | | | | | | | | | | | | (425) ~ (all_52_4 = e3)
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | REDUCE: (345), (424) imply:
% 135.78/19.11 | | | | | | | | | | | | (426) ~ (all_52_8 = e3)
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | REDUCE: (347), (424) imply:
% 135.78/19.11 | | | | | | | | | | | | (427) ~ (all_52_12 = e3)
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | BETA: splitting (239) gives:
% 135.78/19.11 | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | (428) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 135.78/19.11 | | | | | | | | | | | | | & op(e3, e2) = e3)
% 135.78/19.11 | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | BETA: splitting (428) gives:
% 135.78/19.11 | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | (429) all_57_0 = e3 & op(e3, e3) = e3
% 135.78/19.11 | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | ALPHA: (429) implies:
% 135.78/19.11 | | | | | | | | | | | | | | (430) all_57_0 = e3
% 135.78/19.11 | | | | | | | | | | | | | | (431) op(e3, e3) = e3
% 135.78/19.11 | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 135.78/19.11 | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | (432) ~ (all_48_2 = e0)
% 135.78/19.11 | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | REDUCE: (299), (432) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | (433) ~ (all_4_2 = e0)
% 135.78/19.11 | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 135.78/19.11 | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | (434) all_54_10 = e3
% 135.78/19.11 | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (434) are inconsistent by sub-proof
% 135.78/19.11 | | | | | | | | | | | | | | | | #1112.
% 135.78/19.11 | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | Case 2:
% 135.78/19.11 | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | (435) ~ (all_54_10 = e3)
% 135.78/19.11 | | | | | | | | | | | | | | | | (436) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 135.78/19.11 | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | BETA: splitting (436) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | (437) all_54_10 = e2
% 135.78/19.11 | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (437) are inconsistent by sub-proof
% 135.78/19.11 | | | | | | | | | | | | | | | | | #1111.
% 135.78/19.11 | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.11 | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | (438) ~ (all_54_10 = e2)
% 135.78/19.11 | | | | | | | | | | | | | | | | | (439) all_54_10 = e1 | all_54_10 = e0
% 135.78/19.11 | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | BETA: splitting (439) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (440) all_54_10 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (440) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (441) all_4_2 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | SIMP: (441) implies:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (442) all_4_2 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | REDUCE: (349), (442) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (443) ~ (all_52_2 = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | REDUCE: (360), (442) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (444) ~ (all_52_6 = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | REDUCE: (367), (442) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (445) ~ (all_52_14 = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | REDUCE: (375), (442) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (446) ~ (e3 = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | REDUCE: (372), (442) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (447) ~ (e2 = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | REDUCE: (36), (442) imply:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | (448) op(e1, e1) = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | (449) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (449) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (450) all_57_6 = e1 & op(e1, e3) = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (450) implies:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (451) all_57_6 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (212),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (220), (221),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (222), (223), (225), (226), (227), (228), (229),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (235), (236), (237),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (451), (function-axioms) are inconsistent by
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | sub-proof #926.
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (452) all_57_7 = e1 & op(e1, e2) = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (452) implies:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | (453) all_57_7 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | (454) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (454) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | (455) all_57_6 = e2 & op(e1, e3) = e2
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (455) implies:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | (456) all_57_6 = e2
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | | (457) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (457) gives:
% 135.78/19.11 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (458) all_57_4 = e1 & op(e3, e1) = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (458) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (459) all_57_4 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (212),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (220), (221),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (222), (223), (225), (226), (227), (228), (229),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (235), (236), (237),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (456), (459), (function-axioms) are inconsistent
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #917.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (460) all_57_5 = e1 & op(e2, e1) = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (460) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | (461) all_57_5 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | (462) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (462) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (463) all_57_4 = e2 & op(e3, e1) = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (463) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (464) all_57_4 = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (465) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (399), (425),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (465), (function-axioms) are
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1101.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (466) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (466) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (467) all_57_4 = e0 & op(e3, e1) = e0
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (464), (467) are inconsistent by sub-proof
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1013.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (468) all_57_9 = e0 & op(e3, e0) = e0
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (468) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (469) all_57_9 = e0
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (470) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (470) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (471) all_57_2 = e2 & op(e2, e3) = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (471) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (472) all_57_2 = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (473) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (473) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (474) all_57_1 = e2 & op(e3, e2) = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (474) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (475) all_57_1 = e2
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (476) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (476) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (477) all_57_6 = e3 & op(e1, e3) = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (456), (477) are inconsistent by sub-proof
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #916.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (478) all_57_7 = e3 & op(e1, e2) = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (478) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (479) all_57_7 = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (453), (479) are inconsistent by sub-proof
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #915.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (480) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (480) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (481) all_57_8 = e3 & op(e1, e1) = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (481) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (482) op(e1, e1) = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (448), (482), (function-axioms) are
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (483) all_57_11 = e3 & op(e1, e0) = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (483) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (484) all_57_11 = e3
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (485) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (485) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (486) all_57_0 = e1 & op(e3, e3) = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (486) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (487) all_57_0 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (430), (487) imply:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (488) e3 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (484), (488) imply:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (489) all_57_11 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (168), (169), (170), (206),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (212), (213), (216), (218),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219), (220), (222), (223), (226), (227), (228),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (235), (237),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (375), (398), (399), (400), (401), (402),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (405), (417), (419), (425), (426), (427),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430), (448), (461), (464), (489),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #905.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (490) all_57_1 = e1 & op(e3, e2) = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (168), (169), (170), (206), (207),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (226), (232), (239), (375),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (400), (401), (405), (417), (419), (425),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (448), (456), (472), (475), (490),
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #906.
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (491) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (491) gives:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (492) all_57_4 = e1 & op(e3, e1) = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (492) implies:
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (493) all_57_4 = e1
% 135.78/19.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (212),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (220), (221),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (223), (225), (226), (227), (228), (229),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (235), (236), (237),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (456), (493), (function-axioms) are inconsistent
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #917.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (494) all_57_9 = e1 & op(e3, e0) = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (494) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (495) all_57_9 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (469), (495) are inconsistent by sub-proof
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1079.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (496) all_57_3 = e2 & op(e2, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (496) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (497) op(e2, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (497), (function-axioms) are
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (498) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (498) gives:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (499) all_57_7 = e2 & op(e1, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (499) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (500) all_57_7 = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (500) imply:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (501) e2 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (472), (501) imply:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (502) all_57_2 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (168), (169), (170), (206), (207),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (226), (232), (239), (375),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (398), (400), (401), (405), (417), (419), (425),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (448), (456), (502),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #944.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (503) all_57_13 = e2 & op(e0, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (503) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (504) all_57_13 = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (210), (212),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (402), (419), (448), (464), (504),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #904.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (505) all_57_3 = e2 & op(e2, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (505) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (506) op(e2, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (506), (function-axioms) are
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (507) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (507) gives:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (508) all_57_5 = e2 & op(e2, e1) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (508) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (509) all_57_5 = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (509) imply:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (510) e2 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (510) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (511) e2 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (464), (511) imply:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (512) all_57_4 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (165), (168), (169),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (210), (212), (220), (223), (231), (239),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (402), (405), (419), (425), (426), (427), (430),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (509), (512), (function-axioms) are
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #921.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (513) all_57_10 = e2 & op(e2, e0) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (513) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (514) op(e2, e0) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (417), (514), (function-axioms) are
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (515) all_57_5 = e2 & op(e2, e1) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (515) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (516) all_57_5 = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (461), (516) imply:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (517) e2 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (456), (517) imply:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (518) all_57_6 = e1
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (212),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (220), (221),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (223), (225), (226), (227), (228), (229),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (235), (236), (237),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (518), (function-axioms) are inconsistent by
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #926.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (519) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (169), (223), (426), (448), (461),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | (519), (function-axioms) are inconsistent by
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1009.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (520) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (215),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (225),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (228), (231), (232), (233), (236),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | (520), (function-axioms) are inconsistent by
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #927.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | (521) all_57_7 = e2 & op(e1, e2) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (453), (521) are inconsistent by sub-proof
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | #997.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | (522) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (522) gives:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | (523) all_57_8 = e2 & op(e1, e1) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (523) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | (524) op(e1, e1) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (448), (524), (function-axioms) are
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | (525) all_57_11 = e2 & op(e1, e0) = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (525) implies:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | (526) all_57_11 = e2
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.13 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | (527) all_57_15 = e0 & op(e0, e0) = e0
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (527) implies:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | (528) op(e0, e0) = e0
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (419), (528), (function-axioms) are
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | (529) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (529) implies:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | (530) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | (531) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (531) gives:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | (532) all_57_1 = e2 & op(e3, e2) = e2
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (532) implies:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | (533) all_57_1 = e2
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (530) gives:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (534) all_57_9 = e0 & op(e3, e0) = e0
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (534) implies:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | (535) all_57_9 = e0
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (536) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (536) gives:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (537) all_57_4 = e1 & op(e3, e1) = e1
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (537) implies:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (538) all_57_4 = e1
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (168), (169),
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (210), (212), (218), (219), (220), (222),
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (231), (239), (402), (405), (419), (425),
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (448), (526), (538),
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #903.
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (539) all_57_5 = e1 & op(e2, e1) = e1
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (539) implies:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (540) all_57_5 = e1
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 135.78/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (541) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (541) gives:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (542) all_57_4 = e2 & op(e3, e1) = e2
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (542) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (543) all_57_4 = e2
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (544) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (426), (540), (544), (function-axioms)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1034.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (545) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (545) gives:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (546) all_57_8 = e3 & op(e1, e1) = e3
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (546) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (547) op(e1, e1) = e3
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (448), (547), (function-axioms) are
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (548) all_57_14 = e3 & op(e0, e1) = e3
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (548) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (549) all_57_14 = e3
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (550) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (550) gives:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (551) all_57_0 = e1 & op(e3, e3) = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (551) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (552) all_57_0 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (430), (552) imply:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (553) e3 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (549), (553) imply:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (554) all_57_14 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (169), (220), (222),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (426), (448), (554), (function-axioms) are
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1038.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (555) all_57_1 = e1 & op(e3, e2) = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (555) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (556) all_57_1 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (533), (556) imply:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (557) e2 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (543), (557) imply:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (558) all_57_4 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (168), (169),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (210), (212), (218), (219), (220), (222),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (231), (239), (402), (405), (419), (425),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (448), (526), (558),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #903.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (559) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (559) gives:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (560) all_57_4 = e1 & op(e3, e1) = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (560) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (561) all_57_4 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (168), (169),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (210), (212), (218), (219), (220), (222),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (231), (239), (402), (405), (419), (425),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (448), (526), (561),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #903.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (562) all_57_9 = e1 & op(e3, e0) = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (562) implies:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (563) all_57_9 = e1
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (535), (563) are inconsistent by sub-proof
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1079.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (564) all_57_5 = e2 & op(e2, e1) = e2
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (168), (169), (170), (206),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (212), (213), (216), (218),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219), (220), (222), (223), (226), (227), (228),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (235), (237),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (375), (398), (399), (400), (401), (402),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (405), (417), (419), (425), (426), (427),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430), (448), (526), (540), (564),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #901.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (169), (223), (426), (448), (540),
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (565), (function-axioms) are inconsistent by
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1009.
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | (566) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 136.00/19.14 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (215),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (225),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (228), (231), (232), (233), (236),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (566), (function-axioms) are inconsistent by
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #927.
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (567) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (567) gives:
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (568) all_57_10 = e0 & op(e2, e0) = e0
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (403), (568), (function-axioms) are
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.00/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (569) all_57_11 = e0 & op(e1, e0) = e0
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (526), (569) are inconsistent by sub-proof
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | #992.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (570) all_57_3 = e2 & op(e2, e2) = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (570) implies:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (571) op(e2, e2) = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (571), (function-axioms) are
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | (572) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (572) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (573) all_57_7 = e2 & op(e1, e2) = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (573) implies:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (574) all_57_7 = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (453), (574) imply:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (575) e2 = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (526), (575) imply:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (576) all_57_11 = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (212),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (220), (221),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (222), (223), (225), (226), (227), (228), (229),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (235), (236), (237),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (576), (function-axioms) are inconsistent by
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #900.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (577) all_57_13 = e2 & op(e0, e2) = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (577) implies:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | (578) all_57_13 = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (579) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (579) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (580) all_57_4 = e1 & op(e3, e1) = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (580) implies:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (581) all_57_4 = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (582) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (165), (402), (581), (582), (function-axioms)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1090.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (583) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (210), (212), (419),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (448), (578), (583), (function-axioms) are
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1063.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (584) all_57_5 = e1 & op(e2, e1) = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (584) implies:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | (585) all_57_5 = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (586) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (586) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (587) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (587) implies:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (588) all_57_4 = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (210), (212),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (220), (402), (419), (448), (578), (588),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #904.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (589) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (168), (169), (170), (206),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (212), (213), (216), (218),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219), (220), (222), (223), (226), (227), (228),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (232), (233), (235), (237),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (375), (398), (399), (400), (401), (402),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (403), (405), (417), (419), (425), (426), (427),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (430), (448), (526), (585), (589),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #901.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (169), (223), (426), (448), (585),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (590), (function-axioms) are inconsistent by
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1009.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (591) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (215),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (225),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (226), (227), (228), (231), (232), (233), (236),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (591), (function-axioms) are inconsistent by
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #927.
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.15 | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | (592) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 136.03/19.15 | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (592) gives:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | | (593) all_57_8 = e1 & op(e1, e1) = e1
% 136.03/19.15 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (215),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (225),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (226), (227), (228), (231), (232), (233), (236),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (593),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | #928.
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (594) all_57_11 = e1 & op(e1, e0) = e1
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | ALPHA: (594) implies:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (595) all_57_11 = e1
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (110), (112),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (113), (120), (126), (133), (141), (143), (144),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (164), (165), (167),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (168), (169), (170), (193), (195), (196), (197),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (201), (206), (207), (209), (210), (211), (212),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (213), (215), (216), (218), (219), (220), (221),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (222), (223), (225), (226), (227), (228), (229),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (230), (231), (232), (233), (235), (236), (237),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (239), (250), (258), (259), (260), (270), (375),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (395), (398), (399), (400), (401), (402), (403),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (405), (408), (416), (417), (418), (419), (425),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (426), (427), (430), (443), (444), (445), (448),
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (595), (function-axioms) are inconsistent by
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | sub-proof #900.
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | (596) all_54_10 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (433), (596) are inconsistent by sub-proof
% 136.03/19.16 | | | | | | | | | | | | | | | | | | #899.
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | End of split
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | End of split
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | End of split
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | Case 2:
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | (597) all_48_2 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | (598) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0
% 136.03/19.16 | | | | | | | | | | | | | | | & op(e1, e0) = all_48_1 & $i(all_48_0) &
% 136.03/19.16 | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0)
% 136.03/19.16 | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | COMBINE_EQS: (299), (597) imply:
% 136.03/19.16 | | | | | | | | | | | | | | | (599) all_4_2 = e0
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | COMBINE_EQS: (295), (599) imply:
% 136.03/19.16 | | | | | | | | | | | | | | | (600) all_50_2 = e0
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | REDUCE: (362), (599) imply:
% 136.03/19.16 | | | | | | | | | | | | | | | (601) ~ (all_52_8 = e0)
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | REDUCE: (365), (599) imply:
% 136.03/19.16 | | | | | | | | | | | | | | | (602) ~ (all_52_11 = e0)
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | REDUCE: (372), (599) imply:
% 136.03/19.16 | | | | | | | | | | | | | | | (603) ~ (e2 = e0)
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 136.03/19.16 | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | Case 1:
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | (604) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (399), (425),
% 136.03/19.16 | | | | | | | | | | | | | | | | (426), (427), (604), (function-axioms) are
% 136.03/19.16 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1101.
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | Case 2:
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | (605) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | BETA: splitting (605) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | (606) all_57_4 = e0 & op(e3, e1) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (601), (606), (function-axioms) are
% 136.03/19.16 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | (607) all_57_9 = e0 & op(e3, e0) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | ALPHA: (607) implies:
% 136.03/19.16 | | | | | | | | | | | | | | | | | (608) all_57_9 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | (609) op(e3, e0) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | (610) all_57_15 = e0 & op(e0, e0) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | ALPHA: (610) implies:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | (611) op(e0, e0) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (419), (611), (function-axioms) are
% 136.03/19.16 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | (612) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.03/19.16 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.03/19.16 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | ALPHA: (612) implies:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | (613) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.03/19.16 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | BETA: splitting (613) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | (614) all_57_12 = e0 & op(e0, e3) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | ALPHA: (614) implies:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | (615) all_57_12 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | (616) op(e0, e3) = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (616) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | (617) all_52_3 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (609) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | (618) all_52_12 = e0
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (617) imply:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | (619) ~ (all_52_7 = e0)
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (620) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (620) gives:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.16 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (621) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (621) implies:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (622) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (419), (616), (622), (function-axioms) are
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (623) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (623) implies:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (624) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (625) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (401), (419), (624), (625),
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | #975.
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (626) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (626) gives:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (627) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (627) implies:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (628) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (629) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (630) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (631) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (632) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | (633) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (630) gives:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | (634) all_56_11 = e1 & op(e2, e2) = e1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (634) implies:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | (635) op(e2, e2) = e1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (405), (635), (function-axioms) are
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | (636) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (636) implies:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | (637) ~ (all_56_4 = e2)
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | (638) op(e2, e1) = all_56_4
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (631) gives:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | | (639) all_56_9 = e1 & op(e3, e3) = e1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (639) implies:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | | (640) all_56_9 = e1
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (426), (633), (640), (function-axioms) are
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #898.
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.17 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | (641) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (641) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | (642) ~ (all_56_1 = e3)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | (643) op(e3, e1) = all_56_1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (632) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (644) all_56_4 = e2 & op(e2, e1) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (644) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (645) all_56_4 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (637), (645) imply:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (646) $false
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (646) is inconsistent.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (647) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (647) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (648) ~ (all_56_11 = e1)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | (649) op(e2, e2) = all_56_11
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (628) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (650) all_56_15 = e1 & op(e0, e0) = e1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (650) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (651) op(e0, e0) = e1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (419), (651), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (652) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (652) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (653) ~ (all_56_14 = e0)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | (654) op(e0, e1) = all_56_14
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (629) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (655) all_56_14 = e0 & op(e0, e1) = e0
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (655) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (656) op(e0, e1) = e0
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (653), (654), (656), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (657) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (657) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (658) ~ (all_56_15 = e1)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | (659) op(e0, e0) = all_56_15
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (633) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (660) all_56_1 = e3 & op(e3, e1) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (660) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (661) op(e3, e1) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (426), (661), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (662) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (662) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (663) op(e3, e3) = all_56_9
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (419), (659)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (664) all_56_15 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e1, e2, simplifying with (165), (638)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (665) all_56_4 = all_52_9
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (405), (649)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (666) all_56_11 = e0
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, e1, e3, simplifying with (169), (643)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (667) all_56_1 = all_52_8
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (431), (663) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (668) all_56_9 = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (637), (665) imply:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (669) ~ (all_52_9 = e2)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (648), (666) imply:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | (670) ~ (e1 = e0)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (671) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (671) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (672) all_57_2 = e2 & op(e2, e3) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (672) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (673) all_57_2 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (674) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (674) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (675) all_57_4 = e2 & op(e3, e1) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (675) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (676) all_57_4 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (677) op(e3, e1) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (678) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (678) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (679) all_57_0 = e1 & op(e3, e3) = e1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (426), (430), (633), (668), (679),
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #897.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (680) all_57_1 = e1 & op(e3, e2) = e1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (680) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (681) all_57_1 = e1
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (682) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (682) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (683) all_57_1 = e2 & op(e3, e2) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (681), (683) are inconsistent by sub-proof
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1074.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (684) all_57_3 = e2 & op(e2, e2) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (684) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (685) op(e2, e2) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (685), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (686) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (686) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (687) all_57_7 = e2 & op(e1, e2) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (687) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (688) all_57_7 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (689) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (689) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (690) all_57_6 = e3 & op(e1, e3) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (169), (234), (426), (430), (615),
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (633), (668), (673), (690), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #895.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (691) all_57_7 = e3 & op(e1, e2) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (688), (691) are inconsistent by sub-proof
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1036.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (692) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (692) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (693) all_57_8 = e3 & op(e1, e1) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (693) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (694) op(e1, e1) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (694), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (695) all_57_11 = e3 & op(e1, e0) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (695) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (696) op(e1, e0) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (160), (169), (598), (600), (677), (696),
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #893.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (697) all_57_13 = e2 & op(e0, e2) = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (697) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (698) all_57_13 = e2
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (699) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (699) gives:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (700) all_57_12 = e3 & op(e0, e3) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (700) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (701) all_57_12 = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (425), (426),
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427), (430), (615), (701), (function-axioms) are
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #892.
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (702) all_57_13 = e3 & op(e0, e2) = e3
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (702) implies:
% 136.03/19.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (703) all_57_13 = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (698), (703) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1068.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (704) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (704) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (705) all_57_14 = e3 & op(e0, e1) = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (705) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (706) all_57_14 = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (707) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (707) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (708) all_57_12 = e1 & op(e0, e3) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (708) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (709) all_57_12 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (615), (709) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1002.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (710) all_57_13 = e1 & op(e0, e2) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (710) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (711) all_57_13 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (698), (711) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1057.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (712) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (712) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (713) all_57_14 = e1 & op(e0, e1) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (713) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (714) all_57_14 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (706), (714) imply:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (715) e3 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (715) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (716) e3 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (668), (716) imply:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (717) all_56_9 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (426), (633), (717), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #898.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (718) all_57_15 = e1 & op(e0, e0) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (718) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (719) op(e0, e0) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (419), (719), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (720) all_57_15 = e3 & op(e0, e0) = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (720) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (721) op(e0, e0) = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (419), (721), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (722) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (722) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (723) all_57_4 = e1 & op(e3, e1) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (676), (723) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #891.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (724) all_57_9 = e1 & op(e3, e0) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (608), (724) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1095.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (725) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (725) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (726) op(e2, e1) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (669), (726), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (727) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (727) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (728) all_57_8 = e2 & op(e1, e1) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (728) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (729) op(e1, e1) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (729), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (730) all_57_14 = e2 & op(e0, e1) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (730) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (731) all_57_14 = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (732) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (732) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (733) all_57_12 = e1 & op(e0, e3) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (615), (733) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #896.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (734) all_57_13 = e1 & op(e0, e2) = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (734) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (735) all_57_13 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (736) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (736) gives:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (737) all_57_12 = e3 & op(e0, e3) = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (737) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (738) all_57_12 = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (615), (738) imply:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (739) e3 = e0
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (430), (739) imply:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (740) all_57_0 = e0
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (425), (426),
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (427), (740), (function-axioms) are inconsistent
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1103.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (741) all_57_13 = e3 & op(e0, e2) = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (741) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (742) all_57_13 = e3
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (735), (742) imply:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (743) e3 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (668), (743) imply:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (744) all_56_9 = e1
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (426), (633), (744), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #898.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (745) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (419), (731), (745), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #889.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (746) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (419), (731), (746), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #888.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (747) all_57_3 = e2 & op(e2, e2) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (747) implies:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (748) op(e2, e2) = e2
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (748), (function-axioms) are
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (749) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (165), (417), (669), (749),
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #887.
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.19 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | (750) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (36), (164), (207), (375),
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | (405), (417), (419), (616), (750),
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | | #946.
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (751) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.03/19.20 | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (401), (602), (751),
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | #885.
% 136.03/19.20 | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | (752) all_57_1 = e3 & op(e3, e2) = e3
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | ALPHA: (752) implies:
% 136.03/19.20 | | | | | | | | | | | | | | (753) op(e3, e2) = e3
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | REF_CLOSE: (170), (425), (753), (function-axioms) are
% 136.03/19.20 | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | (754) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 136.03/19.20 | | | | | | | | | | | | | & op(e3, e0) = e3)
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | REF_CLOSE: (168), (169), (426), (427), (754),
% 136.03/19.20 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.20 | | | | | | | | | | | | | #1104.
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | (755) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | REF_CLOSE: (279), (377), (410), (421), (755) are inconsistent
% 136.03/19.20 | | | | | | | | | | | | by sub-proof #883.
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | End of split
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | (756) all_36_2 = e2
% 136.03/19.20 | | | | | | | | | | | (757) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 136.03/19.20 | | | | | | | | | | | & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 136.03/19.20 | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2)
% 136.03/19.20 | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | COMBINE_EQS: (305), (756) imply:
% 136.03/19.20 | | | | | | | | | | | (758) all_14_2 = e2
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | SIMP: (758) implies:
% 136.03/19.20 | | | | | | | | | | | (759) all_14_2 = e2
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | COMBINE_EQS: (281), (759) imply:
% 136.03/19.20 | | | | | | | | | | | (760) all_44_2 = e2
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | REDUCE: (337), (759) imply:
% 136.03/19.20 | | | | | | | | | | | (761) ~ (all_52_1 = e2)
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | REDUCE: (51), (759) imply:
% 136.03/19.20 | | | | | | | | | | | (762) op(e3, e3) = e2
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | BETA: splitting (226) gives:
% 136.03/19.20 | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | (763) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 136.03/19.20 | | | | | | | | | | | | & op(e2, e2) = e2)
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | REF_CLOSE: (5), (167), (405), (761), (763), (function-axioms)
% 136.03/19.20 | | | | | | | | | | | | are inconsistent by sub-proof #881.
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | (764) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 136.03/19.20 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | BETA: splitting (764) gives:
% 136.03/19.20 | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | (765) all_57_5 = e2 & op(e2, e1) = e2
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | ALPHA: (765) implies:
% 136.03/19.20 | | | | | | | | | | | | | (766) all_57_5 = e2
% 136.03/19.20 | | | | | | | | | | | | | (767) op(e2, e1) = e2
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | BETA: splitting (236) gives:
% 136.03/19.20 | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | (768) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 136.03/19.20 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | BETA: splitting (768) gives:
% 136.03/19.20 | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | (769) all_57_0 = e2 & op(e3, e3) = e2
% 136.03/19.20 | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | ALPHA: (769) implies:
% 136.03/19.20 | | | | | | | | | | | | | | | (770) all_57_0 = e2
% 136.03/19.20 | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.03/19.20 | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | (771) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.03/19.20 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.03/19.20 | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | BETA: splitting (771) gives:
% 136.03/19.20 | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | (772) all_57_6 = e2 & op(e1, e3) = e2
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (164),
% 136.03/19.20 | | | | | | | | | | | | | | | | | (206), (207), (225), (227), (232), (375), (401),
% 136.03/19.20 | | | | | | | | | | | | | | | | | (405), (417), (419), (762), (766), (767), (772),
% 136.03/19.20 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.03/19.20 | | | | | | | | | | | | | | | | | #874.
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | Case 2:
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | (773) all_57_7 = e2 & op(e1, e2) = e2
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | ALPHA: (773) implies:
% 136.03/19.20 | | | | | | | | | | | | | | | | | (774) all_57_7 = e2
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 136.03/19.20 | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (767) gives:
% 136.03/19.20 | | | | | | | | | | | | | | | | | (775) all_52_9 = e2
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | REDUCE: (117), (775) imply:
% 136.03/19.20 | | | | | | | | | | | | | | | | | (776) ~ (all_52_13 = e2)
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 136.03/19.20 | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (777) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.03/19.20 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 136.03/19.20 | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | BETA: splitting (777) gives:
% 136.03/19.20 | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | Case 1:
% 136.03/19.20 | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (778) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 136.03/19.20 | | | | | | | | | | | | | | | | | | |
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | ALPHA: (778) implies:
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (779) op(e3, e3) = all_56_9
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (780) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (781) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | (782) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 136.03/19.20 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 136.03/19.21 | | | | | | | | | | | | | | | | | | | (783) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.03/19.21 | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.03/19.21 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | (784) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | (785) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 136.29/19.21 | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (780) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | (786) all_56_15 = e3 & op(e0, e0) = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (786) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | (787) op(e0, e0) = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (419), (787), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | (788) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | ALPHA: (788) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | (789) ~ (all_56_10 = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | (790) op(e0, e3) = all_56_10
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (782) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | (791) all_56_11 = e3 & op(e2, e2) = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | ALPHA: (791) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | (792) op(e2, e2) = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (405), (792), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | (793) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | ALPHA: (793) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | (794) ~ (all_56_3 = e2)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | (795) op(e2, e3) = all_56_3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (781) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | (796) all_56_13 = e3 & op(e1, e1) = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (796) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | (797) op(e1, e1) = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (797), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | (798) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (798) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | (799) ~ (all_56_6 = e1)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (783) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | (800) all_56_10 = e0 & op(e0, e3) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (800) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | (801) op(e0, e3) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (789), (790), (801), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #954.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | (802) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (802) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | (803) ~ (all_56_15 = e3)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | (804) op(e0, e0) = all_56_15
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (784) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | (805) all_56_6 = e1 & op(e1, e3) = e1
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (805) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | (806) all_56_6 = e1
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (799), (806) imply:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | (807) $false
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (807) is inconsistent.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | (808) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (808) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | (809) ~ (all_56_13 = e3)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | (810) op(e1, e1) = all_56_13
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (785) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (811) all_56_3 = e2 & op(e2, e3) = e2
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (811) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (812) op(e2, e3) = e2
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (794), (795), (812), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (813) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (813) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (814) ~ (all_56_11 = e3)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (815) op(e2, e2) = all_56_11
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (419), (804)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (816) all_56_15 = e2
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10, e3, e0, simplifying with (159), (790)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (817) all_56_10 = all_52_3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (36), (810)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (818) all_56_13 = all_4_2
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (405), (815)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (819) all_56_11 = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (762), (779) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (820) all_56_9 = e2
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (789), (817) imply:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (821) ~ (all_52_3 = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (803), (816) imply:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | (822) ~ (e3 = e2)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (823) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (405),
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (762), (766), (823), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #875.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (824) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (824) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (825) all_57_6 = e0 & op(e1, e3) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (825) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (826) all_57_6 = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (827) op(e1, e3) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (828) all_57_15 = e0 & op(e0, e0) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (828) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (829) op(e0, e0) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (419), (829), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (830) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (830) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (831) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (832) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (831) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (833) all_57_12 = e0 & op(e0, e3) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (833) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (834) op(e0, e3) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (821), (834), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (835) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (835) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (836) all_57_13 = e0 & op(e0, e2) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (836) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (837) op(e0, e2) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (401), (837), (function-axioms) are
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (838) all_57_14 = e0 & op(e0, e1) = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (838) implies:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (839) all_57_14 = e0
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (840) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (840) gives:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (841) all_57_6 = e3 & op(e1, e3) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (841) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (842) all_57_6 = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (826), (842) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (843) all_57_7 = e3 & op(e1, e2) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (774), (843) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1036.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (844) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (844) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (845) all_57_8 = e3 & op(e1, e1) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (845) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (846) op(e1, e1) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (846), (function-axioms) are
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (847) all_57_11 = e3 & op(e1, e0) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (847) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (848) all_57_11 = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (832) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (849) all_57_9 = e0 & op(e3, e0) = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (849) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (850) all_57_9 = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (851) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (851) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (852) all_57_6 = e1 & op(e1, e3) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (852) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (853) all_57_6 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (826), (853) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1026.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (854) all_57_7 = e1 & op(e1, e2) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (854) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (855) all_57_7 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (774), (855) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (856) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (856) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (857) all_57_8 = e1 & op(e1, e1) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (857) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (858) all_57_8 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (859) op(e1, e1) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (860) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (860) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (861) all_57_4 = e3 & op(e3, e1) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (861) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (862) all_57_4 = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (863) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (863) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (864) all_57_0 = e1 & op(e3, e3) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (864) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (865) all_57_0 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (770), (865) imply:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (866) e2 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (766), (866) imply:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (867) all_57_5 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (222), (839), (858), (862), (867)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #870.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (868) all_57_1 = e1 & op(e3, e2) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (868) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (869) op(e3, e2) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (757), (760), (827), (869),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #868.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (870) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (870) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (871) all_57_4 = e1 & op(e3, e1) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (871) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (872) all_57_4 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (862), (872) imply:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (873) e3 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (873) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (874) e3 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (848), (874) imply:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (875) all_57_11 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (219), (774), (826), (859), (875),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #866.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (876) all_57_9 = e1 & op(e3, e0) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (876) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (877) all_57_9 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (850), (877) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1079.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (878) all_57_5 = e3 & op(e2, e1) = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (878) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (879) all_57_5 = e3
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (766), (879) imply:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (880) e3 = e2
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (848), (880) imply:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881) all_57_11 = e2
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (206), (207), (215), (216), (217), (219),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (232), (375), (400), (401), (405),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (417), (419), (762), (766), (767), (774), (832),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (881), (function-axioms) are inconsistent by
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #860.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (882) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (839), (859), (882), (function-axioms)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #859.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (883) all_57_11 = e1 & op(e1, e0) = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (883) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (884) all_57_11 = e1
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (848), (884) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #912.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (885) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (885) gives:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (886) all_57_10 = e0 & op(e2, e0) = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (886) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (887) all_57_10 = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (225), (227), (405),
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (766), (887), (function-axioms) are inconsistent
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #934.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (888) all_57_11 = e0 & op(e1, e0) = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (888) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (889) all_57_11 = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (848), (889) are inconsistent by sub-proof
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #858.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (890) all_57_12 = e0 & op(e0, e3) = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (890) implies:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (891) op(e0, e3) = e0
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (821), (891), (function-axioms) are
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.22 | | | | | | | | | | | | | | | | | | |
% 136.29/19.22 | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.22 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (892) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | ALPHA: (892) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (893) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (894) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (401), (419), (893), (894),
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | #975.
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (895) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (164), (405), (417), (767), (895),
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.23 | | | | | | | | | | | | | | | | | | #855.
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | End of split
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | End of split
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | (896) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.29/19.23 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | BETA: splitting (896) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | (897) all_57_8 = e2 & op(e1, e1) = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | ALPHA: (897) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | (898) op(e1, e1) = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (898), (function-axioms) are
% 136.29/19.23 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | (899) all_57_11 = e2 & op(e1, e0) = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | ALPHA: (899) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | (900) all_57_11 = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (213), (215),
% 136.29/19.23 | | | | | | | | | | | | | | | | | (225), (227), (405), (419), (766), (900),
% 136.29/19.23 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.23 | | | | | | | | | | | | | | | | | #849.
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | End of split
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | End of split
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | (901) all_57_2 = e2 & op(e2, e3) = e2
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | ALPHA: (901) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | (902) op(e2, e3) = e2
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | REF_CLOSE: (167), (761), (902), (function-axioms) are
% 136.29/19.23 | | | | | | | | | | | | | | | inconsistent by sub-proof #882.
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | End of split
% 136.29/19.23 | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | (903) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 136.29/19.23 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 136.29/19.23 | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | BETA: splitting (903) gives:
% 136.29/19.23 | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | (904) all_57_6 = e2 & op(e1, e3) = e2
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (164),
% 136.29/19.23 | | | | | | | | | | | | | | | (206), (207), (225), (227), (232), (375), (401),
% 136.29/19.23 | | | | | | | | | | | | | | | (405), (417), (419), (762), (766), (767), (904),
% 136.29/19.23 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.23 | | | | | | | | | | | | | | | #874.
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | (905) all_57_12 = e2 & op(e0, e3) = e2
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | ALPHA: (905) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | (906) all_57_12 = e2
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.29/19.23 | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | (907) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | BETA: splitting (907) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | (908) all_57_6 = e2 & op(e1, e3) = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (164),
% 136.29/19.23 | | | | | | | | | | | | | | | | | (206), (207), (225), (227), (232), (375), (401),
% 136.29/19.23 | | | | | | | | | | | | | | | | | (405), (417), (419), (762), (766), (767), (908),
% 136.29/19.23 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.23 | | | | | | | | | | | | | | | | | #874.
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | (909) all_57_7 = e2 & op(e1, e2) = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | ALPHA: (909) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | (910) all_57_7 = e2
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (911) all_57_15 = e0 & op(e0, e0) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ALPHA: (911) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (912) op(e0, e0) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (419), (912), (function-axioms) are
% 136.29/19.23 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (913) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.29/19.23 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | ALPHA: (913) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (914) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.29/19.23 | | | | | | | | | | | | | | | | | | (915) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 136.29/19.23 | | | | | | | | | | | | | | | | | | e0) = e0)
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | BETA: splitting (914) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (916) all_57_12 = e0 & op(e0, e3) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | ALPHA: (916) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (917) op(e0, e3) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (36), (158), (164), (206),
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (207), (375), (401), (405), (417), (419), (767),
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (917), (function-axioms) are inconsistent by
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | sub-proof #945.
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | (918) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (918) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | (919) all_57_13 = e0 & op(e0, e2) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (919) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | (920) op(e0, e2) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (401), (920), (function-axioms) are
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | (921) all_57_14 = e0 & op(e0, e1) = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (921) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | (922) all_57_14 = e0
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | (923) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (923) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | (924) all_57_12 = e1 & op(e0, e3) = e1
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (906), (924) are inconsistent by sub-proof
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | #848.
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | (925) all_57_13 = e1 & op(e0, e2) = e1
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (925) implies:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | (926) all_57_13 = e1
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.23 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | (927) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (405),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | (762), (766), (927), (function-axioms) are
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #875.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | (928) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (928) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (929) all_57_6 = e0 & op(e1, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (929) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (930) all_57_6 = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (164), (206), (207), (212), (215), (216), (217),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (219), (225), (227), (232), (375), (400), (401),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (405), (417), (419), (762), (766), (767), (906),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (910), (915), (922), (926), (930),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | #847.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (931) all_57_12 = e0 & op(e0, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (931) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (932) op(e0, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (36), (158), (164), (206),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (207), (375), (401), (405), (417), (419), (767),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (932), (function-axioms) are inconsistent by
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #945.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | (933) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (419), (922), (933), (function-axioms)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1069.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | (934) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.29/19.24 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.29/19.24 | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | BETA: splitting (934) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | (935) all_57_8 = e2 & op(e1, e1) = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | ALPHA: (935) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | (936) op(e1, e1) = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (936), (function-axioms) are
% 136.29/19.24 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | (937) all_57_11 = e2 & op(e1, e0) = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | ALPHA: (937) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | (938) all_57_11 = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | (939) all_57_15 = e0 & op(e0, e0) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | ALPHA: (939) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | (940) op(e0, e0) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (419), (940), (function-axioms) are
% 136.29/19.24 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | (941) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.29/19.24 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | ALPHA: (941) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | (942) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | (943) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 136.29/19.24 | | | | | | | | | | | | | | | | | | e0) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | BETA: splitting (942) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | (944) all_57_12 = e0 & op(e0, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | ALPHA: (944) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | (945) op(e0, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (36), (158), (164), (206),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | (207), (375), (401), (405), (417), (419), (767),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | (945), (function-axioms) are inconsistent by
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | sub-proof #945.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | (946) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (946) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | (947) all_57_13 = e0 & op(e0, e2) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | ALPHA: (947) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | (948) op(e0, e2) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (401), (948), (function-axioms) are
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | (949) all_57_14 = e0 & op(e0, e1) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | ALPHA: (949) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | (950) all_57_14 = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | (951) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (951) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | (952) all_57_12 = e1 & op(e0, e3) = e1
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (906), (952) are inconsistent by sub-proof
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | #848.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | (953) all_57_13 = e1 & op(e0, e2) = e1
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (953) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | (954) all_57_13 = e1
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | (955) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (225), (227), (405),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | (762), (766), (955), (function-axioms) are
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #875.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | (956) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (956) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (957) all_57_6 = e0 & op(e1, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (957) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (958) all_57_6 = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | (959) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (959) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (960) all_57_6 = e3 & op(e1, e3) = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (960) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (961) all_57_6 = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (958), (961) are inconsistent by sub-proof
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (962) all_57_7 = e3 & op(e1, e2) = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (962) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | (963) all_57_7 = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (964) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (964) gives:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (965) all_57_12 = e3 & op(e0, e3) = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (965) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (966) all_57_12 = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (906), (966) imply:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (967) e3 = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (967) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (968) e3 = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (963), (968) imply:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (969) all_57_7 = e2
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (206), (207), (212), (215), (216), (217),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219), (225), (227), (232), (375), (400), (401),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (405), (417), (419), (762), (766), (767), (906),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (943), (950), (954), (958), (969),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #847.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (970) all_57_13 = e3 & op(e0, e2) = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (970) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (971) all_57_13 = e3
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (954), (971) are inconsistent by sub-proof
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1001.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | (972) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (419), (950), (972), (function-axioms)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1065.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | (973) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (375), (938), (973), (function-axioms)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #861.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (974) all_57_12 = e0 & op(e0, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (974) implies:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (975) op(e0, e3) = e0
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (36), (158), (164), (206),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (207), (375), (401), (405), (417), (419), (767),
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | (975), (function-axioms) are inconsistent by
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #945.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | (976) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (419), (950), (976), (function-axioms)
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1069.
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | | End of split
% 136.29/19.24 | | | | | | | | | | | | |
% 136.29/19.24 | | | | | | | | | | | | Case 2:
% 136.29/19.24 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | (977) all_57_10 = e2 & op(e2, e0) = e2
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | ALPHA: (977) implies:
% 136.29/19.25 | | | | | | | | | | | | | (978) op(e2, e0) = e2
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | REF_CLOSE: (164), (417), (978), (function-axioms) are
% 136.29/19.25 | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | (979) all_22_2 = e1
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | COMBINE_EQS: (321), (979) imply:
% 136.29/19.25 | | | | | | | | | (980) all_14_2 = e1
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | SIMP: (980) implies:
% 136.29/19.25 | | | | | | | | | (981) all_14_2 = e1
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | REDUCE: (337), (981) imply:
% 136.29/19.25 | | | | | | | | | (982) ~ (all_52_1 = e1)
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | REDUCE: (343), (981) imply:
% 136.29/19.25 | | | | | | | | | (983) ~ (all_52_4 = e1)
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | REDUCE: (347), (981) imply:
% 136.29/19.25 | | | | | | | | | (984) ~ (all_52_12 = e1)
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | REDUCE: (51), (981) imply:
% 136.29/19.25 | | | | | | | | | (985) op(e3, e3) = e1
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | BETA: splitting (67) gives:
% 136.29/19.25 | | | | | | | | |
% 136.29/19.25 | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | (986) ~ (all_24_2 = e2)
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | REDUCE: (319), (986) imply:
% 136.29/19.25 | | | | | | | | | | (987) ~ (all_10_2 = e2)
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | REF_CLOSE: (4), (7), (36), (45), (51), (207), (375), (376),
% 136.29/19.25 | | | | | | | | | | (377), (405), (987), (function-axioms) are
% 136.29/19.25 | | | | | | | | | | inconsistent by sub-proof #1113.
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | (988) all_24_2 = e2
% 136.29/19.25 | | | | | | | | | | (989) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 &
% 136.29/19.25 | | | | | | | | | | op(e0, e2) = all_24_1 & $i(all_24_0) &
% 136.29/19.25 | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2)
% 136.29/19.25 | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | COMBINE_EQS: (319), (988) imply:
% 136.29/19.25 | | | | | | | | | | (990) all_10_2 = e2
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | COMBINE_EQS: (307), (990) imply:
% 136.29/19.25 | | | | | | | | | | (991) all_40_2 = e2
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | REDUCE: (368), (990) imply:
% 136.29/19.25 | | | | | | | | | | (992) ~ (all_52_11 = e2)
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | REDUCE: (370), (990) imply:
% 136.29/19.25 | | | | | | | | | | (993) ~ (all_52_13 = e2)
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | REDUCE: (371), (990) imply:
% 136.29/19.25 | | | | | | | | | | (994) ~ (all_52_14 = e2)
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | REDUCE: (45), (990) imply:
% 136.29/19.25 | | | | | | | | | | (995) op(e0, e0) = e2
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | BETA: splitting (91) gives:
% 136.29/19.25 | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | (996) ~ (all_40_2 = e2)
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | REDUCE: (991), (996) imply:
% 136.29/19.25 | | | | | | | | | | | (997) $false
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | CLOSE: (997) is inconsistent.
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | (998) ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 136.29/19.25 | | | | | | | | | | | & op(e0, e2) = all_40_1 & $i(all_40_0) &
% 136.29/19.25 | | | | | | | | | | | $i(all_40_1)) | ( ~ (all_40_1 = e1) & op(e0, e2)
% 136.29/19.25 | | | | | | | | | | | = all_40_1 & $i(all_40_1))
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | BETA: splitting (103) gives:
% 136.29/19.25 | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | (999) ~ (all_48_2 = e0)
% 136.29/19.25 | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | REDUCE: (299), (999) imply:
% 136.29/19.25 | | | | | | | | | | | | (1000) ~ (all_4_2 = e0)
% 136.29/19.25 | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | BETA: splitting (194) gives:
% 136.29/19.25 | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | (1001) all_54_10 = e3
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | REF_CLOSE: (335), (375), (1001) are inconsistent by sub-proof
% 136.29/19.25 | | | | | | | | | | | | | #1112.
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | (1002) ~ (all_54_10 = e3)
% 136.29/19.25 | | | | | | | | | | | | | (1003) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | BETA: splitting (1003) gives:
% 136.29/19.25 | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | (1004) all_54_10 = e2
% 136.29/19.25 | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (1004) are inconsistent by sub-proof
% 136.29/19.25 | | | | | | | | | | | | | | #1111.
% 136.29/19.25 | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | (1005) ~ (all_54_10 = e2)
% 136.29/19.25 | | | | | | | | | | | | | | (1006) all_54_10 = e1 | all_54_10 = e0
% 136.29/19.25 | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | BETA: splitting (1006) gives:
% 136.29/19.25 | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | (1007) all_54_10 = e1
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | COMBINE_EQS: (335), (1007) imply:
% 136.29/19.25 | | | | | | | | | | | | | | | (1008) all_4_2 = e1
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | SIMP: (1008) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | (1009) all_4_2 = e1
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | REDUCE: (349), (1009) imply:
% 136.29/19.25 | | | | | | | | | | | | | | | (1010) ~ (all_52_2 = e1)
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | REDUCE: (375), (1009) imply:
% 136.29/19.25 | | | | | | | | | | | | | | | (1011) ~ (e3 = e1)
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | REDUCE: (372), (1009) imply:
% 136.29/19.25 | | | | | | | | | | | | | | | (1012) ~ (e2 = e1)
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | REDUCE: (36), (1009) imply:
% 136.29/19.25 | | | | | | | | | | | | | | | (1013) op(e1, e1) = e1
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 136.29/19.25 | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | (1014) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 136.29/19.25 | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (405), (982), (1014),
% 136.29/19.25 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.25 | | | | | | | | | | | | | | | | #845.
% 136.29/19.25 | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | (1015) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 136.29/19.25 | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.29/19.25 | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | BETA: splitting (1015) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | (1016) all_57_5 = e1 & op(e2, e1) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | ALPHA: (1016) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | (1017) all_57_5 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | (1018) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 136.29/19.25 | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (405), (983), (1018),
% 136.29/19.25 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.29/19.25 | | | | | | | | | | | | | | | | | | #843.
% 136.29/19.25 | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | (1019) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 136.29/19.25 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.29/19.25 | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | BETA: splitting (1019) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | (1020) all_57_7 = e1 & op(e1, e2) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | ALPHA: (1020) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | (1021) all_57_7 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | (1022) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1022) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | (1023) all_57_2 = e2 & op(e2, e3) = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1023) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | (1024) all_57_2 = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | (1025) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1025) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | (1026) all_57_1 = e2 & op(e3, e2) = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1026) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | (1027) all_57_1 = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (1028) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (405), (1027), (1028), (function-axioms)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #841.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | (1029) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1029) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1030) all_57_7 = e3 & op(e1, e2) = e3
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1030) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1031) all_57_7 = e3
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1021), (1031) are inconsistent by sub-proof
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | #915.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1032) all_57_13 = e3 & op(e0, e2) = e3
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1032) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | (1033) all_57_13 = e3
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1034) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1034) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1035) all_57_12 = e1 & op(e0, e3) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1035) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1036) all_57_12 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (167), (209),
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (212), (232), (238), (398), (401), (985),
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (995), (1024), (1033), (1036), (function-axioms)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #832.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1037) all_57_13 = e1 & op(e0, e2) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1037) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1038) all_57_13 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1033), (1038) are inconsistent by sub-proof
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1001.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (1039) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1039) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1040) all_57_14 = e1 & op(e0, e1) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1040) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1041) all_57_14 = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013), (1017), (1041), (function-axioms) are
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #829.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1042) all_57_15 = e1 & op(e0, e0) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1042) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1043) op(e0, e0) = e1
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (995), (1043), (function-axioms) are
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | (1044) all_57_3 = e2 & op(e2, e2) = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1044) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | (1045) op(e2, e2) = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (1045), (function-axioms) are
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | (1046) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1046) gives:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | (1047) all_57_7 = e2 & op(e1, e2) = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1047) implies:
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | | (1048) all_57_7 = e2
% 136.29/19.25 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1021), (1048) are inconsistent by sub-proof
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | | #872.
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | | (1049) all_57_13 = e2 & op(e0, e2) = e2
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | | (212), (401), (995), (1049), (function-axioms) are
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #825.
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | (1050) all_57_3 = e2 & op(e2, e2) = e2
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.29/19.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1050) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1051) op(e2, e2) = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (1051), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | (1052) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (993), (1017), (1052),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | #824.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | (1053) all_57_13 = e1 & op(e0, e2) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | ALPHA: (1053) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | (1054) all_57_13 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | (1055) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1055) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1056) all_57_2 = e2 & op(e2, e3) = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1056) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1057) all_57_2 = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | (1058) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (405), (1057), (1058), (function-axioms)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #822.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | (1059) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1059) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | (1060) all_57_5 = e3 & op(e2, e1) = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1060) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | (1061) all_57_5 = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1017), (1061) are inconsistent by sub-proof
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | #1035.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | (1062) all_57_10 = e3 & op(e2, e0) = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1062) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | (1063) all_57_10 = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | (1064) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1064) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | (1065) all_57_4 = e2 & op(e3, e1) = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1065) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | (1066) all_57_4 = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (1067) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (1017), (1066), (1067) are inconsistent
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #820.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (1068) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1068) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1069) all_57_8 = e3 & op(e1, e1) = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1069) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1070) op(e1, e1) = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1013), (1070), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1071) all_57_14 = e3 & op(e0, e1) = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1071) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1072) all_57_14 = e3
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1073) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1073) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1074) all_57_9 = e1 & op(e3, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1074) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1075) all_57_9 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (233), (237),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (399), (985), (1075), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #812.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1076) all_57_10 = e1 & op(e2, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1076) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1077) all_57_10 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1063), (1077) imply:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1078) e3 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1078) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1079) e3 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1072), (1079) imply:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1080) all_57_14 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1013), (1017), (1080), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #829.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1081) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1081) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1082) all_57_11 = e1 & op(e1, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1082) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1083) all_57_11 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (216), (218),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219), (400), (1013), (1083), (function-axioms)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #806.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1084) all_57_15 = e1 & op(e0, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1084) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1085) op(e0, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (995), (1085), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | (1086) all_57_5 = e2 & op(e2, e1) = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1086) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | (1087) all_57_5 = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1017), (1087) are inconsistent by sub-proof
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | | #1031.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | (1088) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (210), (212),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | (995), (1013), (1054), (1088), (function-axioms)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #799.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1089) all_57_3 = e2 & op(e2, e2) = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1089) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1090) op(e2, e2) = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (405), (1090), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | (1091) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (993), (1017), (1091),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | #824.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | End of split
% 136.50/19.26 | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | (1092) all_57_10 = e1 & op(e2, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | ALPHA: (1092) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | (1093) op(e2, e0) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | (1094) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (405), (983), (1094),
% 136.50/19.26 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.26 | | | | | | | | | | | | | | | | | | #843.
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | (1095) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | BETA: splitting (1095) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | (1096) all_57_7 = e1 & op(e1, e2) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | ALPHA: (1096) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | (1097) all_57_7 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | (1098) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1098) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1099) all_57_12 = e1 & op(e0, e3) = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1099) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | (1100) all_57_12 = e1
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | (1101) all_57_15 = e0 & op(e0, e0) = e0
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1101) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | (1102) op(e0, e0) = e0
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (995), (1102), (function-axioms) are
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | (1103) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1103) implies:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | (1104) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | (1105) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1105) gives:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1106) all_57_6 = e2 & op(e1, e3) = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1106) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1107) all_57_6 = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (1108) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (398), (985), (1108),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | #839.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (1109) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1109) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1110) all_57_6 = e0 & op(e1, e3) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1107), (1110) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | #994.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1111) all_57_12 = e0 & op(e0, e3) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1100), (1111) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | #837.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1112) all_57_7 = e2 & op(e1, e2) = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1097), (1112) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | #997.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | (1113) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1113) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1114) all_57_8 = e2 & op(e1, e1) = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1114) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1115) op(e1, e1) = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1013), (1115), (function-axioms) are
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1116) all_57_11 = e2 & op(e1, e0) = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1116) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | (1117) all_57_11 = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (1118) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (398), (985), (1118),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | #839.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | (1119) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1119) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1120) all_57_6 = e0 & op(e1, e3) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1120) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1121) all_57_6 = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1104) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1122) all_57_12 = e0 & op(e0, e3) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1122) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1123) all_57_12 = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1100), (1123) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1002.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1124) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1124) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1125) all_57_13 = e0 & op(e0, e2) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1125) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1126) op(e0, e2) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (401), (1126), (function-axioms) are
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1127) all_57_14 = e0 & op(e0, e1) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1127) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1128) all_57_14 = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1129) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1129) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1130) all_57_12 = e3 & op(e0, e3) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1100), (1130) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #798.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1131) all_57_13 = e3 & op(e0, e2) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1131) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1132) all_57_13 = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1133) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1133) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1134) all_57_0 = e3 & op(e3, e3) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1134) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1135) op(e3, e3) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (985), (1135), (function-axioms) are
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1136) all_57_2 = e3 & op(e2, e3) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1136) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1137) all_57_2 = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1138) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1138) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1139) all_57_6 = e3 & op(e1, e3) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1139) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1140) all_57_6 = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1121), (1140) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1141) all_57_7 = e3 & op(e1, e2) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1141) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1142) op(e1, e2) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (395), (408), (1093), (1142), (function-axioms)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1020.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1143) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1143) gives:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1144) all_57_8 = e3 & op(e1, e1) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1144) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1145) op(e1, e1) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1013), (1145), (function-axioms) are
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1146) all_57_11 = e3 & op(e1, e0) = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1146) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1147) all_57_11 = e3
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1117), (1147) imply:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1148) e3 = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1148) implies:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1149) e3 = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1137), (1149) imply:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1150) all_57_2 = e2
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (167), (209),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (212), (232), (238), (398), (401), (985),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (995), (1100), (1132), (1150), (function-axioms)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #832.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1151) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (1100), (1121), (1151) are inconsistent
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #833.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1152) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (995), (1128), (1152), (function-axioms)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1065.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (1153) all_57_12 = e0 & op(e0, e3) = e0
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1100), (1153) are inconsistent by sub-proof
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | | #837.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (1154) all_57_13 = e1 & op(e0, e2) = e1
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (112), (126), (128), (141), (143), (145),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (149), (158), (160), (162), (164), (167), (168),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (170), (193), (195), (196), (200), (206), (209),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (210), (212), (222), (233), (250), (258), (259),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (269), (395), (398), (399), (400), (401), (405),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (408), (985), (989), (993), (994), (995), (998),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | (1010), (1013), (1093), (1154), (function-axioms)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #787.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | (1155) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | (995), (1013), (1155), (function-axioms) are
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (1156) all_57_13 = e1 & op(e0, e2) = e1
% 136.50/19.27 | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (110), (112), (126), (128), (141), (143), (145),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (149), (158), (160), (162), (164), (167), (168),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (170), (193), (195), (196), (200), (206), (209),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (210), (212), (222), (233), (250), (258), (259),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (269), (395), (398), (399), (400), (401), (405),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (408), (985), (989), (993), (994), (995), (998),
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | (1010), (1013), (1093), (1156), (function-axioms)
% 136.50/19.27 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #787.
% 136.50/19.27 | | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | (1157) all_54_10 = e0
% 136.50/19.27 | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | | REF_CLOSE: (335), (1000), (1157) are inconsistent by
% 136.50/19.27 | | | | | | | | | | | | | | | sub-proof #899.
% 136.50/19.27 | | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | | End of split
% 136.50/19.27 | | | | | | | | | | | |
% 136.50/19.27 | | | | | | | | | | | Case 2:
% 136.50/19.27 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | (1158) all_48_2 = e0
% 136.50/19.28 | | | | | | | | | | | | (1159) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0
% 136.50/19.28 | | | | | | | | | | | | & op(e1, e0) = all_48_1 & $i(all_48_0) &
% 136.50/19.28 | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0)
% 136.50/19.28 | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 136.50/19.28 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | COMBINE_EQS: (299), (1158) imply:
% 136.50/19.28 | | | | | | | | | | | | (1160) all_4_2 = e0
% 136.50/19.28 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | COMBINE_EQS: (295), (1160) imply:
% 136.50/19.28 | | | | | | | | | | | | (1161) all_50_2 = e0
% 136.50/19.28 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | REDUCE: (362), (1160) imply:
% 136.50/19.28 | | | | | | | | | | | | (1162) ~ (all_52_8 = e0)
% 136.50/19.28 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | REDUCE: (372), (1160) imply:
% 136.50/19.28 | | | | | | | | | | | | (1163) ~ (e2 = e0)
% 136.50/19.28 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | BETA: splitting (232) gives:
% 136.50/19.28 | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | (1164) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 136.50/19.28 | | | | | | | | | | | | | & op(e2, e3) = e0)
% 136.50/19.28 | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | REF_CLOSE: (4), (167), (398), (985), (1164),
% 136.50/19.28 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | #839.
% 136.50/19.28 | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | (1165) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 136.50/19.28 | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 136.50/19.28 | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | BETA: splitting (1165) gives:
% 136.50/19.28 | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | (1166) all_57_6 = e0 & op(e1, e3) = e0
% 136.50/19.28 | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | ALPHA: (1166) implies:
% 136.50/19.28 | | | | | | | | | | | | | | (1167) all_57_6 = e0
% 136.50/19.28 | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 136.50/19.28 | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | (1168) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 136.50/19.28 | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 136.50/19.28 | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (399), (985), (1168),
% 136.50/19.28 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | | | #819.
% 136.50/19.28 | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | (1169) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 136.50/19.28 | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 136.50/19.28 | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | BETA: splitting (1169) gives:
% 136.50/19.28 | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | (1170) all_57_4 = e0 & op(e3, e1) = e0
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1162), (1170), (function-axioms) are
% 136.50/19.28 | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | (1171) all_57_9 = e0 & op(e3, e0) = e0
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | ALPHA: (1171) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | (1172) all_57_9 = e0
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | (1173) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.50/19.28 | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | BETA: splitting (1173) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | (1174) all_57_6 = e2 & op(e1, e3) = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1167), (1174) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | | | | | | #783.
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | (1175) all_57_7 = e2 & op(e1, e2) = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | ALPHA: (1175) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | (1176) all_57_7 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | (1177) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | BETA: splitting (1177) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | (1178) all_57_0 = e2 & op(e3, e3) = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | ALPHA: (1178) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | (1179) op(e3, e3) = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (985), (1179), (function-axioms) are
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | (1180) all_57_2 = e2 & op(e2, e3) = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | ALPHA: (1180) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | (1181) all_57_2 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | (1182) all_57_15 = e0 & op(e0, e0) = e0
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1182) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | (1183) op(e0, e0) = e0
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (995), (1183), (function-axioms) are
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | (1184) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1184) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | (1185) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | (1186) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | (1187) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1187) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1188) all_57_0 = e3 & op(e3, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1188) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1189) op(e3, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (985), (1189), (function-axioms) are
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1190) all_57_2 = e3 & op(e2, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1181), (1190) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | #823.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | (1191) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1191) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1192) all_57_6 = e3 & op(e1, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1192) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1193) all_57_6 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1167), (1193) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | #873.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1194) all_57_12 = e3 & op(e0, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1194) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | (1195) all_57_12 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (1196) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1196) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1197) all_57_6 = e3 & op(e1, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1197) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1198) all_57_6 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1167), (1198) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1199) all_57_7 = e3 & op(e1, e2) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1199) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1200) all_57_7 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1176), (1200) imply:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1201) e3 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1201) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1202) e3 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1195), (1202) imply:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1203) all_57_12 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (164),
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (170), (223), (226), (229), (231), (233), (234),
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (237), (238), (375), (399), (401), (405), (983),
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (985), (993), (1167), (1176), (1185), (1203),
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | #769.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | (1204) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1204) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1205) all_57_8 = e3 & op(e1, e1) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1205) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1206) op(e1, e1) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (1206), (function-axioms) are
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1207) all_57_11 = e3 & op(e1, e0) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1207) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1208) all_57_11 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | (1209) op(e1, e0) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | (1210) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1210) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1211) all_57_9 = e1 & op(e3, e0) = e1
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1211) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1212) all_57_9 = e1
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (233), (237),
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (399), (985), (1212), (function-axioms) are
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #812.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1213) all_57_10 = e1 & op(e2, e0) = e1
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1213) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1214) all_57_10 = e1
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1215) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1215) gives:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1216) all_57_2 = e3 & op(e2, e3) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1216) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1217) all_57_2 = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1181), (1217) imply:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1218) e3 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1218) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1219) e3 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1208), (1219) imply:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1220) all_57_11 = e2
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (995),
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1172), (1220), (function-axioms) are inconsistent
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #851.
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1221) all_57_3 = e3 & op(e2, e2) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1221) implies:
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1222) op(e2, e2) = e3
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.28 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (405), (1222), (function-axioms) are
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1223) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1223) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1224) all_57_5 = e3 & op(e2, e1) = e3
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1224) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1225) all_57_5 = e3
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1226) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1226) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1227) all_57_4 = e2 & op(e3, e1) = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1227) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228) op(e3, e1) = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (106), (160), (169), (1159), (1161), (1209),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1228), (function-axioms) are inconsistent by
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #893.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1229) all_57_5 = e2 & op(e2, e1) = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1229) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1230) all_57_5 = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1225), (1230) imply:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1231) e3 = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1208), (1231) imply:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1232) all_57_11 = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (213), (215), (225),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (227), (405), (995), (1186), (1230), (1232),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #850.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1233) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (372), (995), (1233), (function-axioms) are
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #766.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1234) all_57_10 = e3 & op(e2, e0) = e3
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1234) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1235) all_57_10 = e3
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1214), (1235) are inconsistent by sub-proof
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | (1236) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (995), (1208), (1236), (function-axioms)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1032.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | (1237) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | BETA: splitting (1237) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | (1238) all_57_6 = e2 & op(e1, e3) = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (1238) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | (1239) all_57_6 = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1167), (1239) are inconsistent by sub-proof
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | #811.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | (1240) all_57_12 = e2 & op(e0, e3) = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | ALPHA: (1240) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | (1241) all_57_12 = e2
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (1242) all_57_15 = e0 & op(e0, e0) = e0
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1242) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (1243) op(e0, e0) = e0
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (995), (1243), (function-axioms) are
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (1244) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1244) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (1245) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (164),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (170), (223), (226), (229), (231), (233), (234),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (237), (238), (375), (399), (401), (405), (983),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (985), (993), (1167), (1176), (1241), (1245),
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | | #769.
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | (1246) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (213), (215),
% 136.50/19.29 | | | | | | | | | | | | | | | | | (372), (995), (1172), (1246), (function-axioms)
% 136.50/19.29 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #765.
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | End of split
% 136.50/19.29 | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | (1247) all_57_12 = e0 & op(e0, e3) = e0
% 136.50/19.29 | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | ALPHA: (1247) implies:
% 136.50/19.29 | | | | | | | | | | | | | | (1248) op(e0, e3) = e0
% 136.50/19.29 | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 136.50/19.29 | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | (1249) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 136.50/19.29 | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (399), (985), (1249),
% 136.50/19.29 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.29 | | | | | | | | | | | | | | | #819.
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | (1250) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 136.50/19.29 | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | BETA: splitting (1250) gives:
% 136.50/19.29 | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | (1251) all_57_4 = e0 & op(e3, e1) = e0
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1162), (1251), (function-axioms) are
% 136.50/19.29 | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | (1252) all_57_9 = e0 & op(e3, e0) = e0
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | ALPHA: (1252) implies:
% 136.50/19.29 | | | | | | | | | | | | | | | | (1253) op(e3, e0) = e0
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (1248) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | (1254) all_52_3 = e0
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 136.50/19.29 | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (1253) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | | (1255) all_52_12 = e0
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | REDUCE: (140), (1254) imply:
% 136.50/19.29 | | | | | | | | | | | | | | | | (1256) ~ (all_52_7 = e0)
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | REDUCE: (984), (1255) imply:
% 136.50/19.29 | | | | | | | | | | | | | | | | (1257) ~ (e1 = e0)
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 136.50/19.29 | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | (1258) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.50/19.29 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 136.50/19.29 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.50/19.29 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.50/19.29 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 136.50/19.29 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 136.50/19.29 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 136.50/19.29 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.50/19.29 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 136.50/19.29 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.50/19.29 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 136.50/19.29 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.50/19.29 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 136.50/19.29 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 136.50/19.29 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 136.50/19.29 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (158), (401), (995), (1248), (1258),
% 136.50/19.29 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.29 | | | | | | | | | | | | | | | | | #952.
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.29 | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.29 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | (1259) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 136.50/19.30 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 136.50/19.30 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | BETA: splitting (1259) gives:
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (1260) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 136.50/19.30 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 136.50/19.30 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 136.50/19.30 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 136.50/19.30 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | ALPHA: (1260) implies:
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (1261) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (1262) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (1263) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (118), (121), (123), (157), (165),
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (169), (190), (198), (247), (261), (402), (405),
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (985), (992), (995), (1261), (1262), (1263),
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.30 | | | | | | | | | | | | | | | | | | #756.
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (1264) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 136.50/19.30 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 136.50/19.30 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 136.50/19.30 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (36), (164), (207), (375),
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (405), (993), (995), (1248), (1264),
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.30 | | | | | | | | | | | | | | | | | | #946.
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | End of split
% 136.50/19.30 | | | | | | | | |
% 136.50/19.30 | | | | | | | | End of split
% 136.50/19.30 | | | | | | | |
% 136.50/19.30 | | | | | | | End of split
% 136.50/19.30 | | | | | | |
% 136.50/19.30 | | | | | | End of split
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | Case 2:
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | (1265) all_14_2 = e0
% 136.50/19.30 | | | | | | (1266) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3,
% 136.50/19.30 | | | | | | e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~
% 136.50/19.30 | | | | | | (all_14_1 = e2) & op(e3, e0) = all_14_1 & $i(all_14_1))
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | COMBINE_EQS: (315), (1265) imply:
% 136.50/19.30 | | | | | | (1267) all_28_2 = e0
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | REDUCE: (337), (1265) imply:
% 136.50/19.30 | | | | | | (1268) ~ (all_52_1 = e0)
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | REDUCE: (339), (1265) imply:
% 136.50/19.30 | | | | | | (1269) ~ (all_52_2 = e0)
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | REDUCE: (341), (1265) imply:
% 136.50/19.30 | | | | | | (1270) ~ (all_52_3 = e0)
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | REDUCE: (343), (1265) imply:
% 136.50/19.30 | | | | | | (1271) ~ (all_52_4 = e0)
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | REDUCE: (345), (1265) imply:
% 136.50/19.30 | | | | | | (1272) ~ (all_52_8 = e0)
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | REDUCE: (347), (1265) imply:
% 136.50/19.30 | | | | | | (1273) ~ (all_52_12 = e0)
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | BETA: splitting (233) gives:
% 136.50/19.30 | | | | | |
% 136.50/19.30 | | | | | | Case 1:
% 136.50/19.30 | | | | | | |
% 136.50/19.30 | | | | | | | (1274) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 136.50/19.30 | | | | | | | op(e3, e2) = e0)
% 136.50/19.30 | | | | | | |
% 136.50/19.30 | | | | | | | BETA: splitting (1274) gives:
% 136.50/19.30 | | | | | | |
% 136.50/19.30 | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | |
% 136.50/19.30 | | | | | | | | (1275) all_57_0 = e0 & op(e3, e3) = e0
% 136.50/19.30 | | | | | | | |
% 136.50/19.30 | | | | | | | | ALPHA: (1275) implies:
% 136.50/19.30 | | | | | | | | (1276) all_57_0 = e0
% 136.50/19.30 | | | | | | | | (1277) op(e3, e3) = e0
% 136.50/19.30 | | | | | | | |
% 136.50/19.30 | | | | | | | | BETA: splitting (55) gives:
% 136.50/19.30 | | | | | | | |
% 136.50/19.30 | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | |
% 136.50/19.30 | | | | | | | | | (1278) ~ (all_16_2 = e0)
% 136.50/19.30 | | | | | | | | |
% 136.50/19.30 | | | | | | | | | REDUCE: (328), (1278) imply:
% 136.50/19.30 | | | | | | | | | (1279) ~ (all_6_2 = e0)
% 136.50/19.30 | | | | | | | | |
% 136.50/19.30 | | | | | | | | | BETA: splitting (61) gives:
% 136.50/19.30 | | | | | | | | |
% 136.50/19.30 | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | (1280) ~ (all_20_2 = e1)
% 136.50/19.30 | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | REDUCE: (283), (1280) imply:
% 136.50/19.30 | | | | | | | | | | (1281) ~ (all_6_2 = e1)
% 136.50/19.30 | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | BETA: splitting (199) gives:
% 136.50/19.30 | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | (1282) all_54_5 = e3
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | COMBINE_EQS: (268), (1282) imply:
% 136.50/19.30 | | | | | | | | | | | (1283) all_6_2 = e3
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | REDUCE: (373), (1283) imply:
% 136.50/19.30 | | | | | | | | | | | (1284) $false
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | CLOSE: (1284) is inconsistent.
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | Case 2:
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | (1285) ~ (all_54_5 = e3)
% 136.50/19.30 | | | | | | | | | | | (1286) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | BETA: splitting (1286) gives:
% 136.50/19.30 | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | (1287) all_54_5 = e2
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | COMBINE_EQS: (268), (1287) imply:
% 136.50/19.30 | | | | | | | | | | | | (1288) all_6_2 = e2
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | REDUCE: (348), (1288) imply:
% 136.50/19.30 | | | | | | | | | | | | (1289) ~ (all_52_1 = e2)
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | REDUCE: (357), (1288) imply:
% 136.50/19.30 | | | | | | | | | | | | (1290) ~ (all_52_9 = e2)
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | REDUCE: (359), (1288) imply:
% 136.50/19.30 | | | | | | | | | | | | (1291) ~ (all_52_13 = e2)
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | REDUCE: (373), (1288) imply:
% 136.50/19.30 | | | | | | | | | | | | (1292) ~ (e3 = e2)
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | REDUCE: (39), (1288) imply:
% 136.50/19.30 | | | | | | | | | | | | (1293) op(e2, e2) = e2
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | BETA: splitting (67) gives:
% 136.50/19.30 | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | (1294) ~ (all_24_2 = e2)
% 136.50/19.30 | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | REDUCE: (319), (1294) imply:
% 136.50/19.30 | | | | | | | | | | | | | (1295) ~ (all_10_2 = e2)
% 136.50/19.30 | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | BETA: splitting (73) gives:
% 136.50/19.30 | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | (1296) ~ (all_28_2 = e0)
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | REDUCE: (1267), (1296) imply:
% 136.50/19.30 | | | | | | | | | | | | | | (1297) $false
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | CLOSE: (1297) is inconsistent.
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | Case 2:
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | (1298) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0
% 136.50/19.30 | | | | | | | | | | | | | | & op(e3, e0) = all_28_1 & $i(all_28_0) &
% 136.50/19.30 | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e0)
% 136.50/19.30 | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 136.50/19.30 | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | (1299) ~ (all_42_2 = e3)
% 136.50/19.30 | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | REDUCE: (303), (1299) imply:
% 136.50/19.30 | | | | | | | | | | | | | | | (1300) ~ (all_10_2 = e3)
% 136.50/19.30 | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 136.50/19.30 | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | (1301) all_54_15 = e3
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | REF_CLOSE: (246), (1300), (1301) are inconsistent by
% 136.50/19.30 | | | | | | | | | | | | | | | | sub-proof #755.
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | Case 2:
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | (1302) ~ (all_54_15 = e3)
% 136.50/19.30 | | | | | | | | | | | | | | | | (1303) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | BETA: splitting (1303) gives:
% 136.50/19.30 | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | (1304) all_54_15 = e2
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (1295), (1304) are inconsistent by
% 136.50/19.30 | | | | | | | | | | | | | | | | | sub-proof #754.
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | (1305) ~ (all_54_15 = e2)
% 136.50/19.30 | | | | | | | | | | | | | | | | | (1306) all_54_15 = e1 | all_54_15 = e0
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 136.50/19.30 | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | (1307) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 136.50/19.30 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 136.50/19.30 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 136.50/19.30 | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 136.50/19.30 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 136.50/19.30 | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 136.50/19.30 | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 136.50/19.30 | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 136.50/19.30 | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1277), (1307), (function-axioms) are
% 136.50/19.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.30 | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.30 | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (1308) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 136.50/19.31 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 136.50/19.31 | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 136.50/19.31 | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 136.50/19.31 | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | BETA: splitting (1308) gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | (1309) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (1309) gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1310) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (1310) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1311) op(e0, e0) = e3
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (246), (376), (1300), (1306), (1311),
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | #750.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1312) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (1312) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1313) op(e2, e2) = e1
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1293), (1313), (function-axioms) are
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | (1314) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | BETA: splitting (1314) gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1315) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | ALPHA: (1315) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1316) op(e2, e2) = e1
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1293), (1316), (function-axioms) are
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (1317) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1317) gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (1318) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1318) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (1319) op(e2, e2) = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1293), (1319), (function-axioms) are
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (1320) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1320) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (1321) op(e0, e0) = all_56_15
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (1322) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1306) gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1323) all_54_15 = e1
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (376), (1323) are inconsistent by sub-proof
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | #748.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1324) all_54_15 = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1324) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1325) all_10_2 = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1325) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1326) all_10_2 = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (1326) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1327) ~ (all_52_7 = e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (1326) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1328) ~ (all_52_11 = e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1300), (1326) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1329) ~ (e3 = e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1295), (1326) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1330) ~ (e2 = e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (376), (1326) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | (1331) ~ (e1 = e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1332) all_57_15 = e0 & op(e0, e0) = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1332) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1333) op(e0, e0) = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (1321), (1333)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1334) all_56_15 = e0
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (372), (375), (1293), (1321),
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1322), (1333), (1334), (function-axioms) are
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #743.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1335) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1335) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1336) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (1270), (1327), (1328),
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | (1336), (function-axioms) are inconsistent by
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | End of split
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | Case 2:
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | (1337) all_42_2 = e3
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (1337) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | (1338) all_10_2 = e3
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | SIMP: (1338) implies:
% 136.50/19.31 | | | | | | | | | | | | | | | (1339) all_10_2 = e3
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | REDUCE: (350), (1339) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | (1340) ~ (all_52_3 = e3)
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | REDUCE: (368), (1339) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | (1341) ~ (all_52_11 = e3)
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | REDUCE: (369), (1339) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | (1342) ~ (all_52_12 = e3)
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | REDUCE: (370), (1339) imply:
% 136.50/19.31 | | | | | | | | | | | | | | | (1343) ~ (all_52_13 = e3)
% 136.50/19.31 | | | | | | | | | | | | | | |
% 136.50/19.31 | | | | | | | | | | | | | | | REDUCE: (45), (1339) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | (1344) op(e0, e0) = e3
% 136.50/19.32 | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 136.50/19.32 | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | (1345) ~ (all_48_2 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | REDUCE: (299), (1345) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | (1346) ~ (all_4_2 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | (1347) all_54_10 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (1347) are inconsistent by sub-proof
% 136.50/19.32 | | | | | | | | | | | | | | | | | #1112.
% 136.50/19.32 | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | (1348) ~ (all_54_10 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | (1349) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | BETA: splitting (1349) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | (1350) all_54_10 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (1350) are inconsistent by sub-proof
% 136.50/19.32 | | | | | | | | | | | | | | | | | | #1111.
% 136.50/19.32 | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | (1351) ~ (all_54_10 = e2)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | (1352) all_54_10 = e1 | all_54_10 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | BETA: splitting (1352) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1353) all_54_10 = e1
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (1353) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1354) all_4_2 = e1
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | SIMP: (1354) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1355) all_4_2 = e1
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (349), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1356) ~ (all_52_2 = e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (362), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1357) ~ (all_52_8 = e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (363), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1358) ~ (all_52_9 = e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (365), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1359) ~ (all_52_11 = e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (375), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1360) ~ (e3 = e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (372), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1361) ~ (e2 = e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | REDUCE: (36), (1355) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | (1362) op(e1, e1) = e1
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1363) all_54_4 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1363) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1364) all_52_1 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | SIMP: (1364) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1365) all_52_1 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (1365) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1366) ~ (all_52_2 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | SIMP: (1366) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1367) ~ (all_52_2 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (1365) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1368) ~ (all_52_9 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | SIMP: (1368) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | (1369) ~ (all_52_9 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | (1370) all_54_8 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1367), (1370) are inconsistent by
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | (1371) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1371) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | (1372) all_54_8 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (1372) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | (1373) all_52_2 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | SIMP: (1373) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | (1374) all_52_2 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (1374) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | (1375) op(e1, e3) = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | (1376) all_54_6 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1369), (1376) are inconsistent by
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | (1377) ~ (all_54_6 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | (1378) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1378) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | (1379) all_54_6 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1290), (1379) are inconsistent by
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #762.
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | (1380) all_54_6 = e1 | all_54_6 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1380) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1381) all_54_6 = e1
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (1358), (1381) are inconsistent by
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1382) all_54_6 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (1382) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1383) all_52_9 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1383) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1384) all_52_9 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (1384) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1385) ~ (all_52_11 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1385) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1386) ~ (all_52_11 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (1384) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1387) ~ (all_52_13 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1387) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1388) ~ (all_52_13 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1369), (1384) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1389) ~ (e3 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1358), (1384) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | (1390) ~ (e1 = e0)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1391) all_54_14 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1391) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1392) all_52_11 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1341), (1392) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1393) $false
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1393) is inconsistent.
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1394) ~ (all_54_14 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (1395) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1395) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1396) all_54_14 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1396) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1397) all_52_11 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (1397) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1398) ~ (all_52_8 = e2)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1399) all_54_2 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (1399) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1400) all_52_8 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1400) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1401) all_52_8 = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (1401) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1402) ~ (all_52_12 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (1401) imply:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1403) op(e3, e1) = e3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1404) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1404) gives:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1405) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1405) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1406) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1270), (1344), (1406), (function-axioms)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1407) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1407) implies:
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1408) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 136.50/19.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (157), (159), (209), (1270), (1344),
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1386), (1408), (function-axioms) are inconsistent
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #735.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1409) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1409) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1410) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1277), (1403), (1410), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1411) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1411) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1412) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (168), (207), (1277),
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342), (1344), (1362), (1412), (function-axioms)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #730.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1413) ~ (all_54_2 = e3)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (271), (1413) imply:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1414) ~ (all_52_8 = e3)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1415) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1415) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1416) all_57_4 = e3 & op(e3, e1) = e3
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1416) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1417) op(e3, e1) = e3
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1414), (1417), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1418) all_57_5 = e3 & op(e2, e1) = e3
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1418) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1419) all_57_5 = e3
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1420) all_57_15 = e0 & op(e0, e0) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1420) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1421) op(e0, e0) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1344), (1421), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1422) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1422) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1423) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1423) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1424) all_57_12 = e0 & op(e0, e3) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1424) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1425) op(e0, e3) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1270), (1425), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1426) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1426) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1427) all_57_13 = e0 & op(e0, e2) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1427) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1428) all_57_13 = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1429) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1429) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1430) all_57_2 = e0 & op(e2, e3) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1430) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431) all_57_2 = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1432) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1432) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1433) all_57_4 = e0 & op(e3, e1) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1272), (1433), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1434) all_57_5 = e0 & op(e2, e1) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1419), (1434) are inconsistent by sub-proof
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #729.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1435) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1435) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1436) all_57_8 = e0 & op(e1, e1) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1436) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1437) all_57_8 = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (168), (170),
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (211), (218), (225), (227), (228),
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (231), (234), (236), (238), (1271), (1273),
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276), (1277), (1289), (1293), (1344), (1428),
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1431), (1437), (function-axioms) are inconsistent
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #706.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1438) all_57_14 = e0 & op(e0, e1) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1438) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1439) op(e0, e1) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1386), (1439), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1440) all_57_3 = e0 & op(e2, e2) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1440) implies:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1441) op(e2, e2) = e0
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1293), (1441), (function-axioms) are
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1442) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1442) gives:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1443) all_57_5 = e0 & op(e2, e1) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1419), (1443) are inconsistent by sub-proof
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #729.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1444) all_57_10 = e0 & op(e2, e0) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1388), (1444), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1445) all_57_14 = e0 & op(e0, e1) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1445) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1446) op(e0, e1) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1386), (1446), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1447) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1447) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1448) all_57_8 = e3 & op(e1, e1) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1448) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1449) op(e1, e1) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1362), (1449), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1450) all_57_14 = e3 & op(e0, e1) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1450) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451) all_57_14 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1452) all_57_15 = e0 & op(e0, e0) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1452) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1453) op(e0, e0) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1344), (1453), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1454) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1454) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1455) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1456) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1455) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1457) all_57_12 = e0 & op(e0, e3) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (210), (211), (1344),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1451), (1457), (function-axioms) are inconsistent
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #702.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1458) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1458) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1459) all_57_13 = e0 & op(e0, e2) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1459) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460) all_57_13 = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1461) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1461) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1462) all_57_12 = e2 & op(e0, e3) = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1462) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1463) all_57_12 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1464) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1464) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1465) all_57_6 = e2 & op(e1, e3) = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1465) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1466) all_57_6 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1467) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1467) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1468) all_57_2 = e3 & op(e2, e3) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1468) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469) all_57_2 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (1277), (1463), (1466),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1469), (function-axioms) are inconsistent by
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #698.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1470) all_57_3 = e3 & op(e2, e2) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1470) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1471) op(e2, e2) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1293), (1471), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1472) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1472) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1473) all_57_5 = e3 & op(e2, e1) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1473) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1474) all_57_5 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1475) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1475) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1476) all_57_0 = e3 & op(e3, e3) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1276), (1476) are inconsistent by sub-proof
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1108.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1477) all_57_2 = e3 & op(e2, e3) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1477) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1478) all_57_2 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1479) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (1293), (1478), (1479),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #696.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1480) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1480) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1481) all_57_5 = e0 & op(e2, e1) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1474), (1481) are inconsistent by sub-proof
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #729.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1482) all_57_10 = e0 & op(e2, e0) = e0
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1388), (1482), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1483) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1483) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1484) all_57_6 = e3 & op(e1, e3) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1484) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1485) all_57_6 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1466), (1485) imply:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1486) e3 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1486) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1487) e3 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1474), (1487) imply:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1488) all_57_5 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1489) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1489) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1490) all_57_2 = e3 & op(e2, e3) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1490) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491) all_57_2 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (224), (1293), (1388), (1488),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1491), (function-axioms) are inconsistent by
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #695.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1492) all_57_3 = e3 & op(e2, e2) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1492) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1493) op(e2, e2) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1293), (1493), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1472) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1474), (1488) are inconsistent by sub-proof
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #936.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1494) all_57_10 = e3 & op(e2, e0) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1494) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1495) all_57_10 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (213), (214),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344), (1456), (1495), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #687.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1496) all_57_12 = e3 & op(e0, e3) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1496) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1497) all_57_12 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (210), (211),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (228), (229), (231), (1271), (1293), (1344),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460), (1497), (function-axioms) are inconsistent
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #708.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1498) all_57_10 = e3 & op(e2, e0) = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1498) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1499) all_57_10 = e3
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (213), (214),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1344), (1456), (1499), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #687.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1500) all_57_7 = e2 & op(e1, e2) = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1500) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1501) all_57_7 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (229), (231), (1293),
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1460), (1501), (function-axioms) are inconsistent
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #720.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1502) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1502) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1503) all_57_8 = e2 & op(e1, e1) = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1503) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1504) op(e1, e1) = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1362), (1504), (function-axioms) are
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1505) all_57_11 = e2 & op(e1, e0) = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1505) implies:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1506) all_57_11 = e2
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.34 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1507) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1507) gives:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1508) all_57_9 = e1 & op(e3, e0) = e1
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1508) implies:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1509) op(e3, e0) = e1
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1266), (1298), (1375), (1509), (function-axioms)
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #683.
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1510) all_57_10 = e1 & op(e2, e0) = e1
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1510) implies:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1511) all_57_10 = e1
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (168), (1273), (1456), (1506), (1511),
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #716.
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1512) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (1344), (1506), (1512),
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #693.
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1513) all_57_13 = e2 & op(e0, e2) = e2
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1513) implies:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1514) all_57_13 = e2
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (228), (229),
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (1271), (1293), (1514), (function-axioms)
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #710.
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1515) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1344), (1451), (1515), (function-axioms) are
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #703.
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1516) all_57_14 = e0 & op(e0, e1) = e0
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1516) implies:
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1517) op(e0, e1) = e0
% 136.50/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1386), (1517), (function-axioms) are
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1518) all_54_14 = e1 | all_54_14 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1359), (1386), (1518) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #761.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | (1519) all_54_8 = e1 | all_54_8 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (1269), (1356), (1519) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | sub-proof #791.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | (1520) ~ (all_54_4 = e3)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | (1521) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | REDUCE: (269), (1520) imply:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | (1522) ~ (all_52_1 = e3)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | (1523) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1523) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | (1524) all_57_2 = e3 & op(e2, e3) = e3
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1524) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | (1525) all_57_2 = e3
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | (1526) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (1277), (1525), (1526),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | #775.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | (1527) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1527) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (1528) all_57_6 = e1 & op(e1, e3) = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1528) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (1529) all_57_6 = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (1530) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1530) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1531) all_57_6 = e2 & op(e1, e3) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1531) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1532) all_57_6 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1529), (1532) are inconsistent by sub-proof
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | #700.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1533) all_57_7 = e2 & op(e1, e2) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (228), (229),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (1271), (1293), (1533), (function-axioms)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #681.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (1534) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1534) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1535) all_57_8 = e2 & op(e1, e1) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1535) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1536) op(e1, e1) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1362), (1536), (function-axioms) are
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1537) all_57_11 = e2 & op(e1, e0) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1537) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1538) all_57_11 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (216), (219),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (236), (238), (1276), (1277), (1289),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1362), (1529), (1538), (function-axioms) are
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #678.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (1539) all_57_12 = e1 & op(e0, e3) = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1539) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | (1540) all_57_12 = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (1541) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1277), (1289), (1541),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | #707.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | (1542) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1542) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1543) all_57_6 = e2 & op(e1, e3) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1543) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1544) all_57_6 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1545) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1545) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1546) all_57_12 = e2 & op(e0, e3) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1546) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547) all_57_12 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (1277), (1525), (1544),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1547), (function-axioms) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #698.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1548) all_57_13 = e2 & op(e0, e2) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1548) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1549) all_57_13 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (228), (229),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (1271), (1293), (1549), (function-axioms)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #710.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1550) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1550) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1551) all_57_14 = e2 & op(e0, e1) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1551) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1552) all_57_14 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1521) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1553) all_54_4 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1289), (1553) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #677.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1554) all_54_4 = e1 | all_54_4 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1555) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1555) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1556) all_57_4 = e0 & op(e3, e1) = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1272), (1556), (function-axioms) are
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1557) all_57_5 = e0 & op(e2, e1) = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1557) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1558) op(e2, e1) = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1554) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1559) all_54_4 = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1559) imply:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1560) all_52_1 = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1560) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1561) all_52_1 = e1
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (1561) imply:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1562) ~ (all_52_13 = e1)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1562) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1563) ~ (all_52_13 = e1)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1564) all_54_7 = e3
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1343), (1564) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1007.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1565) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1565) gives:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1566) all_54_7 = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (1291), (1566) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1006.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1567) all_54_7 = e1 | all_54_7 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (117), (165), (260), (1558), (1563), (1567),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #675.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1568) all_54_4 = e0
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1268), (1568) are inconsistent by
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #794.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1569) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1362), (1552), (1569),
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #919.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1570) all_57_15 = e2 & op(e0, e0) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1570) implies:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1571) op(e0, e0) = e2
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1344), (1571), (function-axioms) are
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.35 | | | | | | | | | | | | | | | | | | | | | | | | | | (1572) all_57_12 = e2 & op(e0, e3) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1540), (1572) are inconsistent by sub-proof
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | #674.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | (1573) all_57_3 = e3 & op(e2, e2) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1573) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | (1574) op(e2, e2) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1293), (1574), (function-axioms) are
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | (1575) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1575) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | (1576) all_57_5 = e3 & op(e2, e1) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1576) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | (1577) all_57_5 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | (1578) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1578) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1579) all_57_2 = e0 & op(e2, e3) = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1579) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1580) all_57_2 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (1581) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1276), (1580), (1581) are inconsistent by
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #725.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (1582) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1582) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1583) all_57_6 = e3 & op(e1, e3) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1583) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1584) all_57_6 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (125), (139), (148), (157), (158),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (167), (168), (170), (190), (192), (206),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (216), (218), (228),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (231), (234), (236), (238), (247), (249),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (335), (372), (1268), (1270), (1271),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1276), (1277), (1289), (1293), (1340), (1341),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1342), (1344), (1346), (1352), (1359), (1362),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1522), (1584), (function-axioms) are
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1585) all_57_12 = e3 & op(e0, e3) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1585) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1586) all_57_12 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (125), (139), (148), (158), (190), (192),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (211), (247), (249), (269), (1268),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1289), (1340), (1341), (1344), (1359),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1522), (1586), (function-axioms) are
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #655.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1587) all_57_3 = e0 & op(e2, e2) = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1587) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1588) op(e2, e2) = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1293), (1588), (function-axioms) are
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | (1589) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1589) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1590) all_57_5 = e0 & op(e2, e1) = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1590) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1591) all_57_5 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1577), (1591) are inconsistent by sub-proof
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | #1041.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1592) all_57_10 = e0 & op(e2, e0) = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1592) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | (1593) all_57_10 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (1594) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1594) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1595) all_57_9 = e1 & op(e3, e0) = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1595) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1596) op(e3, e0) = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1521) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1597) all_54_4 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1289), (1597) are inconsistent by
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #677.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1598) ~ (all_54_4 = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1599) all_54_4 = e1 | all_54_4 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1599) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1600) all_54_4 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1600) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1601) all_52_1 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1601) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1602) all_52_1 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (1602) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1603) ~ (all_52_3 = e1)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1603) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1604) ~ (all_52_3 = e1)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1605) all_54_12 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1605) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1606) all_52_3 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1340), (1606) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1607) $false
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1607) is inconsistent.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1608) ~ (all_54_12 = e3)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1609) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1609) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1610) all_54_12 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1610) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1611) all_52_3 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1611) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1612) ~ (all_52_11 = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1612) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1613) ~ (all_52_11 = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1614) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1614) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1615) all_57_6 = e2 & op(e1, e3) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1615) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616) op(e1, e3) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (73), (163), (168), (1266), (1267), (1596),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1616), (function-axioms) are inconsistent by
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #654.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1617) all_57_7 = e2 & op(e1, e2) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (228), (229),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (1271), (1293), (1617), (function-axioms)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #681.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1618) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1618) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1619) all_57_8 = e2 & op(e1, e1) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1619) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1620) op(e1, e1) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1362), (1620), (function-axioms) are
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1621) all_57_11 = e2 & op(e1, e0) = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1621) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1622) all_57_11 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (9), (36), (125), (157), (158),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (167), (168), (190), (206), (207), (209),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (211), (216), (231), (234), (236), (238),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (247), (335), (372), (1270), (1276), (1277),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1289), (1293), (1341), (1342), (1344), (1346),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1352), (1359), (1362), (1613), (1622),
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #663.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1623) all_54_12 = e1 | all_54_12 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1270), (1604), (1623) are inconsistent by
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #661.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1624) all_54_4 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1268), (1624) are inconsistent by
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #794.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1625) all_57_10 = e1 & op(e2, e0) = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1593), (1625) are inconsistent by sub-proof
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | #937.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | (1626) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1626) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1627) all_57_11 = e1 & op(e1, e0) = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1627) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | (1628) all_57_11 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1629) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1629) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1630) all_57_0 = e3 & op(e3, e3) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1276), (1630) are inconsistent by sub-proof
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1108.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1631) all_57_2 = e3 & op(e2, e3) = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1631) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1632) all_57_2 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1521) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1633) all_54_4 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1289), (1633) are inconsistent by
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #677.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1634) ~ (all_54_4 = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1635) all_54_4 = e1 | all_54_4 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1635) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1636) all_54_4 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (1636) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1637) all_52_1 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1637) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1638) all_52_1 = e1
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (1638) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1639) ~ (all_52_3 = e1)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1639) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1640) ~ (all_52_3 = e1)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1641) all_54_12 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1641) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1642) all_52_3 = e3
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1340), (1642) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1643) $false
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1643) is inconsistent.
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1644) ~ (all_54_12 = e3)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1645) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1645) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1646) all_54_12 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (1646) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1647) all_52_3 = e2
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (1647) imply:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1648) ~ (all_52_11 = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1648) implies:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1649) ~ (all_52_11 = e2)
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.36 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1650) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1650) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1651) all_57_6 = e2 & op(e1, e3) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1651) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1652) all_57_6 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1653) all_54_14 = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1653) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1654) all_52_11 = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1341), (1654) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1655) $false
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1655) is inconsistent.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1656) ~ (all_54_14 = e3)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1657) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1657) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1658) all_54_14 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1658) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1659) all_52_11 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1649), (1659) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1660) $false
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1660) is inconsistent.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1661) ~ (all_54_14 = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1662) all_54_14 = e1 | all_54_14 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1663) all_57_15 = e0 & op(e0, e0) = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1663) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1664) op(e0, e0) = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1344), (1664), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1665) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1665) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1666) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1662) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1667) all_54_14 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (1359), (1667) are inconsistent by
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #673.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1668) all_54_14 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (1668) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1669) all_52_11 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1669) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1670) all_52_11 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (1670) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1671) ~ (all_52_7 = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1341), (1670) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1672) ~ (e3 = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1649), (1670) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1673) ~ (e2 = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1359), (1670) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1674) ~ (e1 = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1675) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1675) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1676) all_57_6 = e0 & op(e1, e3) = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1652), (1676) are inconsistent by sub-proof
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #994.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1677) all_57_7 = e0 & op(e1, e2) = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1677) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1678) all_57_7 = e0
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1679) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1679) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1680) all_57_12 = e2 & op(e0, e3) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1680) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1681) all_57_12 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1682) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1682) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1683) all_57_6 = e3 & op(e1, e3) = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1683) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1684) all_57_6 = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1652), (1684) are inconsistent by sub-proof
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1004.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1685) all_57_7 = e3 & op(e1, e2) = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1685) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1686) all_57_7 = e3
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1687) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1687) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1688) all_57_0 = e1 & op(e3, e3) = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1688) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1689) op(e3, e3) = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1277), (1689), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1690) all_57_2 = e1 & op(e2, e3) = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1690) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1691) all_57_2 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1632), (1691) imply:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1692) e3 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (1692) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693) e3 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (219), (1362), (1628), (1652), (1686),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1693), (function-axioms) are inconsistent by
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #907.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1694) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1652), (1681), (1694) are inconsistent by
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #699.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1695) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1362), (1628), (1695), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #911.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1696) all_57_13 = e2 & op(e0, e2) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1696) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1697) all_57_13 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (229), (231), (1293),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1678), (1697), (function-axioms) are inconsistent
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #711.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1698) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1698) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1699) all_57_14 = e2 & op(e0, e1) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (159), (1270), (1666), (1671), (1699),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #652.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1700) all_57_15 = e2 & op(e0, e0) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1700) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1701) op(e0, e0) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1344), (1701), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1702) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1362), (1628), (1702), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #807.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1703) all_57_7 = e2 & op(e1, e2) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (228), (229),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (1271), (1293), (1703), (function-axioms)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #681.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1704) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1704) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1705) all_57_8 = e2 & op(e1, e1) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1705) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1706) op(e1, e1) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1362), (1706), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1707) all_57_11 = e2 & op(e1, e0) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1707) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1708) all_57_11 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1709) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1277), (1289), (1709),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #707.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1710) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1710) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1711) all_57_6 = e2 & op(e1, e3) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1711) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1712) all_57_6 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (216), (219),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (236), (238), (1276), (1277), (1289),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362), (1708), (1712), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #651.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1713) all_57_12 = e2 & op(e0, e3) = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1713) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1714) all_57_12 = e2
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1715) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (1277), (1632), (1715),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #775.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1716) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1716) gives:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1717) all_57_6 = e1 & op(e1, e3) = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1717) implies:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1718) all_57_6 = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (216), (219),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (236), (238), (1276), (1277), (1289),
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1362), (1708), (1718), (function-axioms) are
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #678.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1719) all_57_12 = e1 & op(e0, e3) = e1
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1714), (1719) are inconsistent by sub-proof
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #848.
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1720) all_54_12 = e1 | all_54_12 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (1270), (1640), (1720) are inconsistent by
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #661.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1721) all_54_4 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (1268), (1721) are inconsistent by
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #794.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1722) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1722) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1723) all_57_6 = e3 & op(e1, e3) = e3
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1723) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1724) all_57_6 = e3
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (125), (139), (148), (157), (158),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (167), (168), (170), (190), (192), (206),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (216), (218), (228),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (231), (234), (236), (238), (247), (249),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (269), (335), (372), (1268), (1270), (1271),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1276), (1277), (1289), (1293), (1340), (1341),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1342), (1344), (1346), (1352), (1359), (1362),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1522), (1724), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #660.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1725) all_57_12 = e3 & op(e0, e3) = e3
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1725) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1726) all_57_12 = e3
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (125), (139), (148), (158), (190), (192),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (211), (247), (249), (269), (1268),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1289), (1340), (1341), (1344), (1359),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1521), (1522), (1726), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #655.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (1727) all_57_15 = e1 & op(e0, e0) = e1
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1727) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (1728) op(e0, e0) = e1
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1344), (1728), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1729) all_57_10 = e3 & op(e2, e0) = e3
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1729) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1730) all_57_10 = e3
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (213), (214),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1344), (1730), (function-axioms) are inconsistent
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #650.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | (1731) all_54_10 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (1346), (1731) are inconsistent by
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | (1732) all_48_2 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | (1733) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0
% 136.89/19.38 | | | | | | | | | | | | | | | | & op(e1, e0) = all_48_1 & $i(all_48_0) &
% 136.89/19.38 | | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (1732) imply:
% 136.89/19.38 | | | | | | | | | | | | | | | | (1734) all_4_2 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | REDUCE: (360), (1734) imply:
% 136.89/19.38 | | | | | | | | | | | | | | | | (1735) ~ (all_52_6 = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | REDUCE: (363), (1734) imply:
% 136.89/19.38 | | | | | | | | | | | | | | | | (1736) ~ (all_52_9 = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | REDUCE: (365), (1734) imply:
% 136.89/19.38 | | | | | | | | | | | | | | | | (1737) ~ (all_52_11 = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | REDUCE: (375), (1734) imply:
% 136.89/19.38 | | | | | | | | | | | | | | | | (1738) ~ (e3 = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | REDUCE: (372), (1734) imply:
% 136.89/19.38 | | | | | | | | | | | | | | | | (1739) ~ (e2 = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | (1740) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (1272), (1736), (1740),
% 136.89/19.38 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.38 | | | | | | | | | | | | | | | | | #980.
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | (1741) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 136.89/19.38 | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | BETA: splitting (1741) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | (1742) all_57_8 = e0 & op(e1, e1) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | ALPHA: (1742) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | (1743) all_57_8 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | (1744) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (1744) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1745) all_57_2 = e0 & op(e2, e3) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (1745) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1746) all_57_2 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | (1747) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1271), (1293), (1747),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | #714.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | (1748) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1748) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1749) all_57_7 = e0 & op(e1, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1749) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1750) op(e1, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1735), (1750), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1751) all_57_13 = e0 & op(e0, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1751) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1752) all_57_13 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (168), (170),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (209), (210), (211), (218), (225), (227), (228),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (229), (231), (234), (236), (238), (1271), (1273),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1276), (1277), (1289), (1293), (1344), (1743),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1746), (1752), (function-axioms) are inconsistent
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #706.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1753) all_57_3 = e0 & op(e2, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (1753) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1754) op(e2, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1293), (1754), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | (1755) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | BETA: splitting (1755) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1756) all_57_5 = e0 & op(e2, e1) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (1756) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1757) op(e2, e1) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (1736), (1757), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1758) all_57_10 = e0 & op(e2, e0) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | ALPHA: (1758) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1759) all_57_10 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | (1760) op(e2, e0) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | (1761) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (1271), (1293), (1761),
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | #714.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | (1762) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1762) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1763) all_57_7 = e0 & op(e1, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1763) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1764) op(e1, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (1735), (1764), (function-axioms) are
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1765) all_57_13 = e0 & op(e0, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1765) implies:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1766) all_57_13 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1767) op(e0, e2) = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (1767) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1768) all_52_7 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (1760) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | (1769) all_52_13 = e0
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.38 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (1770) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1770) gives:
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1771) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1771) implies:
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1772) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1270), (1344), (1772), (function-axioms)
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1773) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1773) implies:
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1774) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1344), (1767), (1774), (function-axioms) are
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #737.
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 136.89/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (1775) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1775) gives:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1776) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1776) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1777) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1778) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1779) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1780) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1781) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | (1782) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1777) gives:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1783) all_56_15 = e1 & op(e0, e0) = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1783) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1784) op(e0, e0) = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1344), (1784), (function-axioms) are
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1785) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1785) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1786) ~ (all_56_14 = e0)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | (1787) op(e0, e1) = all_56_14
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1779) gives:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1788) all_56_11 = e1 & op(e2, e2) = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1788) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1789) op(e2, e2) = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1293), (1789), (function-axioms) are
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1790) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1790) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | (1791) ~ (all_56_4 = e2)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1780) gives:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1792) all_56_9 = e1 & op(e3, e3) = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1792) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1793) op(e3, e3) = e1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1277), (1793), (function-axioms) are
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1794) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1794) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1795) ~ (all_56_1 = e3)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1796) op(e3, e1) = all_56_1
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1781) gives:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1797) all_56_4 = e2 & op(e2, e1) = e2
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1797) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1798) all_56_4 = e2
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1791), (1798) imply:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1799) $false
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1799) is inconsistent.
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1800) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1800) implies:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1801) ~ (all_56_11 = e1)
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1802) op(e2, e2) = all_56_11
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1778) gives:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.39 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1803) all_56_14 = e0 & op(e0, e1) = e0
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1803) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1804) op(e0, e1) = e0
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1786), (1787), (1804), (function-axioms) are
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1805) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1805) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1806) ~ (all_56_15 = e1)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1807) op(e0, e0) = all_56_15
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1782) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1808) all_56_1 = e3 & op(e3, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1808) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1809) all_56_1 = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1795), (1809) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1810) $false
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1810) is inconsistent.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1811) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1811) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1812) ~ (all_56_9 = e1)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1813) op(e3, e3) = all_56_9
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (1344), (1807)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1814) all_56_15 = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (1293), (1802)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1815) all_56_11 = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, e1, e3, simplifying with (169), (1796)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1816) all_56_1 = all_52_8
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_9,
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1277), (1813) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1817) all_56_9 = e0
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1795), (1816) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1818) ~ (all_52_8 = e3)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1812), (1817) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1819) ~ (e1 = e0)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1820) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1820) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1821) all_57_4 = e3 & op(e3, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1821) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1822) op(e3, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (1818), (1822), (function-axioms) are
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1823) all_57_5 = e3 & op(e2, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1823) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1824) all_57_5 = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1825) op(e2, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1826) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1826) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1827) all_57_2 = e1 & op(e2, e3) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1827) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828) all_57_2 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (210), (211),
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (228), (229), (231), (238), (1271), (1276),
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1293), (1344), (1733), (1743), (1766), (1825),
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1828), (function-axioms) are inconsistent by
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #647.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1829) all_57_3 = e1 & op(e2, e2) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1829) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1830) op(e2, e2) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (1293), (1830), (function-axioms) are
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1831) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1831) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1832) all_57_5 = e1 & op(e2, e1) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1832) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1833) all_57_5 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1824), (1833) are inconsistent by sub-proof
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1035.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1834) all_57_10 = e1 & op(e2, e0) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1759), (1834) are inconsistent by sub-proof
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #937.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1835) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1835) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1836) all_57_8 = e3 & op(e1, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1836) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1837) all_57_8 = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1743), (1837) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1838) e3 = e0
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7), (1838) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1839) $false
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (1839) is inconsistent.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1840) all_57_14 = e3 & op(e0, e1) = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1840) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1841) all_57_14 = e3
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1842) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1842) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1843) all_57_12 = e1 & op(e0, e3) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1843) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1844) all_57_12 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1845) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1845) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1846) all_57_12 = e2 & op(e0, e3) = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1846) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1847) all_57_12 = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1844), (1847) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1848) e2 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1815), (1848) imply:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1849) all_56_11 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1781), (1791), (1849) are inconsistent by
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1850) all_57_13 = e2 & op(e0, e2) = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1850) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1851) all_57_13 = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (228), (229),
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (1271), (1293), (1851), (function-axioms)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #710.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1852) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1852) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1853) all_57_14 = e2 & op(e0, e1) = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1853) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1854) all_57_14 = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1841), (1854) are inconsistent by sub-proof
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1011.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1855) all_57_15 = e2 & op(e0, e0) = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1855) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1856) op(e0, e0) = e2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1344), (1856), (function-axioms) are
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1857) all_57_13 = e1 & op(e0, e2) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1766), (1857) are inconsistent by sub-proof
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #805.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1858) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1858) gives:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1859) all_57_14 = e1 & op(e0, e1) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1859) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1860) all_57_14 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1841), (1860) are inconsistent by sub-proof
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1045.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1861) all_57_15 = e1 & op(e0, e0) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (1861) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1862) op(e0, e0) = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1344), (1862), (function-axioms) are
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | (1863) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (168), (207), (1277),
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | (1293), (1342), (1344), (1863), (function-axioms)
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #644.
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | (1864) all_57_14 = e0 & op(e0, e1) = e0
% 137.06/19.40 | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | ALPHA: (1864) implies:
% 137.06/19.40 | | | | | | | | | | | | | | | | | | (1865) op(e0, e1) = e0
% 137.06/19.40 | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (1737), (1865), (function-axioms) are
% 137.06/19.40 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 137.06/19.40 | | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | End of split
% 137.06/19.40 | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | Case 2:
% 137.06/19.40 | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | (1866) all_24_2 = e2
% 137.06/19.40 | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | COMBINE_EQS: (319), (1866) imply:
% 137.06/19.40 | | | | | | | | | | | | | (1867) all_10_2 = e2
% 137.06/19.40 | | | | | | | | | | | | |
% 137.06/19.40 | | | | | | | | | | | | | REDUCE: (45), (1867) imply:
% 137.06/19.41 | | | | | | | | | | | | | (1868) op(e0, e0) = e2
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (207), (1277), (1293), (1868),
% 137.06/19.41 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.06/19.41 | | | | | | | | | | | | | #642.
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | End of split
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | Case 2:
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | (1869) all_54_5 = e1 | all_54_5 = e0
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | REF_CLOSE: (268), (1279), (1281), (1869) are inconsistent by
% 137.06/19.41 | | | | | | | | | | | | sub-proof #641.
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | End of split
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | End of split
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | Case 2:
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | (1870) all_20_2 = e1
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | COMBINE_EQS: (283), (1870) imply:
% 137.06/19.41 | | | | | | | | | | (1871) all_6_2 = e1
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | REDUCE: (351), (1871) imply:
% 137.06/19.41 | | | | | | | | | | (1872) ~ (all_52_4 = e1)
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | REDUCE: (357), (1871) imply:
% 137.06/19.41 | | | | | | | | | | (1873) ~ (all_52_9 = e1)
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | REDUCE: (359), (1871) imply:
% 137.06/19.41 | | | | | | | | | | (1874) ~ (all_52_13 = e1)
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | REDUCE: (373), (1871) imply:
% 137.06/19.41 | | | | | | | | | | (1875) ~ (e3 = e1)
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | REDUCE: (39), (1871) imply:
% 137.06/19.41 | | | | | | | | | | (1876) op(e2, e2) = e1
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | BETA: splitting (229) gives:
% 137.06/19.41 | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | (1877) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 137.06/19.41 | | | | | | | | | | | & op(e2, e2) = e1)
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | BETA: splitting (1877) gives:
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | (1878) all_57_1 = e1 & op(e3, e2) = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | ALPHA: (1878) implies:
% 137.06/19.41 | | | | | | | | | | | | (1879) op(e3, e2) = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e1,
% 137.06/19.41 | | | | | | | | | | | | e2, e3, simplifying with (170), (1879) gives:
% 137.06/19.41 | | | | | | | | | | | | (1880) all_52_4 = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | REDUCE: (1872), (1880) imply:
% 137.06/19.41 | | | | | | | | | | | | (1881) $false
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | CLOSE: (1881) is inconsistent.
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | Case 2:
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | (1882) all_57_3 = e1 & op(e2, e2) = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | ALPHA: (1882) implies:
% 137.06/19.41 | | | | | | | | | | | | (1883) all_57_3 = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (45), (67), (73), (94),
% 137.06/19.41 | | | | | | | | | | | | (100), (103), (110), (112), (118), (121), (123),
% 137.06/19.41 | | | | | | | | | | | | (125), (126), (140), (157), (158), (159), (160),
% 137.06/19.41 | | | | | | | | | | | | (162), (163), (164), (165), (167), (168), (169),
% 137.06/19.41 | | | | | | | | | | | | (170), (189), (190), (193), (194), (202), (206),
% 137.06/19.41 | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 137.06/19.41 | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (224),
% 137.06/19.41 | | | | | | | | | | | | (225), (226), (227), (228), (230), (231), (234),
% 137.06/19.41 | | | | | | | | | | | | (235), (236), (238), (239), (246), (247), (250),
% 137.06/19.41 | | | | | | | | | | | | (271), (297), (299), (303), (319), (335), (360),
% 137.06/19.41 | | | | | | | | | | | | (362), (363), (368), (369), (370), (371), (372),
% 137.06/19.41 | | | | | | | | | | | | (375), (376), (1266), (1267), (1268), (1270),
% 137.06/19.41 | | | | | | | | | | | | (1271), (1272), (1273), (1276), (1277), (1873),
% 137.06/19.41 | | | | | | | | | | | | (1874), (1876), (1883), (function-axioms) are
% 137.06/19.41 | | | | | | | | | | | | inconsistent by sub-proof #523.
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | End of split
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | Case 2:
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | (1884) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 137.06/19.41 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | BETA: splitting (1884) gives:
% 137.06/19.41 | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | (1885) all_57_7 = e1 & op(e1, e2) = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | ALPHA: (1885) implies:
% 137.06/19.41 | | | | | | | | | | | | (1886) all_57_7 = e1
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | BETA: splitting (228) gives:
% 137.06/19.41 | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | (1887) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 137.06/19.41 | | | | | | | | | | | | | & op(e2, e2) = e0)
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | REF_CLOSE: (4), (170), (1271), (1876), (1887),
% 137.06/19.41 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.06/19.41 | | | | | | | | | | | | | #1062.
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | Case 2:
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | (1888) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 137.06/19.41 | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | BETA: splitting (1888) gives:
% 137.06/19.41 | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | (1889) all_57_7 = e0 & op(e1, e2) = e0
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | REF_CLOSE: (4), (1886), (1889) are inconsistent by sub-proof
% 137.06/19.41 | | | | | | | | | | | | | | #604.
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | Case 2:
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | (1890) all_57_13 = e0 & op(e0, e2) = e0
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | ALPHA: (1890) implies:
% 137.06/19.41 | | | | | | | | | | | | | | (1891) all_57_13 = e0
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 137.06/19.41 | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | (1892) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 137.06/19.41 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 137.06/19.41 | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | BETA: splitting (1892) gives:
% 137.06/19.41 | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | | (1893) all_57_1 = e3 & op(e3, e2) = e3
% 137.06/19.41 | | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | | ALPHA: (1893) implies:
% 137.06/19.41 | | | | | | | | | | | | | | | | (1894) all_57_1 = e3
% 137.06/19.41 | | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 137.06/19.41 | | | | | | | | | | | | | | | |
% 137.06/19.41 | | | | | | | | | | | | | | | | Case 1:
% 137.06/19.41 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | (1895) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 137.37/19.44 | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (1876), (1894), (1895),
% 137.37/19.44 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.37/19.44 | | | | | | | | | | | | | | | | | #522.
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | Case 2:
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | (1896) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 137.37/19.44 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1886), (1891), (1896) are inconsistent
% 137.37/19.44 | | | | | | | | | | | | | | | | | by sub-proof #521.
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | End of split
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | Case 2:
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | (1897) all_57_3 = e3 & op(e2, e2) = e3
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | ALPHA: (1897) implies:
% 137.37/19.44 | | | | | | | | | | | | | | | | (1898) all_57_3 = e3
% 137.37/19.44 | | | | | | | | | | | | | | | | (1899) op(e2, e2) = e3
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | Case 1:
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | (1900) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 137.37/19.44 | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | BETA: splitting (1900) gives:
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | Case 1:
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2,
% 137.37/19.44 | | | | | | | | | | | | | | | | | | e2, simplifying with (1876), (1899) gives:
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (1901) e3 = e1
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (1898), (1901) imply:
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (1902) all_57_3 = e1
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (45), (67), (73), (94),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (100), (103), (110), (112), (118), (121), (123),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (125), (126), (140), (157), (158), (159), (160),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (162), (163), (164), (165), (167), (168), (169),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (170), (189), (190), (193), (194), (202), (206),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (224),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (225), (226), (227), (228), (230), (231), (234),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (235), (236), (238), (239), (246), (247), (250),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (271), (297), (299), (303), (319), (335), (360),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (362), (363), (368), (369), (370), (371), (372),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (375), (376), (1266), (1267), (1268), (1270),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (1271), (1272), (1273), (1276), (1277), (1873),
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (1874), (1876), (1902), (function-axioms) are
% 137.37/19.44 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #523.
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | Case 2:
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (1903) all_57_3 = e2 & op(e2, e2) = e2
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | | ALPHA: (1903) implies:
% 137.37/19.44 | | | | | | | | | | | | | | | | | | (1904) op(e2, e2) = e2
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (1899), (1904), (function-axioms) are
% 137.37/19.44 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 137.37/19.44 | | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | End of split
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | Case 2:
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | (1905) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 137.37/19.44 | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1886), (1891), (1905) are inconsistent
% 137.37/19.44 | | | | | | | | | | | | | | | | | by sub-proof #521.
% 137.37/19.44 | | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | End of split
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | End of split
% 137.37/19.44 | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | Case 2:
% 137.37/19.44 | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | (1906) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 137.37/19.44 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 137.37/19.44 | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | BETA: splitting (1906) gives:
% 137.37/19.44 | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | Case 1:
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | (1907) all_57_7 = e3 & op(e1, e2) = e3
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.44 | | | | | | | | | | | | | | | | ALPHA: (1907) implies:
% 137.37/19.44 | | | | | | | | | | | | | | | | (1908) all_57_7 = e3
% 137.37/19.44 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1886), (1908) are inconsistent by sub-proof
% 137.37/19.45 | | | | | | | | | | | | | | | | #915.
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | Case 2:
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | (1909) all_57_13 = e3 & op(e0, e2) = e3
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | ALPHA: (1909) implies:
% 137.37/19.45 | | | | | | | | | | | | | | | | (1910) all_57_13 = e3
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1891), (1910) are inconsistent by sub-proof
% 137.37/19.45 | | | | | | | | | | | | | | | | #804.
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | End of split
% 137.37/19.45 | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | End of split
% 137.37/19.45 | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | End of split
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | End of split
% 137.37/19.45 | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | Case 2:
% 137.37/19.45 | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | (1911) all_57_13 = e1 & op(e0, e2) = e1
% 137.37/19.45 | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | ALPHA: (1911) implies:
% 137.37/19.45 | | | | | | | | | | | | (1912) all_57_13 = e1
% 137.37/19.45 | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | BETA: splitting (228) gives:
% 137.37/19.45 | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | Case 1:
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | (1913) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 137.37/19.45 | | | | | | | | | | | | | & op(e2, e2) = e0)
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | REF_CLOSE: (4), (170), (1271), (1876), (1913),
% 137.37/19.45 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.37/19.45 | | | | | | | | | | | | | #1062.
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | Case 2:
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | (1914) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 137.37/19.45 | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | BETA: splitting (1914) gives:
% 137.37/19.45 | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | Case 1:
% 137.37/19.45 | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | (1915) all_57_7 = e0 & op(e1, e2) = e0
% 137.37/19.45 | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | ALPHA: (1915) implies:
% 137.37/19.45 | | | | | | | | | | | | | | (1916) all_57_7 = e0
% 137.37/19.45 | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 137.37/19.45 | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | Case 1:
% 137.37/19.45 | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | (1917) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 137.37/19.45 | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 137.37/19.45 | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | BETA: splitting (1917) gives:
% 137.37/19.45 | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | Case 1:
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | (1918) all_57_1 = e3 & op(e3, e2) = e3
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | ALPHA: (1918) implies:
% 137.37/19.45 | | | | | | | | | | | | | | | | (1919) all_57_1 = e3
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (230), (1876), (1912), (1916),
% 137.37/19.45 | | | | | | | | | | | | | | | | (1919), (function-axioms) are inconsistent by
% 137.37/19.45 | | | | | | | | | | | | | | | | sub-proof #520.
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | Case 2:
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | (1920) all_57_3 = e3 & op(e2, e2) = e3
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | ALPHA: (1920) implies:
% 137.37/19.45 | | | | | | | | | | | | | | | | (1921) all_57_3 = e3
% 137.37/19.45 | | | | | | | | | | | | | | | | (1922) op(e2, e2) = e3
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, e3, e2,
% 137.37/19.45 | | | | | | | | | | | | | | | | e2, simplifying with (1876), (1922) gives:
% 137.37/19.45 | | | | | | | | | | | | | | | | (1923) e3 = e1
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.37/19.45 | | | | | | | | | | | | | | | | COMBINE_EQS: (1921), (1923) imply:
% 137.37/19.45 | | | | | | | | | | | | | | | | (1924) all_57_3 = e1
% 137.37/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (9), (36), (45), (67), (73), (94),
% 137.41/19.45 | | | | | | | | | | | | | | | | (100), (103), (110), (112), (118), (121), (123),
% 137.41/19.45 | | | | | | | | | | | | | | | | (125), (126), (140), (157), (158), (159), (160),
% 137.41/19.45 | | | | | | | | | | | | | | | | (162), (163), (164), (165), (167), (168), (169),
% 137.41/19.45 | | | | | | | | | | | | | | | | (170), (189), (190), (193), (194), (202), (206),
% 137.41/19.45 | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 137.41/19.45 | | | | | | | | | | | | | | | | (216), (218), (219), (220), (222), (223), (224),
% 137.41/19.45 | | | | | | | | | | | | | | | | (225), (226), (227), (228), (230), (231), (234),
% 137.41/19.45 | | | | | | | | | | | | | | | | (235), (236), (238), (239), (246), (247), (250),
% 137.41/19.45 | | | | | | | | | | | | | | | | (271), (297), (299), (303), (319), (335), (360),
% 137.41/19.45 | | | | | | | | | | | | | | | | (362), (363), (368), (369), (370), (371), (372),
% 137.41/19.45 | | | | | | | | | | | | | | | | (375), (376), (1266), (1267), (1268), (1270),
% 137.41/19.45 | | | | | | | | | | | | | | | | (1271), (1272), (1273), (1276), (1277), (1873),
% 137.41/19.45 | | | | | | | | | | | | | | | | (1874), (1876), (1924), (function-axioms) are
% 137.41/19.45 | | | | | | | | | | | | | | | | inconsistent by sub-proof #523.
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | (1925) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 137.41/19.45 | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | BETA: splitting (1925) gives:
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | (1926) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1916), (1926) are inconsistent by sub-proof
% 137.41/19.45 | | | | | | | | | | | | | | | | #713.
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | (1927) all_57_13 = e3 & op(e0, e2) = e3
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | ALPHA: (1927) implies:
% 137.41/19.45 | | | | | | | | | | | | | | | | (1928) all_57_13 = e3
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1912), (1928) are inconsistent by sub-proof
% 137.41/19.45 | | | | | | | | | | | | | | | | #1001.
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | (1929) all_57_13 = e0 & op(e0, e2) = e0
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | REF_CLOSE: (4), (1912), (1929) are inconsistent by sub-proof
% 137.41/19.45 | | | | | | | | | | | | | | #519.
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | End of split
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | (1930) all_16_2 = e0
% 137.41/19.45 | | | | | | | | | (1931) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 &
% 137.41/19.45 | | | | | | | | | op(e2, e0) = all_16_1 & $i(all_16_0) &
% 137.41/19.45 | | | | | | | | | $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0) =
% 137.41/19.45 | | | | | | | | | all_16_1 & $i(all_16_1))
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | COMBINE_EQS: (328), (1930) imply:
% 137.41/19.45 | | | | | | | | | (1932) all_6_2 = e0
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | SIMP: (1932) implies:
% 137.41/19.45 | | | | | | | | | (1933) all_6_2 = e0
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | COMBINE_EQS: (326), (1933) imply:
% 137.41/19.45 | | | | | | | | | (1934) all_18_2 = e0
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | REDUCE: (353), (1933) imply:
% 137.41/19.45 | | | | | | | | | (1935) ~ (all_52_6 = e0)
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | REDUCE: (355), (1933) imply:
% 137.41/19.45 | | | | | | | | | (1936) ~ (all_52_7 = e0)
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | REDUCE: (357), (1933) imply:
% 137.41/19.45 | | | | | | | | | (1937) ~ (all_52_9 = e0)
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | REDUCE: (359), (1933) imply:
% 137.41/19.45 | | | | | | | | | (1938) ~ (all_52_13 = e0)
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | REDUCE: (373), (1933) imply:
% 137.41/19.45 | | | | | | | | | (1939) ~ (e3 = e0)
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | BETA: splitting (228) gives:
% 137.41/19.45 | | | | | | | | |
% 137.41/19.45 | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | (1940) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 137.41/19.45 | | | | | | | | | | & op(e2, e2) = e0)
% 137.41/19.45 | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | BETA: splitting (1940) gives:
% 137.41/19.45 | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | (1941) all_57_1 = e0 & op(e3, e2) = e0
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | REF_CLOSE: (170), (1271), (1941), (function-axioms) are
% 137.41/19.45 | | | | | | | | | | | inconsistent by sub-proof #1102.
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | (1942) all_57_3 = e0 & op(e2, e2) = e0
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | ALPHA: (1942) implies:
% 137.41/19.45 | | | | | | | | | | | (1943) all_57_3 = e0
% 137.41/19.45 | | | | | | | | | | | (1944) op(e2, e2) = e0
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | BETA: splitting (58) gives:
% 137.41/19.45 | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | (1945) ~ (all_18_2 = e0)
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | REDUCE: (1934), (1945) imply:
% 137.41/19.45 | | | | | | | | | | | | (1946) $false
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | CLOSE: (1946) is inconsistent.
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | (1947) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0
% 137.41/19.45 | | | | | | | | | | | | & op(e2, e0) = all_18_1 & $i(all_18_0) &
% 137.41/19.45 | | | | | | | | | | | | $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0)
% 137.41/19.45 | | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | BETA: splitting (67) gives:
% 137.41/19.45 | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | (1948) ~ (all_24_2 = e2)
% 137.41/19.45 | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | REDUCE: (319), (1948) imply:
% 137.41/19.45 | | | | | | | | | | | | | (1949) ~ (all_10_2 = e2)
% 137.41/19.45 | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | BETA: splitting (94) gives:
% 137.41/19.45 | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | (1950) ~ (all_42_2 = e3)
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | REDUCE: (303), (1950) imply:
% 137.41/19.45 | | | | | | | | | | | | | | (1951) ~ (all_10_2 = e3)
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 137.41/19.45 | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | (1952) all_54_15 = e3
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | REF_CLOSE: (246), (1951), (1952) are inconsistent by
% 137.41/19.45 | | | | | | | | | | | | | | | sub-proof #755.
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | (1953) ~ (all_54_15 = e3)
% 137.41/19.45 | | | | | | | | | | | | | | | (1954) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | BETA: splitting (1954) gives:
% 137.41/19.45 | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | (1955) all_54_15 = e2
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | REF_CLOSE: (246), (1949), (1955) are inconsistent by
% 137.41/19.45 | | | | | | | | | | | | | | | | sub-proof #754.
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | (1956) ~ (all_54_15 = e2)
% 137.41/19.45 | | | | | | | | | | | | | | | | (1957) all_54_15 = e1 | all_54_15 = e0
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | BETA: splitting (1957) gives:
% 137.41/19.45 | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1958) all_54_15 = e1
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (376), (1958) are inconsistent by sub-proof
% 137.41/19.45 | | | | | | | | | | | | | | | | | #748.
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1959) all_54_15 = e0
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (1959) imply:
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1960) all_10_2 = e0
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | SIMP: (1960) implies:
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1961) all_10_2 = e0
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | REDUCE: (368), (1961) imply:
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1962) ~ (all_52_11 = e0)
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | REDUCE: (1949), (1961) imply:
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1963) ~ (e2 = e0)
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | REDUCE: (376), (1961) imply:
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1964) ~ (e1 = e0)
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | REDUCE: (45), (1961) imply:
% 137.41/19.45 | | | | | | | | | | | | | | | | | (1965) op(e0, e0) = e0
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 137.41/19.45 | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (1966) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 137.41/19.45 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 137.41/19.45 | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 137.41/19.45 | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 137.41/19.45 | | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1277), (1966), (function-axioms) are
% 137.41/19.45 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 137.41/19.45 | | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.45 | | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (1967) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 137.41/19.45 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 137.41/19.45 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 137.41/19.45 | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 137.41/19.45 | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 137.41/19.45 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.45 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.45 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.45 | | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | BETA: splitting (1967) gives:
% 137.41/19.45 | | | | | | | | | | | | | | | | | |
% 137.41/19.45 | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.45 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (1968) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (1968) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1969) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | ALPHA: (1969) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1970) op(e0, e0) = e3
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1965), (1970), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1971) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | ALPHA: (1971) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1972) op(e2, e2) = e1
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1944), (1972), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (1973) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | BETA: splitting (1973) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1974) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | ALPHA: (1974) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1975) op(e2, e2) = e1
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1944), (1975), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (1976) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | BETA: splitting (1976) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (1977) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1977) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (1978) op(e0, e0) = e2
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1965), (1978), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (1979) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | ALPHA: (1979) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (1980) op(e0, e0) = all_56_15
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (1981) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (157), (165), (169), (220), (372),
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (375), (1272), (1937), (1962), (1965), (1980),
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | (1981), (function-axioms) are inconsistent by
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | End of split
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | (1982) all_42_2 = e3
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | COMBINE_EQS: (303), (1982) imply:
% 137.41/19.46 | | | | | | | | | | | | | | (1983) all_10_2 = e3
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | SIMP: (1983) implies:
% 137.41/19.46 | | | | | | | | | | | | | | (1984) all_10_2 = e3
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | REDUCE: (369), (1984) imply:
% 137.41/19.46 | | | | | | | | | | | | | | (1985) ~ (all_52_12 = e3)
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | REDUCE: (371), (1984) imply:
% 137.41/19.46 | | | | | | | | | | | | | | (1986) ~ (all_52_14 = e3)
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | REDUCE: (45), (1984) imply:
% 137.41/19.46 | | | | | | | | | | | | | | (1987) op(e0, e0) = e3
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 137.41/19.46 | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | (1988) all_57_15 = e0 & op(e0, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | ALPHA: (1988) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | (1989) op(e0, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | REF_CLOSE: (7), (1987), (1989), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | (1990) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.41/19.46 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 137.41/19.46 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 137.41/19.46 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 137.41/19.46 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | ALPHA: (1990) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | (1991) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 137.41/19.46 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 137.41/19.46 | | | | | | | | | | | | | | | e1) = e0)
% 137.41/19.46 | | | | | | | | | | | | | | | (1992) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.41/19.46 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 137.41/19.46 | | | | | | | | | | | | | | | e0) = e0)
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | BETA: splitting (1991) gives:
% 137.41/19.46 | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | (1993) all_57_12 = e0 & op(e0, e3) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | ALPHA: (1993) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | (1994) op(e0, e3) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1270), (1994), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | (1995) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 137.41/19.46 | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | BETA: splitting (1995) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | (1996) all_57_13 = e0 & op(e0, e2) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | ALPHA: (1996) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | (1997) op(e0, e2) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (1997), (function-axioms) are
% 137.41/19.46 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | (1998) all_57_14 = e0 & op(e0, e1) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | ALPHA: (1998) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | (1999) all_57_14 = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | (2000) op(e0, e1) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | BETA: splitting (1992) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | (2001) all_57_9 = e0 & op(e3, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | ALPHA: (2001) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | (2002) op(e3, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (2002) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | (2003) all_52_12 = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | REDUCE: (1273), (2003) imply:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | (2004) $false
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | CLOSE: (2004) is inconsistent.
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | (2005) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 137.41/19.46 | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | BETA: splitting (2005) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (2006) all_57_10 = e0 & op(e2, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | ALPHA: (2006) implies:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (2007) op(e2, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (2007) gives:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (2008) all_52_13 = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | REDUCE: (1938), (2008) imply:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (2009) $false
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | CLOSE: (2009) is inconsistent.
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | (2010) all_57_11 = e0 & op(e1, e0) = e0
% 137.41/19.46 | | | | | | | | | | | | | | | | | | |
% 137.41/19.46 | | | | | | | | | | | | | | | | | | | ALPHA: (2010) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | (2011) all_57_11 = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | (2012) op(e1, e0) = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (2000) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | (2013) all_52_11 = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (2012) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | (2014) all_52_14 = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2014) imply:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | (2015) ~ (all_4_2 = e0)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | SIMP: (2015) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | (2016) ~ (all_4_2 = e0)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | (2017) all_54_10 = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (2017) are inconsistent by sub-proof
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | #1112.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | (2018) ~ (all_54_10 = e3)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | (2019) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2019) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | (2020) all_54_10 = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (2020) are inconsistent by sub-proof
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | #1111.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | (2021) ~ (all_54_10 = e2)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | (2022) all_54_10 = e1 | all_54_10 = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (2023) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2023) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2024) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (36), (159), (207), (335), (372),
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (1270), (1277), (1987), (2000), (2016), (2022),
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2024), (function-axioms) are inconsistent by
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #671.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2025) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2025) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2026) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2027) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2028) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2029) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | (2030) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2022) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (2031) all_54_10 = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2031) imply:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (2032) all_4_2 = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2032) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (2033) all_4_2 = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2033) imply:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (2034) ~ (e3 = e1)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2033) imply:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (2035) ~ (e2 = e1)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2033) imply:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | (2036) op(e1, e1) = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | (2037) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2037) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2038) all_57_4 = e1 & op(e3, e1) = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2038) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | (2039) all_57_4 = e1
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2026) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2040) all_56_13 = e2 & op(e1, e1) = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2040) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2041) op(e1, e1) = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2036), (2041), (function-axioms) are
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2042) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2042) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2043) ~ (all_56_7 = e1)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2044) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2044) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2045) all_57_4 = e2 & op(e3, e1) = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2045) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2046) all_57_4 = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2039), (2046) are inconsistent by sub-proof
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1088.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2047) all_57_5 = e2 & op(e2, e1) = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2047) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2048) all_57_5 = e2
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2027) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2049) all_56_12 = e0 & op(e0, e2) = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2049) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2050) op(e0, e2) = e0
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (2050), (function-axioms) are
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2051) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2051) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2052) ~ (all_56_15 = e2)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2053) op(e0, e0) = all_56_15
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2054) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2054) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2055) all_57_4 = e3 & op(e3, e1) = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2055) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2056) all_57_4 = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2039), (2056) are inconsistent by sub-proof
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #631.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2057) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2057) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2058) all_57_5 = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2048), (2058) are inconsistent by sub-proof
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #936.
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2059) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2059) gives:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2060) all_57_8 = e3 & op(e1, e1) = e3
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2060) implies:
% 137.41/19.47 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2061) all_57_8 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2062) op(e1, e1) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2029) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2063) all_56_7 = e1 & op(e1, e2) = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2063) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2064) all_56_7 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2043), (2064) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2065) $false
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2065) is inconsistent.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2066) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2066) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067) ~ (all_56_13 = e2)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2068) op(e1, e1) = all_56_13
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2028) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2069) all_56_9 = e2 & op(e3, e3) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2069) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2070) op(e3, e3) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1277), (2070), (function-axioms) are
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2071) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2071) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2072) ~ (all_56_0 = e3)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2073) op(e3, e2) = all_56_0
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2074) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2074) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2075) all_57_6 = e1 & op(e1, e3) = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2075) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2076) all_57_6 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2030) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2077) all_56_0 = e3 & op(e3, e2) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2077) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2078) all_56_0 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2072), (2078) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2079) $false
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2079) is inconsistent.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2080) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2080) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2081) ~ (all_56_9 = e2)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2082) op(e3, e3) = all_56_9
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2083) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2083) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2084) all_57_2 = e3 & op(e2, e3) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2084) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2085) all_57_2 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2086) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2086) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2087) all_57_2 = e1 & op(e2, e3) = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2087) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2088) all_57_2 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2085), (2088) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2089) e3 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2089) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090) all_57_8 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (170), (210), (211), (213), (214),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (222), (225), (229), (230), (231), (238),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (1276), (1277), (1931), (1943), (1947),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1987), (1999), (2011), (2036), (2052), (2053),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067), (2068), (2072), (2073), (2081), (2082),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2090), (function-axioms) are inconsistent by
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #510.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2091) all_57_3 = e1 & op(e2, e2) = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1943), (2091) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #513.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2092) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2092) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2093) all_57_5 = e1 & op(e2, e1) = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2093) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2094) all_57_5 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (170), (210),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (213), (214), (218), (222), (223), (225),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (235), (238), (239), (1276),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277), (1931), (1936), (1943), (1947), (1987),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1991), (1999), (2011), (2027), (2028), (2029),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030), (2036), (2043), (2094), (function-axioms)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #507.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2095) all_57_10 = e1 & op(e2, e0) = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2095) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2096) all_57_10 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2097) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2097) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2098) all_57_0 = e3 & op(e3, e3) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1276), (2098) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1108.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2099) all_57_1 = e3 & op(e3, e2) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2100) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2100) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2101) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2101) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2102) all_57_6 = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2076), (2102) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2103) e2 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2048), (2103) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2104) all_57_5 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (170), (210),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (213), (214), (218), (222), (223), (225),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (235), (238), (239), (1276),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277), (1931), (1936), (1943), (1947), (1987),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1991), (1999), (2011), (2027), (2028), (2029),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030), (2036), (2043), (2104), (function-axioms)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #507.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2105) all_57_7 = e2 & op(e1, e2) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2099) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106) all_57_1 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2105) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2107) all_57_7 = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (2062), (2068)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2108) all_56_13 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (2036), (2068)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2109) all_56_13 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2108), (2109) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2110) e3 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2110) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2111) all_57_8 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2112) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2112) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2113) all_57_6 = e3 & op(e1, e3) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2113) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2114) all_57_6 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2115) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2115) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2116) all_57_4 = e3 & op(e3, e1) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2116) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2117) all_57_4 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2039), (2117) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #631.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2118) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2118) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2119) all_57_5 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2044) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2120) all_57_4 = e2 & op(e3, e1) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2120) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2121) all_57_4 = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2039), (2121) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2122) e2 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2122) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2123) e2 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2107), (2123) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) all_57_7 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (2011), (2111), (2114),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2124) are inconsistent by sub-proof #995.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2048), (2119) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #936.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2125) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2125) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2126) all_57_8 = e2 & op(e1, e1) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2126) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2127) all_57_8 = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2111), (2127) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2128) e2 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2128) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2129) e2 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2107), (2129) imply:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) all_57_7 = e1
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (2011), (2111), (2114),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2130) are inconsistent by sub-proof #995.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2131) all_57_14 = e2 & op(e0, e1) = e2
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1999), (2131) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #932.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2059) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2060), (2111) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2132) all_57_14 = e3 & op(e0, e1) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2132) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2133) all_57_14 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (210), (211),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936), (1987), (1991), (2133), (function-axioms)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #509.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2134) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2134) implies:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2135) all_57_7 = e3
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (229), (230), (1943),
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2106), (2135) are inconsistent by sub-proof #515.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2136) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2136) gives:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2060), (2111) are inconsistent by sub-proof
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506.
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.48 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2137) all_57_11 = e3 & op(e1, e0) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2011), (2137) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #957.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2138) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (2011), (2036), (2138),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1082.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2139) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2139) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2140) all_57_4 = e3 & op(e3, e1) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2140) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2141) all_57_4 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2039), (2141) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2142) e3 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2142) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2143) e3 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2143) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144) all_57_8 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (170), (210), (211), (213), (214),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (222), (225), (229), (230), (231), (238),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (1276), (1277), (1931), (1943), (1947),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1987), (1999), (2011), (2036), (2052), (2053),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2067), (2068), (2072), (2073), (2081), (2082),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2144), (function-axioms) are inconsistent by
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #510.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2145) all_57_9 = e3 & op(e3, e0) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2145) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2146) all_57_9 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (214), (1987), (2011), (2096),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2146), (function-axioms) are inconsistent by
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #597.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2147) all_57_3 = e3 & op(e2, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1943), (2147) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #517.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2148) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2148) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2149) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2149) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2150) all_57_5 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2048), (2150) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #936.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2151) all_57_10 = e3 & op(e2, e0) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2151) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2152) all_57_10 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (213), (214), (1987),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2011), (2152), (function-axioms) are inconsistent
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #688.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2153) all_57_7 = e1 & op(e1, e2) = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2153) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2154) all_57_7 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2155) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2155) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2156) all_57_1 = e3 & op(e3, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2156) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2157) all_57_1 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2158) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2158) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2159) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2159) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2160) all_57_6 = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2161) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2161) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2162) all_57_0 = e3 & op(e3, e3) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1276), (2162) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1108.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (2062), (2068)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2163) all_56_13 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (2036), (2068)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2164) all_56_13 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2163), (2164) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2165) e3 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2165) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2166) all_57_8 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2167) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2167) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2168) all_57_6 = e3 & op(e1, e3) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2168) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2169) all_57_6 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (2011), (2154), (2166),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2169) are inconsistent by sub-proof #995.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2170) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2170) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2171) all_57_7 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (229), (230), (1943),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2157), (2171) are inconsistent by sub-proof #515.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2172) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2172) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2060), (2166) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #506.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2173) all_57_11 = e3 & op(e1, e0) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2011), (2173) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #957.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2174) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (210), (211), (1987),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2160), (2174), (function-axioms) are
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #512.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2175) all_57_7 = e2 & op(e1, e2) = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2175) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2176) all_57_7 = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2154), (2176) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2177) e2 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2048), (2177) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2178) all_57_5 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (170), (210),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (213), (214), (218), (222), (223), (225),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (235), (238), (239), (1276),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277), (1931), (1936), (1943), (1947), (1987),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1991), (1999), (2011), (2027), (2028), (2029),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030), (2036), (2043), (2178), (function-axioms)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #507.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2179) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (2011), (2036), (2179),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1082.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2180) all_57_3 = e3 & op(e2, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1943), (2180) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #517.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2181) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2181) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2182) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2182) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2183) all_57_7 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2184) op(e1, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2154), (2183) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2185) e3 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2061), (2185) imply:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2186) all_57_8 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (210), (211), (213),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (214), (218), (222), (225), (229), (230), (238),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (1276), (1931), (1943), (1947), (1987),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2011), (2183), (2184), (2186),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #511.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2187) all_57_13 = e3 & op(e0, e2) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2187) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2188) all_57_13 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (210), (211), (1987),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1999), (2188), (function-axioms) are inconsistent
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #666.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2189) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2189) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2190) all_57_8 = e1 & op(e1, e1) = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2190) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2191) all_57_8 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (170), (210), (211), (213), (214),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (222), (225), (229), (230), (231), (238),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (1276), (1277), (1931), (1943), (1947),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1987), (1999), (2011), (2030), (2036), (2052),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2053), (2067), (2068), (2072), (2073), (2191),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #505.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2192) all_57_11 = e1 & op(e1, e0) = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2192) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2193) all_57_11 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2011), (2193) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #690.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2194) all_57_14 = e3 & op(e0, e1) = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2194) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2195) all_57_14 = e3
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (210), (211),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1936), (1987), (1991), (2195), (function-axioms)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #509.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2196) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (1999), (2036), (2196),
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #508.
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2197) all_57_5 = e1 & op(e2, e1) = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2197) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (2198) all_57_5 = e1
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2026) gives:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2199) all_56_13 = e2 & op(e1, e1) = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2199) implies:
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2200) op(e1, e1) = e2
% 137.41/19.49 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2036), (2200), (function-axioms) are
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2201) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2201) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2202) ~ (all_56_7 = e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (170), (210),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (213), (214), (218), (222), (223), (225),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (235), (238), (239), (1276),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1277), (1931), (1936), (1943), (1947), (1987),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (1991), (1999), (2011), (2027), (2028), (2029),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2030), (2036), (2198), (2202), (function-axioms)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #507.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | (2203) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2203) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (2204) all_57_8 = e1 & op(e1, e1) = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2204) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (2205) all_57_8 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2026) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2206) all_56_13 = e2 & op(e1, e1) = e2
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2206) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2207) op(e1, e1) = e2
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2036), (2207), (function-axioms) are
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2208) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2208) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2209) ~ (all_56_7 = e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2027) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2210) all_56_12 = e0 & op(e0, e2) = e0
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2210) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2211) op(e0, e2) = e0
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (2211), (function-axioms) are
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2212) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2212) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213) ~ (all_56_15 = e2)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2214) op(e0, e0) = all_56_15
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2028) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2215) all_56_9 = e2 & op(e3, e3) = e2
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2215) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2216) op(e3, e3) = e2
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1277), (2216), (function-axioms) are
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2217) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2217) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2218) ~ (all_56_0 = e3)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2219) op(e3, e2) = all_56_0
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2029) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2220) all_56_7 = e1 & op(e1, e2) = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2220) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2221) all_56_7 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2209), (2221) imply:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2222) $false
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2222) is inconsistent.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2223) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2223) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2224) ~ (all_56_13 = e2)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2225) op(e1, e1) = all_56_13
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (8), (170), (210), (211), (213), (214),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (222), (225), (229), (230), (231), (238),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (1276), (1277), (1931), (1943), (1947),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1987), (1999), (2011), (2030), (2036), (2205),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2213), (2214), (2218), (2219), (2224), (2225),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #505.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (2226) all_57_14 = e1 & op(e0, e1) = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2226) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | (2227) all_57_14 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1999), (2227) are inconsistent by sub-proof
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | | #1071.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2228) all_54_10 = e0
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (2016), (2228) are inconsistent by
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (2229) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2229) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | (2230) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2230) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | (2231) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (1987), (2000), (2231), (function-axioms) are
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #664.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | (2232) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2232) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | (2233) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2022) gives:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2234) all_54_10 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2234) imply:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2235) all_4_2 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2235) implies:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2236) all_4_2 = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2236) imply:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2237) ~ (e3 = e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2236) imply:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2238) ~ (e2 = e1)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2236) imply:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2239) op(e1, e1) = e1
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (168), (207), (1277),
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (1985), (1987), (2233), (2239), (function-axioms)
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #730.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | (2240) all_54_10 = e0
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (2016), (2240) are inconsistent by
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | End of split
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | Case 2:
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | (2241) all_24_2 = e2
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | COMBINE_EQS: (319), (2241) imply:
% 137.41/19.50 | | | | | | | | | | | | | (2242) all_10_2 = e2
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | REDUCE: (370), (2242) imply:
% 137.41/19.50 | | | | | | | | | | | | | (2243) ~ (all_52_13 = e2)
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | REDUCE: (371), (2242) imply:
% 137.41/19.50 | | | | | | | | | | | | | (2244) ~ (all_52_14 = e2)
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | REDUCE: (45), (2242) imply:
% 137.41/19.50 | | | | | | | | | | | | | (2245) op(e0, e0) = e2
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | BETA: splitting (209) gives:
% 137.41/19.50 | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | Case 1:
% 137.41/19.50 | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | (2246) all_57_15 = e0 & op(e0, e0) = e0
% 137.41/19.50 | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | ALPHA: (2246) implies:
% 137.41/19.50 | | | | | | | | | | | | | | (2247) op(e0, e0) = e0
% 137.41/19.50 | | | | | | | | | | | | | |
% 137.41/19.50 | | | | | | | | | | | | | | REF_CLOSE: (5), (2245), (2247), (function-axioms) are
% 137.41/19.50 | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 137.41/19.51 | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | (2248) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.41/19.51 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 137.41/19.51 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 137.41/19.51 | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 137.41/19.51 | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | ALPHA: (2248) implies:
% 137.41/19.51 | | | | | | | | | | | | | | (2249) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 137.41/19.51 | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | e1) = e0)
% 137.41/19.51 | | | | | | | | | | | | | | (2250) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.41/19.51 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 137.41/19.51 | | | | | | | | | | | | | | e0) = e0)
% 137.41/19.51 | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | BETA: splitting (2249) gives:
% 137.41/19.51 | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | (2251) all_57_12 = e0 & op(e0, e3) = e0
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | ALPHA: (2251) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | (2252) op(e0, e3) = e0
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | REF_CLOSE: (159), (1270), (2252), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | (2253) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 137.41/19.51 | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | BETA: splitting (2253) gives:
% 137.41/19.51 | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | (2254) all_57_13 = e0 & op(e0, e2) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | ALPHA: (2254) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | (2255) op(e0, e2) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (2255), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | (2256) all_57_14 = e0 & op(e0, e1) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | ALPHA: (2256) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | (2257) all_57_14 = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | (2258) op(e0, e1) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | BETA: splitting (2250) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | (2259) all_57_9 = e0 & op(e3, e0) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | ALPHA: (2259) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | (2260) op(e3, e0) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (1273), (2260), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | (2261) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 137.41/19.51 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | BETA: splitting (2261) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2262) all_57_10 = e0 & op(e2, e0) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (1938), (2262), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2263) all_57_11 = e0 & op(e1, e0) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | ALPHA: (2263) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2264) all_57_11 = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2265) op(e1, e0) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (2258) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2266) all_52_11 = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (2265) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2267) all_52_14 = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | REDUCE: (367), (2267) imply:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2268) ~ (all_4_2 = e0)
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | SIMP: (2268) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2269) ~ (all_4_2 = e0)
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | REDUCE: (2244), (2267) imply:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | (2270) ~ (e2 = e0)
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | (2271) all_54_10 = e3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2271) imply:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | (2272) all_4_2 = e3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2272) imply:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | (2273) $false
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | CLOSE: (2273) is inconsistent.
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | (2274) ~ (all_54_10 = e3)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | (2275) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (2276) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2276) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2277) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2277) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2278) op(e3, e3) = all_56_9
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2279) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2280) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2281) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2282) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2283) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | (2284) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2281) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | (2285) all_56_11 = e3 & op(e2, e2) = e3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2285) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | (2286) op(e2, e2) = e3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (1944), (2286), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | (2287) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2287) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | (2288) ~ (all_56_3 = e2)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | (2289) op(e2, e3) = all_56_3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2282) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | (2290) all_56_10 = e0 & op(e0, e3) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2290) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | (2291) op(e0, e3) = e0
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (1270), (2291), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | (2292) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2292) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | (2293) ~ (all_56_15 = e3)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | (2294) op(e0, e0) = all_56_15
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2284) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | (2295) all_56_3 = e2 & op(e2, e3) = e2
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2295) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | (2296) all_56_3 = e2
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2288), (2296) imply:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | (2297) $false
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2297) is inconsistent.
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | (2298) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2298) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | (2299) ~ (all_56_11 = e3)
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | (2300) op(e2, e2) = all_56_11
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2279) gives:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | | (2301) all_56_15 = e3 & op(e0, e0) = e3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2301) implies:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | | (2302) op(e0, e0) = e3
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2245), (2302), (function-axioms) are
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.51 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | (2303) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2303) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | (2304) ~ (all_56_10 = e0)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | (2305) op(e0, e3) = all_56_10
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2275) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (2306) all_54_10 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2306) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (2307) all_4_2 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2307) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (2308) $false
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2308) is inconsistent.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (2309) ~ (all_54_10 = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | (2310) all_54_10 = e1 | all_54_10 = e0
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2310) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2311) all_54_10 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2311) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2312) all_4_2 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2312) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2313) ~ (e3 = e1)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2312) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2314) ~ (e2 = e1)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2312) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2315) op(e1, e1) = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2316) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2316) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2317) all_57_4 = e1 & op(e3, e1) = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2317) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2318) all_57_4 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (163),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (210), (211), (212), (213), (214), (215),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (218), (219), (222), (223), (226), (227),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (234), (237), (238), (239),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1276), (1277), (1936), (1943), (1944),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245), (2249), (2250), (2257), (2258), (2264),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2282), (2283), (2315), (2318), (function-axioms)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #475.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2319) all_57_5 = e1 & op(e2, e1) = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2319) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2320) all_57_5 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (207),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (211), (212), (213), (214), (215), (217),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (222), (223), (226), (227), (229), (234),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (238), (239), (1270), (1276), (1277), (1936),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943), (1944), (2245), (2249), (2250), (2257),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258), (2264), (2282), (2315), (2320),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #490.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2321) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2321) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2322) all_57_8 = e1 & op(e1, e1) = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2322) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323) all_57_8 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2280) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2324) all_56_13 = e3 & op(e1, e1) = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2324) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2325) op(e1, e1) = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2315), (2325), (function-axioms) are
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2326) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2326) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2327) ~ (all_56_6 = e1)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2328) op(e1, e3) = all_56_6
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2283) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2329) all_56_6 = e1 & op(e1, e3) = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2329) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2330) all_56_6 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2327), (2330) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2331) $false
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2331) is inconsistent.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2332) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2332) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2333) ~ (all_56_13 = e3)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2334) op(e1, e1) = all_56_13
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (2245), (2294)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2335) all_56_15 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10, e3, e0, simplifying with (159), (2305)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2336) all_56_10 = all_52_3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (2315), (2334)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2337) all_56_13 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6, e3, e1, simplifying with (163), (2328)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2338) all_56_6 = all_52_2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (1944), (2300)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2339) all_56_11 = e0
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3, e3, e2, simplifying with (167), (2289)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2340) all_56_3 = all_52_1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_9,
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (1277), (2278) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2341) all_56_9 = e0
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2288), (2340) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2342) ~ (all_52_1 = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2293), (2335) imply:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2343) ~ (e3 = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2344) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2344) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2345) all_57_2 = e2 & op(e2, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2345) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2346) op(e2, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2342), (2346), (function-axioms) are
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #882.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2347) all_57_3 = e2 & op(e2, e2) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1943), (2347) are inconsistent by sub-proof
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #516.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2348) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2348) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2349) all_57_5 = e2 & op(e2, e1) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2349) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2350) all_57_5 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (73), (158), (159),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (167), (168), (207), (210), (211), (212),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (214), (215), (217), (218), (219), (222),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (225), (226), (227), (229), (230), (231),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (235), (236), (237), (238), (239), (1266),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267), (1270), (1276), (1277), (1931), (1936),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943), (1944), (1947), (2245), (2249), (2250),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257), (2258), (2264), (2282), (2283), (2315),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323), (2342), (2350), (function-axioms) are
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #471.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2351) all_57_10 = e2 & op(e2, e0) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2351) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2352) all_57_10 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2353) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (1277), (2342), (2353),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #707.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2354) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2354) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2355) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2355) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2356) all_57_6 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2357) op(e1, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2358) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2358) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2359) all_57_6 = e3 & op(e1, e3) = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2356), (2359) are inconsistent by sub-proof
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #916.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2360) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (73), (163), (168), (213), (1266),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267), (1931), (1947), (2245), (2264), (2357),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2360), (function-axioms) are inconsistent by
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #473.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2361) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (2264), (2315), (2361),
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #956.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2362) all_57_12 = e2 & op(e0, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2362) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2363) all_57_12 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2364) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2364) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2365) all_57_12 = e3 & op(e0, e3) = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2363), (2365) are inconsistent by sub-proof
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #780.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2366) all_57_13 = e3 & op(e0, e2) = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2366) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2367) all_57_13 = e3
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2368) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2368) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2369) all_57_1 = e1 & op(e3, e2) = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2369) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2370) all_57_1 = e1
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2371) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2371) gives:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2372) all_57_0 = e2 & op(e3, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2372) implies:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2373) op(e3, e3) = e2
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1277), (2373), (function-axioms) are
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.52 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2374) all_57_1 = e2 & op(e3, e2) = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2370), (2374) are inconsistent by sub-proof
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1074.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2375) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2375) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2376) all_57_4 = e2 & op(e3, e1) = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2376) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2377) all_57_4 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2378) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2378) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2379) all_57_4 = e3 & op(e3, e1) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2379) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2380) all_57_4 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2377), (2380) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2381) e3 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (210), (212), (2245),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257), (2367), (2381), (function-axioms) are
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #925.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2382) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2382) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2383) all_57_5 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2384) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2384) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2385) all_57_9 = e3 & op(e3, e0) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2385) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2386) all_57_9 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2387) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2387) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2388) all_57_12 = e1 & op(e0, e3) = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2388) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2389) all_57_12 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2363), (2389) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2390) e2 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2377), (2390) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2391) all_57_4 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (163),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (210), (211), (212), (213), (214), (215),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (218), (219), (222), (223), (226), (227),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (230), (231), (234), (237), (238), (239),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1276), (1277), (1936), (1943), (1944),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2245), (2249), (2250), (2257), (2258), (2264),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2282), (2283), (2315), (2391), (function-axioms)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #475.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2392) all_57_13 = e1 & op(e0, e2) = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2392) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2393) all_57_13 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2367), (2393) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2394) e3 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2394) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2395) e3 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2383), (2395) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2396) all_57_5 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (213), (217), (218),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (223), (2245), (2257), (2264), (2315),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2352), (2377), (2386), (2396), (function-axioms)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #493.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2397) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (2245), (2257), (2397),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #470.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2398) all_57_10 = e3 & op(e2, e0) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2398) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2399) all_57_10 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2352), (2399) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2400) e3 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2400) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2401) e3 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2383), (2401) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2402) all_57_5 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (73), (158), (159),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (163), (167), (168), (207), (210), (211), (212),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (213), (214), (215), (217), (218), (219), (222),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (223), (225), (226), (227), (229), (230), (231),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (234), (235), (236), (237), (238), (239), (1266),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267), (1270), (1276), (1277), (1931), (1936),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1943), (1944), (1947), (2245), (2249), (2250),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2257), (2258), (2264), (2282), (2283), (2315),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2323), (2342), (2402), (function-axioms) are
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #471.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2403) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (1936), (2264), (2367), (2403),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #468.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2404) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (2257), (2315), (2404),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #859.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2405) all_57_9 = e2 & op(e3, e0) = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2405) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2406) all_57_9 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2407) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2407) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2408) all_57_9 = e3 & op(e3, e0) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2408) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2409) all_57_9 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2406), (2409) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2410) e3 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2367), (2410) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2411) all_57_13 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (164),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (209), (210), (211), (212), (213), (215),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1273), (1936), (1938), (2245), (2406),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2411), (function-axioms) are inconsistent by
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #465.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2412) all_57_10 = e3 & op(e2, e0) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2412) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2413) all_57_10 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2352), (2413) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2414) e3 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2367), (2414) imply:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2415) all_57_13 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (164),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (168), (209), (210), (211), (212), (213), (215),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1270), (1273), (1936), (1938), (2245), (2406),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2415), (function-axioms) are inconsistent by
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #465.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2416) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (1936), (2264), (2367), (2416),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #468.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2417) all_57_3 = e1 & op(e2, e2) = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2417) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2418) op(e2, e2) = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1944), (2418), (function-axioms) are
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2419) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2419) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2420) all_57_7 = e1 & op(e1, e2) = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2420) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2421) all_57_7 = e1
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2422) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2422) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2423) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2423) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2424) op(e1, e3) = e2
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2425) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2425) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2426) all_57_6 = e3 & op(e1, e3) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2426) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2427) all_57_6 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (218), (2264), (2323), (2421),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2427) are inconsistent by sub-proof #995.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2428) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (73), (163), (168), (213), (1266),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (1267), (1931), (1947), (2245), (2264), (2424),
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2428), (function-axioms) are inconsistent by
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #473.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2429) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2429) gives:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2430) all_57_8 = e3 & op(e1, e1) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2430) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2431) op(e1, e1) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2315), (2431), (function-axioms) are
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2432) all_57_11 = e3 & op(e1, e0) = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2432) implies:
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2433) all_57_11 = e3
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2264), (2433) are inconsistent by sub-proof
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #858.
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.53 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2434) all_57_7 = e2 & op(e1, e2) = e2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2434) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2435) all_57_7 = e2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2421), (2435) are inconsistent by sub-proof
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2436) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (2264), (2315), (2436),
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1082.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2437) all_57_13 = e1 & op(e0, e2) = e1
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2367), (2437) are inconsistent by sub-proof
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1014.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2438) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2438) gives:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2439) all_57_14 = e3 & op(e0, e1) = e3
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2257), (2439) are inconsistent by sub-proof
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #777.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2440) all_57_15 = e3 & op(e0, e0) = e3
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2440) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2441) op(e0, e0) = e3
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (159), (207), (1270), (1277),
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2258), (2282), (2315), (2441), (function-axioms)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #672.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2442) all_57_14 = e1 & op(e0, e1) = e1
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2442) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2443) all_57_14 = e1
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2257), (2443) are inconsistent by sub-proof
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1071.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2444) all_54_10 = e0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2444) imply:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2445) all_4_2 = e0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2269), (2445) imply:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2446) $false
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2446) is inconsistent.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | (2447) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2447) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | (2448) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2448) gives:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | (2449) all_56_12 = e0 & op(e0, e2) = e0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2449) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | (2450) op(e0, e2) = e0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (2450), (function-axioms) are
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | (2451) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2451) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | (2452) ~ (all_56_15 = e2)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (2453) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (1277), (2453), (function-axioms) are
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (2454) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2454) gives:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (2455) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (1944), (2245), (2455),
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | #949.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (2456) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2456) gives:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (2457) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2457) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (2458) op(e2, e2) = e1
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1944), (2458), (function-axioms) are
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (2459) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2459) gives:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (2460) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2460) implies:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | (2461) all_56_15 = e2
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (2448), (2461), (function-axioms)
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #976.
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.54 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (2462) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2462) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (2463) op(e0, e0) = all_56_15
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (2464) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2464) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2465) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2465) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2466) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2466) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2467) all_56_15 = e3
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2463), (2467) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2468) op(e0, e0) = e3
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2245), (2468), (function-axioms) are
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2469) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2469) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2470) all_56_15 = e2
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (1936), (2448), (2470), (function-axioms)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #976.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2471) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2471) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2472) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2472) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2473) all_56_15 = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2452), (2473) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2474) ~ (e2 = e1)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2463), (2473) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2475) op(e0, e0) = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2245), (2475), (function-axioms) are
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2476) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2476) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2477) ~ (all_56_14 = e0)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2478) op(e0, e1) = all_56_14
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2258), (2477), (2478), (function-axioms) are
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (2479) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2479) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | (2480) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2480) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | (2481) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2245), (2258), (2481), (function-axioms) are
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #972.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | (2482) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2482) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | (2483) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2275) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | (2484) all_54_10 = e2
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2484) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | (2485) all_4_2 = e2
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2485) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | (2486) $false
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2486) is inconsistent.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | (2487) all_54_10 = e1 | all_54_10 = e0
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2487) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | (2488) all_54_10 = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2488) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | (2489) all_4_2 = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2489) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | (2490) ~ (e3 = e1)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2489) imply:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | (2491) op(e1, e1) = e1
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2483) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | (2492) all_56_5 = e2 & op(e2, e0) = e2
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2492) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | (2493) op(e2, e0) = e2
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2243), (2493), (function-axioms) are
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | (2494) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2494) implies:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | (2495) ~ (all_56_11 = e0)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | (2496) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2496) gives:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.55 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (2497) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (1277), (2497), (function-axioms) are
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (2498) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2491), (2498), (function-axioms) are
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #971.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (2499) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2499) gives:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (2500) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (1944), (2245), (2500),
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | #949.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (2501) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2501) gives:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2502) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2502) implies:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2503) op(e2, e2) = e1
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (1944), (2503), (function-axioms) are
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2504) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2504) gives:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2505) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2505) implies:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2506) all_56_11 = e0
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2495), (2506) imply:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2507) $false
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2507) is inconsistent.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2508) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2508) implies:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2509) op(e0, e0) = all_56_15
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2510) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9), (2245), (2491), (2495), (2509), (2510),
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #964.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | (2511) all_54_10 = e0
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (2511) imply:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | (2512) all_4_2 = e0
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2269), (2512) imply:
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | (2513) $false
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2513) is inconsistent.
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | (2514) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 137.41/19.56 | | | | | | | | | | e0 & op(e0, e2) = e0)
% 137.41/19.56 | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | | REF_CLOSE: (158), (162), (1935), (1936), (2514),
% 137.41/19.56 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.56 | | | | | | | | | | #464.
% 137.41/19.56 | | | | | | | | | |
% 137.41/19.56 | | | | | | | | | End of split
% 137.41/19.56 | | | | | | | | |
% 137.41/19.56 | | | | | | | | End of split
% 137.41/19.56 | | | | | | | |
% 137.41/19.56 | | | | | | | Case 2:
% 137.41/19.56 | | | | | | | |
% 137.41/19.56 | | | | | | | | (2515) all_57_1 = e0 & op(e3, e2) = e0
% 137.41/19.56 | | | | | | | |
% 137.41/19.56 | | | | | | | | REF_CLOSE: (170), (1271), (2515), (function-axioms) are
% 137.41/19.56 | | | | | | | | inconsistent by sub-proof #1102.
% 137.41/19.56 | | | | | | | |
% 137.41/19.56 | | | | | | | End of split
% 137.41/19.56 | | | | | | |
% 137.41/19.56 | | | | | | Case 2:
% 137.41/19.56 | | | | | | |
% 137.41/19.56 | | | | | | | (2516) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 137.41/19.56 | | | | | | | op(e3, e0) = e0)
% 137.41/19.56 | | | | | | |
% 137.41/19.56 | | | | | | | REF_CLOSE: (168), (169), (1272), (1273), (2516), (function-axioms)
% 137.41/19.56 | | | | | | | are inconsistent by sub-proof #463.
% 137.41/19.56 | | | | | | |
% 137.41/19.56 | | | | | | End of split
% 137.41/19.56 | | | | | |
% 137.41/19.56 | | | | | End of split
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | Case 2:
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | (2517) all_10_2 = e1
% 137.41/19.56 | | | | | (2518) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0,
% 137.41/19.56 | | | | | e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 137.41/19.56 | | | | | (all_10_1 = e3) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | COMBINE_EQS: (309), (2517) imply:
% 137.41/19.56 | | | | | (2519) all_30_2 = e1
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (350), (2517) imply:
% 137.41/19.56 | | | | | (2520) ~ (all_52_3 = e1)
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (361), (2517) imply:
% 137.41/19.56 | | | | | (2521) ~ (all_52_7 = e1)
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (368), (2517) imply:
% 137.41/19.56 | | | | | (2522) ~ (all_52_11 = e1)
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (369), (2517) imply:
% 137.41/19.56 | | | | | (2523) ~ (all_52_12 = e1)
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (370), (2517) imply:
% 137.41/19.56 | | | | | (2524) ~ (all_52_13 = e1)
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (371), (2517) imply:
% 137.41/19.56 | | | | | (2525) ~ (all_52_14 = e1)
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | REDUCE: (45), (2517) imply:
% 137.41/19.56 | | | | | (2526) op(e0, e0) = e1
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | BETA: splitting (207) gives:
% 137.41/19.56 | | | | |
% 137.41/19.56 | | | | | Case 1:
% 137.41/19.56 | | | | | |
% 137.41/19.56 | | | | | | (2527) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 137.41/19.56 | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) =
% 137.41/19.56 | | | | | | e3 & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 &
% 137.41/19.56 | | | | | | ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) =
% 137.41/19.56 | | | | | | all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 =
% 137.41/19.56 | | | | | | e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 137.41/19.56 | | | | | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 137.41/19.56 | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 & ~
% 137.41/19.56 | | | | | | (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 137.41/19.56 | | | | | | all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 137.41/19.56 | | | | | |
% 137.41/19.56 | | | | | | BETA: splitting (2527) gives:
% 137.41/19.56 | | | | | |
% 137.41/19.56 | | | | | | Case 1:
% 137.41/19.56 | | | | | | |
% 137.41/19.57 | | | | | | | (2528) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 137.41/19.57 | | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) =
% 137.41/19.57 | | | | | | | e3 & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 &
% 137.41/19.57 | | | | | | | ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) =
% 137.41/19.57 | | | | | | | all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | REF_CLOSE: (39), (373), (2528), (function-axioms) are inconsistent
% 137.41/19.57 | | | | | | | by sub-proof #1128.
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | Case 2:
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | (2529) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) &
% 137.41/19.57 | | | | | | | op(e3, e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) =
% 137.41/19.57 | | | | | | | e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 &
% 137.41/19.57 | | | | | | | ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 137.41/19.57 | | | | | | | all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | REF_CLOSE: (36), (375), (2529), (function-axioms) are inconsistent
% 137.41/19.57 | | | | | | | by sub-proof #1126.
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | End of split
% 137.41/19.57 | | | | | |
% 137.41/19.57 | | | | | Case 2:
% 137.41/19.57 | | | | | |
% 137.41/19.57 | | | | | | (2530) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 137.41/19.57 | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) =
% 137.41/19.57 | | | | | | e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 &
% 137.41/19.57 | | | | | | ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 137.41/19.57 | | | | | | all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11
% 137.41/19.57 | | | | | | = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 137.41/19.57 | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 137.41/19.57 | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 137.41/19.57 | | | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 137.41/19.57 | | | | | | all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 137.41/19.57 | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.57 | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 137.41/19.57 | | | | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 137.41/19.57 | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0)
% 137.41/19.57 | | | | | | & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.57 | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 137.41/19.57 | | | | | | ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 137.41/19.57 | | | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 137.41/19.57 | | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 137.41/19.57 | | | | | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 137.41/19.57 | | | | | |
% 137.41/19.57 | | | | | | BETA: splitting (2530) gives:
% 137.41/19.57 | | | | | |
% 137.41/19.57 | | | | | | Case 1:
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | (2531) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 137.41/19.57 | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) =
% 137.41/19.57 | | | | | | | e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2
% 137.41/19.57 | | | | | | | & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 137.41/19.57 | | | | | | | all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | REF_CLOSE: (8), (36), (372), (2526), (2531), (function-axioms) are
% 137.41/19.57 | | | | | | | inconsistent by sub-proof #462.
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | Case 2:
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | (2532) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 137.41/19.57 | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) =
% 137.41/19.57 | | | | | | | e2 & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 137.41/19.57 | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 137.41/19.57 | | | | | | | all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0,
% 137.41/19.57 | | | | | | | e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 137.41/19.57 | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 137.41/19.57 | | | | | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 137.41/19.57 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 137.41/19.57 | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.57 | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1
% 137.41/19.57 | | | | | | | & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 137.41/19.57 | | | | | | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0
% 137.41/19.57 | | | | | | | & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 137.41/19.57 | | | | | | | e1) = e0 & op(e0, e1) = all_56_14 &
% 137.41/19.57 | | | | | | | $i(all_56_14))))
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | BETA: splitting (2532) gives:
% 137.41/19.57 | | | | | | |
% 137.41/19.57 | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | | (2533) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 137.41/19.57 | | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) =
% 137.41/19.57 | | | | | | | | e2 & $i(all_56_7)
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | | ALPHA: (2533) implies:
% 137.41/19.57 | | | | | | | | (2534) op(e1, e1) = e2
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | | REF_CLOSE: (36), (372), (2534), (function-axioms) are
% 137.41/19.57 | | | | | | | | inconsistent by sub-proof #1124.
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | | (2535) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2)
% 137.41/19.57 | | | | | | | | & op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 137.41/19.57 | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 137.41/19.57 | | | | | | | | & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 &
% 137.41/19.57 | | | | | | | | ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0,
% 137.41/19.57 | | | | | | | | e3) = all_56_10 & $i(all_56_10)) | (all_56_11
% 137.41/19.57 | | | | | | | | = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 137.41/19.57 | | | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 137.41/19.57 | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.57 | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 137.41/19.57 | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 137.41/19.57 | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 137.41/19.57 | | | | | | | | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14
% 137.41/19.57 | | | | | | | | & $i(all_56_14))))
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | | BETA: splitting (2535) gives:
% 137.41/19.57 | | | | | | | |
% 137.41/19.57 | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | (2536) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2)
% 137.41/19.57 | | | | | | | | | & op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 137.41/19.57 | | | | | | | | | e0) = e2 & $i(all_56_5)
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | ALPHA: (2536) implies:
% 137.41/19.57 | | | | | | | | | (2537) op(e0, e0) = e2
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | REF_CLOSE: (6), (2526), (2537), (function-axioms) are
% 137.41/19.57 | | | | | | | | | inconsistent by sub-proof #1070.
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | (2538) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9
% 137.41/19.57 | | | | | | | | | = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 137.41/19.57 | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.57 | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 137.41/19.57 | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 137.41/19.57 | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 137.41/19.57 | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 137.41/19.57 | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 137.41/19.57 | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 137.41/19.57 | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 137.41/19.57 | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | ALPHA: (2538) implies:
% 137.41/19.57 | | | | | | | | | (2539) op(e0, e0) = all_56_15
% 137.41/19.57 | | | | | | | | | (2540) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 137.41/19.57 | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 137.41/19.57 | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2
% 137.41/19.57 | | | | | | | | | & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 137.41/19.57 | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 =
% 137.41/19.57 | | | | | | | | | e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 137.41/19.57 | | | | | | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8))
% 137.41/19.57 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 137.41/19.57 | | | | | | | | | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 137.41/19.57 | | | | | | | | | $i(all_56_14))
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | BETA: splitting (213) gives:
% 137.41/19.57 | | | | | | | | |
% 137.41/19.57 | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | (2541) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 137.41/19.57 | | | | | | | | | | e1 & op(e2, e0) = e1)
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | BETA: splitting (2541) gives:
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | (2542) all_57_9 = e1 & op(e3, e0) = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | REF_CLOSE: (168), (2523), (2542), (function-axioms) are
% 137.41/19.57 | | | | | | | | | | | inconsistent by sub-proof #461.
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | (2543) all_57_10 = e1 & op(e2, e0) = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | REF_CLOSE: (164), (2524), (2543), (function-axioms) are
% 137.41/19.57 | | | | | | | | | | | inconsistent by sub-proof #460.
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | End of split
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | (2544) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 137.41/19.57 | | | | | | | | | | e1 & op(e0, e0) = e1)
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | BETA: splitting (2544) gives:
% 137.41/19.57 | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | (2545) all_57_11 = e1 & op(e1, e0) = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | ALPHA: (2545) implies:
% 137.41/19.57 | | | | | | | | | | | (2546) op(e1, e0) = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | REF_CLOSE: (160), (2525), (2546), (function-axioms) are
% 137.41/19.57 | | | | | | | | | | | inconsistent by sub-proof #459.
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | (2547) all_57_15 = e1 & op(e0, e0) = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | ALPHA: (2547) implies:
% 137.41/19.57 | | | | | | | | | | | (2548) all_57_15 = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 137.41/19.57 | | | | | | | | | | | all_56_15, e0, e0, simplifying with (2526), (2539)
% 137.41/19.57 | | | | | | | | | | | gives:
% 137.41/19.57 | | | | | | | | | | | (2549) all_56_15 = e1
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | BETA: splitting (52) gives:
% 137.41/19.57 | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | (2550) ~ (all_14_2 = e0)
% 137.41/19.57 | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | BETA: splitting (55) gives:
% 137.41/19.57 | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | (2551) ~ (all_16_2 = e0)
% 137.41/19.57 | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | REDUCE: (328), (2551) imply:
% 137.41/19.57 | | | | | | | | | | | | | (2552) ~ (all_6_2 = e0)
% 137.41/19.57 | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | BETA: splitting (61) gives:
% 137.41/19.57 | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | (2553) ~ (all_20_2 = e1)
% 137.41/19.57 | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | REDUCE: (283), (2553) imply:
% 137.41/19.57 | | | | | | | | | | | | | | (2554) ~ (all_6_2 = e1)
% 137.41/19.57 | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 137.41/19.57 | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | (2555) all_54_5 = e3
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2555) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | (2556) all_6_2 = e3
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | REDUCE: (373), (2556) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | (2557) $false
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | CLOSE: (2557) is inconsistent.
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | (2558) ~ (all_54_5 = e3)
% 137.41/19.57 | | | | | | | | | | | | | | | (2559) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | BETA: splitting (2559) gives:
% 137.41/19.57 | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | (2560) all_54_5 = e2
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (2560) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2561) all_6_2 = e2
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | REDUCE: (348), (2561) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2562) ~ (all_52_1 = e2)
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | REDUCE: (355), (2561) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2563) ~ (all_52_7 = e2)
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | REDUCE: (357), (2561) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2564) ~ (all_52_9 = e2)
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | REDUCE: (359), (2561) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2565) ~ (all_52_13 = e2)
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | REDUCE: (373), (2561) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2566) ~ (e3 = e2)
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | REDUCE: (39), (2561) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | (2567) op(e2, e2) = e2
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 137.41/19.57 | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | (2568) ~ (all_22_2 = e1)
% 137.41/19.57 | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | REDUCE: (321), (2568) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | | (2569) ~ (all_14_2 = e1)
% 137.41/19.57 | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 137.41/19.57 | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.57 | | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | | (2570) ~ (all_30_2 = e1)
% 137.41/19.57 | | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | | REDUCE: (2519), (2570) imply:
% 137.41/19.57 | | | | | | | | | | | | | | | | | | (2571) $false
% 137.41/19.57 | | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | | CLOSE: (2571) is inconsistent.
% 137.41/19.57 | | | | | | | | | | | | | | | | | |
% 137.41/19.57 | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.57 | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | (2572) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 137.41/19.58 | | | | | | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 137.41/19.58 | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | (2573) ~ (all_36_2 = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | REDUCE: (305), (2573) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | (2574) ~ (all_14_2 = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | (2575) all_54_0 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (2575) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | (2576) all_14_2 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (2576) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | (2577) ~ (all_52_4 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (345), (2576) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | (2578) ~ (all_52_8 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (2576) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | (2579) ~ (all_52_12 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | (2580) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2580) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | (2581) all_57_0 = e3 & op(e3, e3) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2581) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | (2582) all_57_0 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | (2583) op(e3, e3) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2584) ~ (all_48_2 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (299), (2584) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2585) ~ (all_4_2 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (51), (194), (335), (372), (375),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2540), (2549), (2550), (2585), (function-axioms)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #455.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2586) all_48_2 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2587) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = all_48_1 & $i(all_48_0) &
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (2586) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2588) all_4_2 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (295), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2589) all_50_2 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2590) ~ (all_52_6 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2591) ~ (all_52_8 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2592) ~ (all_52_9 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2593) ~ (all_52_11 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2594) ~ (all_52_14 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2595) ~ (e3 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2596) ~ (e2 = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (2588) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | (2597) op(e1, e1) = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (2598) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2598) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2599) all_57_6 = e0 & op(e1, e3) = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2599) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2600) all_57_6 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (160), (217),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (218), (219), (372), (375), (2525), (2597),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2600), (function-axioms) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #451.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2601) all_57_7 = e0 & op(e1, e2) = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2601) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2602) op(e1, e2) = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (2590), (2602), (function-axioms) are
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | (2603) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2603) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2604) all_57_8 = e0 & op(e1, e1) = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2604) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | (2605) all_57_8 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (2606) all_54_7 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2606) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (2607) all_52_13 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2607) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (2608) all_52_13 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (2608) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (2609) ~ (all_52_9 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (2608) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (2610) ~ (all_52_14 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2610) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (2611) ~ (all_52_14 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2612) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2612) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2613) all_57_6 = e3 & op(e1, e3) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (164),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (168), (169), (170), (211), (223), (225),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (234), (236), (239), (375), (2524), (2539),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540), (2562), (2563), (2567), (2577), (2578),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2583), (2613), (function-axioms) are
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #443.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2614) all_57_7 = e3 & op(e1, e2) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2614) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2615) all_57_7 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2616) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2616) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2617) all_57_4 = e3 & op(e3, e1) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2617) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2618) op(e3, e1) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2578), (2618), (function-axioms) are
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2619) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2619) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2620) all_57_5 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2621) all_54_6 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2609), (2621) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2622) ~ (all_54_6 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2623) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2623) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2624) all_54_6 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2564), (2624) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #762.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2625) ~ (all_54_6 = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2626) all_54_6 = e1 | all_54_6 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2626) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2627) all_54_6 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2627) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2628) all_52_9 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2628) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2629) all_52_9 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2629) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2630) ~ (all_52_1 = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2609), (2629) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2631) ~ (e3 = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2564), (2629) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2632) ~ (e2 = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (167), (225), (2524), (2567),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2620), (2630), (function-axioms) are inconsistent
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #440.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2633) all_54_6 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2592), (2633) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #759.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2634) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2634) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2635) all_57_8 = e3 & op(e1, e1) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2635) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2636) op(e1, e1) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (2636), (function-axioms) are
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2637) all_57_14 = e3 & op(e0, e1) = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2637) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2638) all_57_14 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2639) all_54_6 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2609), (2639) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2640) ~ (all_54_6 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2641) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2641) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2642) all_54_6 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2564), (2642) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #762.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2643) ~ (all_54_6 = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2644) all_54_6 = e1 | all_54_6 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2644) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2645) all_54_6 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2645) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2646) all_52_9 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2646) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2647) all_52_9 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2647) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2648) ~ (all_52_1 = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2609), (2647) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2649) ~ (e3 = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2564), (2647) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2650) ~ (e2 = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2651) all_54_11 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (2651) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2652) all_52_14 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2611), (2652) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2653) $false
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (2653) is inconsistent.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2654) ~ (all_54_11 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2655) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2656) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2656) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2657) all_57_12 = e2 & op(e0, e3) = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2657) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2658) all_57_12 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2655) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2659) all_54_11 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (2659) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2660) all_52_14 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2660) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2661) all_52_14 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (2661) imply:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2662) ~ (all_52_12 = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2663) all_54_3 = e3
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2579), (2663) are inconsistent by
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #439.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2664) ~ (all_54_3 = e3)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2665) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2666) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2666) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2667) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2667) implies:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2668) all_57_6 = e2
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2669) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (2583), (2648), (2669),
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2670) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2670) gives:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2671) all_57_6 = e1 & op(e1, e3) = e1
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2668), (2671) are inconsistent by sub-proof
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.58 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2672) all_57_12 = e1 & op(e0, e3) = e1
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2658), (2672) are inconsistent by sub-proof
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #848.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2673) all_57_7 = e2 & op(e1, e2) = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2615), (2673) are inconsistent by sub-proof
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1084.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2674) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2674) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2675) all_57_8 = e2 & op(e1, e1) = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2675) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2676) op(e1, e1) = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (2676), (function-axioms) are
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2677) all_57_11 = e2 & op(e1, e0) = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2677) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678) all_57_11 = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2679) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (2583), (2648), (2679),
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2680) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2680) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2681) all_57_6 = e1 & op(e1, e3) = e1
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2681) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2682) op(e1, e3) = e1
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2665) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2683) all_54_3 = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2662), (2683) are inconsistent by
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #983.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2684) ~ (all_54_3 = e2)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2685) all_54_3 = e1 | all_54_3 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2685) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2686) all_54_3 = e1
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2523), (2686) are inconsistent by
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #982.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2687) all_54_3 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (2687) imply:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2688) all_52_12 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2688) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2689) all_52_12 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (2689) imply:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2690) ~ (all_52_4 = e0)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2523), (2689) imply:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2691) ~ (e1 = e0)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2692) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (2567), (2690), (2692),
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #714.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2693) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2693) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2694) all_57_7 = e0 & op(e1, e2) = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2694) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2695) all_57_7 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (217), (219), (2605),
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2678), (2695) are inconsistent by sub-proof #436.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2696) all_57_13 = e0 & op(e0, e2) = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2696) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2697) op(e0, e2) = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2698) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2698) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2699) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2699) implies:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2700) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (2682), (2700), (function-axioms) are
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #434.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (2567), (2697),
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2701), (function-axioms) are inconsistent by
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #433.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2702) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (160), (164), (2525), (2540), (2549),
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550), (2565), (2593), (2702), (function-axioms)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #430.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2703) all_57_12 = e1 & op(e0, e3) = e1
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2658), (2703) are inconsistent by sub-proof
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #848.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2704) all_54_11 = e1 | all_54_11 = e0
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (2525), (2594), (2704) are inconsistent by
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #429.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2705) all_57_13 = e2 & op(e0, e2) = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2563), (2705), (function-axioms) are
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2706) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2706) gives:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2707) all_57_14 = e2 & op(e0, e1) = e2
% 137.41/19.59 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2707) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2708) all_57_14 = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2638), (2708) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1011.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2709) all_57_15 = e2 & op(e0, e0) = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2709) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2710) op(e0, e0) = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (2567), (2710),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2711) all_54_6 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2592), (2711) are inconsistent by
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #759.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2712) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2712) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2713) all_57_8 = e3 & op(e1, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2713) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2714) op(e1, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (2714), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2715) all_57_11 = e3 & op(e1, e0) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2715) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2716) op(e1, e0) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2717) all_54_6 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2609), (2717) are inconsistent by
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2718) ~ (all_54_6 = e3)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2719) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2719) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2720) all_54_6 = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2564), (2720) are inconsistent by
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #762.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2721) ~ (all_54_6 = e2)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2722) all_54_6 = e1 | all_54_6 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2722) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2723) all_54_6 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (2723) imply:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2724) all_52_9 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2724) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2725) all_52_9 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (2725) imply:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726) ~ (all_52_1 = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2609), (2725) imply:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2727) ~ (e3 = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2564), (2725) imply:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2728) ~ (e2 = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2729) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2729) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2730) all_57_4 = e3 & op(e3, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2730) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2731) op(e3, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (2578), (2731), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2732) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2732) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2733) all_57_5 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (167), (225), (2524), (2567),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2726), (2733), (function-axioms) are inconsistent
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #440.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2734) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2734) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2735) all_57_8 = e3 & op(e1, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2735) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2736) op(e1, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (2736), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2737) all_57_14 = e3 & op(e0, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2737) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2738) all_57_14 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (106), (160), (165), (169), (222),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (2564), (2587), (2589), (2716), (2738),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #428.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2739) all_54_6 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (2592), (2739) are inconsistent by
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #759.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | (2740) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2741) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2741) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2742) all_57_2 = e3 & op(e2, e3) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2742) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2743) all_57_2 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2744) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2744) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2745) all_57_0 = e1 & op(e3, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2745) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2746) op(e3, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2583), (2746), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2747) all_57_2 = e1 & op(e2, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2743), (2747) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #939.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2748) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2748) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2749) all_57_6 = e1 & op(e1, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2749) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2750) all_57_6 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2751) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2751) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2752) all_57_0 = e0 & op(e3, e3) = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2752) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2753) all_57_0 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (2577), (2578),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2753), (function-axioms) are inconsistent
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1103.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2754) all_57_2 = e0 & op(e2, e3) = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (2743), (2754) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #697.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2755) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2755) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2756) all_57_6 = e0 & op(e1, e3) = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2750), (2756) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #427.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2757) all_57_12 = e0 & op(e0, e3) = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2757) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2758) all_57_12 = e0
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2759) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (2563), (2758), (2759),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #426.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2760) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (36), (164), (169), (223),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (375), (2524), (2539), (2540), (2567),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578), (2743), (2760), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2761) all_57_12 = e1 & op(e0, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2761) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2762) all_57_12 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2763) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (158), (2563), (2762), (2763),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #445.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2764) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (36), (164), (169), (223),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (375), (2524), (2539), (2540), (2567),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578), (2743), (2764), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #425.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2765) all_57_3 = e3 & op(e2, e2) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2765) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2766) op(e2, e2) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2567), (2766), (function-axioms) are
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2767) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2767) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2768) all_57_5 = e3 & op(e2, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2768) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2769) all_57_5 = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2770) op(e2, e1) = e3
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2771) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2771) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2772) all_57_2 = e1 & op(e2, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2772) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2773) all_57_2 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2774) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2774) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2775) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2775) implies:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2776) all_57_6 = e2
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2777) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2777) gives:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2778) all_57_6 = e1 & op(e1, e3) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2776), (2778) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2779) all_57_7 = e1 & op(e1, e2) = e1
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (113), (117), (120), (133), (134), (135),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (158), (160), (165), (169), (201), (202),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203), (206), (209), (220), (260), (270), (271),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272), (372), (375), (2523), (2524), (2525),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526), (2539), (2540), (2549), (2565), (2577),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578), (2579), (2591), (2593), (2740), (2779),
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417.
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2780) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 137.41/19.60 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (2525), (2597), (2780),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2781) all_57_7 = e2 & op(e1, e2) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2781) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2782) all_57_7 = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2783) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2783) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2784) all_57_6 = e1 & op(e1, e3) = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2784) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2785) all_57_6 = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2786) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2786) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2787) all_57_0 = e0 & op(e3, e3) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2787) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2788) all_57_0 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (2577), (2578),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2788), (function-axioms) are inconsistent
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1103.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2789) all_57_2 = e0 & op(e2, e3) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2789) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2790) all_57_2 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2773), (2790) imply:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2791) e1 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2785), (2791) imply:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792) all_57_6 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (160), (217),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (219), (372), (375), (2525), (2597),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2792), (function-axioms) are inconsistent by
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #451.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2793) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2793) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2794) all_57_6 = e0 & op(e1, e3) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2794) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795) all_57_6 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (160), (217),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (219), (372), (375), (2525), (2597),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2795), (function-axioms) are inconsistent by
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #451.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2796) all_57_12 = e0 & op(e0, e3) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2796) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2797) all_57_12 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2798) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (231),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567), (2782), (2798), (function-axioms) are
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #415.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2799) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2799) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2800) all_57_7 = e1 & op(e1, e2) = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2782), (2800) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #864.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2801) all_57_13 = e1 & op(e0, e2) = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2801) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2802) all_57_13 = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2803) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (158), (2563), (2797), (2803),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #426.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2804) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2804) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2805) all_57_14 = e2 & op(e0, e1) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2805) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2806) all_57_14 = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (212), (2526), (2797), (2802),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2806), (function-axioms) are inconsistent by
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #412.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2807) all_57_15 = e2 & op(e0, e0) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2807) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2808) op(e0, e0) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (2567), (2808),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2809) all_57_7 = e1 & op(e1, e2) = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (113), (117), (120), (133), (134), (135),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (158), (160), (165), (169), (201), (202),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (203), (206), (209), (220), (260), (270), (271),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (272), (372), (375), (2523), (2524), (2525),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2526), (2539), (2540), (2549), (2565), (2577),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2578), (2579), (2591), (2593), (2740), (2809),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #417.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2810) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (2525), (2597), (2810),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2811) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2811) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2812) all_57_8 = e2 & op(e1, e1) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2812) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2813) op(e1, e1) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (2813), (function-axioms) are
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2814) all_57_11 = e2 & op(e1, e0) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2814) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2815) op(e1, e0) = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2587), (2770), (2815), (function-axioms) are
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #648.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2816) all_57_3 = e1 & op(e2, e2) = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2816) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2817) op(e2, e2) = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2567), (2817), (function-axioms) are
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2818) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (164), (2524), (2769), (2818),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #441.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2819) all_57_10 = e3 & op(e2, e0) = e3
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2819) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2820) all_57_10 = e3
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2821) all_57_15 = e0 & op(e0, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2821) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2822) op(e0, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (157), (165), (169), (220), (372),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375), (2539), (2540), (2591), (2592), (2593),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2822), (function-axioms) are inconsistent by
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2823) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2823) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2824) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2824) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2825) all_57_9 = e0 & op(e3, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2825) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2826) op(e3, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2740) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2827) all_54_7 = e2
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2565), (2827) are inconsistent by
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1006.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2828) all_54_7 = e1 | all_54_7 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2828) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2829) all_54_7 = e1
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (2524), (2829) are inconsistent by
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #676.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2830) all_54_7 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2830) imply:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2831) all_52_13 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2831) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2832) all_52_13 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2832) imply:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2833) ~ (all_52_12 = e0)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2826), (2833), (function-axioms) are
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2834) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2834) gives:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2835) all_57_10 = e0 & op(e2, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2835) implies:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2836) all_57_10 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2820), (2836) imply:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2837) e3 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2582), (2837) imply:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2838) all_57_0 = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (2577), (2578),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2838), (function-axioms) are inconsistent
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1103.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2839) all_57_11 = e0 & op(e1, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (160),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (168), (169), (170), (211), (217),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (219), (223), (225), (232), (234), (236),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (372), (375), (2524), (2525), (2539),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540), (2562), (2563), (2567), (2577), (2578),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2582), (2583), (2597), (2839),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #409.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (2840) all_57_11 = e0 & op(e1, e0) = e0
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (160),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (164), (167), (168), (169), (170), (211), (217),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (218), (219), (223), (225), (232), (234), (236),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (239), (372), (375), (2524), (2525), (2539),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (2540), (2562), (2563), (2567), (2577), (2578),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (2579), (2582), (2583), (2597), (2840),
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | | #409.
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.61 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | (2841) all_57_1 = e3 & op(e3, e2) = e3
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2841) implies:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | (2842) op(e3, e2) = e3
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (2577), (2842), (function-axioms) are
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (2843) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (2578), (2579), (2843),
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | #1104.
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | (2844) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (2550), (2569), (2574), (2844) are
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | End of split
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | (2845) all_36_2 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (2845) imply:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | (2846) all_14_2 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | SIMP: (2846) implies:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | (2847) all_14_2 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | REDUCE: (51), (2847) imply:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | (2848) op(e3, e3) = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | (2849) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (233), (235),
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | (239), (2564), (2848), (2849), (function-axioms)
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #406.
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | (2850) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | BETA: splitting (2850) gives:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (2851) all_57_8 = e2 & op(e1, e1) = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2851) implies:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (2852) op(e1, e1) = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (2852), (function-axioms) are
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (2853) all_57_14 = e2 & op(e0, e1) = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | ALPHA: (2853) implies:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (2854) all_57_14 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | (2855) op(e0, e1) = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | (2856) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2856) gives:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2857) all_57_6 = e2 & op(e1, e3) = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2857) implies:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2858) all_57_6 = e2
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.41/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2859) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (238),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2848), (2858), (2859), (function-axioms) are
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #402.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2860) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2860) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2861) all_57_6 = e1 & op(e1, e3) = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2858), (2861) are inconsistent by sub-proof
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | #437.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2862) all_57_12 = e1 & op(e0, e3) = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2862) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2863) all_57_12 = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (36), (209), (212),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (372), (375), (2526), (2539), (2540), (2548),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2549), (2567), (2854), (2863), (function-axioms)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #398.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2864) all_57_7 = e2 & op(e1, e2) = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2864) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2865) all_57_7 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2866) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (231),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2567), (2865), (2866), (function-axioms) are
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #415.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2867) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2867) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2868) all_57_7 = e1 & op(e1, e2) = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (2865), (2868) are inconsistent by sub-proof
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | #864.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2869) all_57_13 = e1 & op(e0, e2) = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2869) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2870) all_57_13 = e1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2871) all_57_15 = e0 & op(e0, e0) = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2871) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2872) all_57_15 = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2548), (2872) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2873) e1 = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2870), (2873) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2874) all_57_13 = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (229), (231), (2567),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2865), (2874), (function-axioms) are inconsistent
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #720.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2875) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2875) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2876) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2876) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2877) all_57_12 = e0 & op(e0, e3) = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2877) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2878) all_57_12 = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (212), (2526), (2854), (2870),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2878), (function-axioms) are inconsistent by
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #412.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2879) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2879) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2880) all_57_13 = e0 & op(e0, e2) = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2880) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2881) all_57_13 = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (229), (231), (2567),
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2865), (2881), (function-axioms) are inconsistent
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #720.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2882) all_57_14 = e0 & op(e0, e1) = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (2854), (2882) are inconsistent by sub-proof
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #920.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | (2883) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2883) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2884) all_57_8 = e2 & op(e1, e1) = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2884) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2885) op(e1, e1) = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (2885), (function-axioms) are
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2886) all_57_11 = e2 & op(e1, e0) = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2886) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2887) all_57_11 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2888) op(e1, e0) = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (157), (2855) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2889) all_52_11 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e1, simplifying with (160), (2888) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2890) all_52_14 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (2890) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2891) ~ (all_52_12 = e2)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (2890) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | (2892) ~ (all_4_2 = e2)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2572) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2893) ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 &
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_30_1 & $i(all_30_0) &
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2893) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2894) ~ (all_30_0 = e3)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2895) op(e0, e1) = all_30_1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | (2896) op(all_30_1, e0) = all_30_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2518) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2897) ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) &
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2897) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2898) op(e0, e1) = all_10_1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2899) op(all_10_1, e0) = all_10_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_30_1,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (2855), (2895) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2900) all_30_1 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | all_30_1, e1, e0, simplifying with (2895), (2898)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2901) all_30_1 = all_10_1
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2900), (2901) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2902) all_10_1 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2896), (2900) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2903) op(e2, e0) = all_30_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2899), (2902) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2904) op(e2, e0) = all_10_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | all_10_0, e0, e2, simplifying with (164), (2904)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2905) all_52_13 = all_10_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | all_30_0, e0, e2, simplifying with (164), (2903)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2906) all_52_13 = all_30_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2905), (2906) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2907) all_30_0 = all_10_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2907) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2908) all_30_0 = all_10_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2905) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2909) all_54_7 = all_10_0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2905) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2910) ~ (all_52_1 = all_10_0)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2905) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2911) ~ (all_52_12 = all_10_0)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2565), (2905) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2912) ~ (all_10_0 = e2)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2524), (2905) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2913) ~ (all_10_0 = e1)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2894), (2908) imply:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | (2914) ~ (all_10_0 = e3)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | (2915) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2915) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2916) all_57_9 = e3 & op(e3, e0) = e3
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2916) implies:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2917) all_57_9 = e3
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2918) op(e3, e0) = e3
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2919) all_54_7 = e3
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2909), (2914), (2919) are inconsistent by
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #397.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2920) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2920) gives:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2921) all_54_7 = e2
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2909), (2912), (2921) are inconsistent by
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #396.
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.62 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2922) ~ (all_54_7 = e2)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923) all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2923) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2924) all_54_7 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2909), (2913), (2924) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #395.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2925) all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2909), (2925) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2926) all_10_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2926) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2927) all_10_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2910), (2927) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2928) ~ (all_52_1 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2911), (2927) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2929) ~ (all_52_12 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2912), (2927) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2930) ~ (e2 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (51), (103), (117), (120), (133),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (164), (165), (167), (168), (169), (170),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (201), (206), (215), (223), (224), (225),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260), (270), (299), (335), (363), (372), (375),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523), (2524), (2525), (2526), (2540), (2549),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550), (2562), (2565), (2567), (2848), (2854),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2855), (2887), (2888), (2891), (2917), (2918),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2923), (2928), (2929), (function-axioms) are
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #388.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2931) all_57_10 = e3 & op(e2, e0) = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2931) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2932) all_57_10 = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2933) all_54_7 = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2909), (2914), (2933) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #397.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2934) ~ (all_54_7 = e3)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2935) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2935) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2936) all_54_7 = e2
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2909), (2912), (2936) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #396.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2937) ~ (all_54_7 = e2)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2938) all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2938) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2939) all_54_7 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2909), (2913), (2939) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #395.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2940) all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2909), (2940) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2941) all_10_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2941) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2942) all_10_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2910), (2942) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2943) ~ (all_52_1 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2914), (2942) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2944) ~ (e3 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2912), (2942) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2945) ~ (e2 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (117), (165), (167), (224), (260), (2524),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567), (2932), (2938), (2943), (2945),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #387.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (2946) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2526), (2887), (2946),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | #385.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2947) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2947) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2948) ~ (all_10_1 = e3)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2949) op(e0, e1) = all_10_1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_30_1,
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (2855), (2895) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2950) all_30_1 = e2
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | all_30_1, e1, e0, simplifying with (2895), (2949)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2951) all_30_1 = all_10_1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2950), (2951) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2952) all_10_1 = e2
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2896), (2950) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2953) op(e2, e0) = all_30_0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | all_30_0, e0, e2, simplifying with (164), (2953)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2954) all_52_13 = all_30_0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (2954) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2955) all_54_7 = all_30_0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (2954) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2956) ~ (all_52_1 = all_30_0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (2954) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2957) ~ (all_52_12 = all_30_0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2565), (2954) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2958) ~ (all_30_0 = e2)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2524), (2954) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | (2959) ~ (all_30_0 = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (2960) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2960) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2961) all_57_9 = e3 & op(e3, e0) = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2961) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2962) all_57_9 = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2963) op(e3, e0) = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2964) all_54_7 = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2894), (2955), (2964) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #384.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2965) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2965) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2966) all_54_7 = e2
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2955), (2958), (2966) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #383.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2967) ~ (all_54_7 = e2)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2968) all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2968) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2969) all_54_7 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2955), (2959), (2969) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #382.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2970) all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2955), (2970) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2971) all_30_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2971) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2972) all_30_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2956), (2972) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2973) ~ (all_52_1 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2957), (2972) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2974) ~ (all_52_12 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2958), (2972) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2975) ~ (e2 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (51), (103), (117), (120), (133),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (160), (164), (165), (167), (168), (169), (170),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (194), (201), (206), (215), (223), (224), (225),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (260), (270), (299), (335), (363), (372), (375),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2523), (2524), (2525), (2526), (2540), (2549),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2550), (2562), (2565), (2567), (2848), (2854),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2855), (2887), (2888), (2891), (2962), (2963),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2968), (2973), (2974), (function-axioms) are
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #388.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2976) all_57_10 = e3 & op(e2, e0) = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2976) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | (2977) all_57_10 = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2978) all_54_7 = e3
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2894), (2955), (2978) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #384.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2979) ~ (all_54_7 = e3)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2980) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2980) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2981) all_54_7 = e2
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2955), (2958), (2981) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #383.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2982) ~ (all_54_7 = e2)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2983) all_54_7 = e1 | all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2983) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2984) all_54_7 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2955), (2959), (2984) are inconsistent by
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #382.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2985) all_54_7 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2955), (2985) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2986) all_30_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (2986) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2987) all_30_0 = e0
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2956), (2987) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2988) ~ (all_52_1 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2894), (2987) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2989) ~ (e3 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2958), (2987) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2990) ~ (e2 = e0)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (117), (165), (167), (224), (260), (2524),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567), (2977), (2983), (2988), (2990),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #387.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (2991) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2526), (2887), (2991),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | | #393.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (2992) ~ (all_30_1 = e2) & op(e0, e1) = all_30_1 &
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (2992) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (2993) ~ (all_30_1 = e2)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | (2994) op(e0, e1) = all_30_1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2518), (2855), (2993), (2994), (function-axioms)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | End of split
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | (2995) all_22_2 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | (2996) ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0
% 137.71/19.63 | | | | | | | | | | | | | | | | | & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 137.71/19.63 | | | | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e3, e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | COMBINE_EQS: (321), (2995) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | (2997) all_14_2 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | SIMP: (2997) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | (2998) all_14_2 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | COMBINE_EQS: (313), (2998) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | (2999) all_34_2 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | REDUCE: (337), (2998) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | (3000) ~ (all_52_1 = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | REDUCE: (343), (2998) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | (3001) ~ (all_52_4 = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | REDUCE: (51), (2998) imply:
% 137.71/19.63 | | | | | | | | | | | | | | | | | (3002) op(e3, e3) = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | (3003) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (2567), (3000), (3003),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.63 | | | | | | | | | | | | | | | | | | #442.
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | (3004) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 137.71/19.63 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | BETA: splitting (3004) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | (3005) all_57_5 = e1 & op(e2, e1) = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | ALPHA: (3005) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | (3006) op(e2, e1) = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | (3007) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (2567), (3001), (3007),
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | #379.
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | (3008) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3008) gives:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | (3009) all_57_7 = e1 & op(e1, e2) = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3009) implies:
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | (3010) all_57_7 = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | | (3011) op(e1, e2) = e1
% 137.71/19.63 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (3011) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3012) all_52_6 = e1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (3006) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3013) all_52_9 = e1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (126), (3012) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3014) ~ (all_52_14 = e1)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (3013) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3015) ~ (all_52_13 = e1)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3013) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3016) ~ (all_4_2 = e1)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | SIMP: (3016) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3017) ~ (all_4_2 = e1)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | REDUCE: (2564), (3013) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | (3018) ~ (e2 = e1)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | (3019) all_54_10 = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (3019) are inconsistent by sub-proof
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | #1112.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | (3020) ~ (all_54_10 = e3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | (3021) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3021) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | (3022) all_54_10 = e2
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (3022) are inconsistent by sub-proof
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | #1111.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | (3023) ~ (all_54_10 = e2)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | (3024) all_54_10 = e1 | all_54_10 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3024) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3025) all_54_10 = e1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (3017), (3025) are inconsistent by
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #378.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3026) all_54_10 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (3026) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3027) all_4_2 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3027) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3028) all_4_2 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (3028) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3029) ~ (all_52_11 = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3028) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3030) ~ (e2 = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3017), (3028) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3031) ~ (e1 = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3028) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | (3032) op(e1, e1) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (3033) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3033) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3034) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3034) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3035) op(e3, e3) = all_56_9
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3036) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3037) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3038) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3039) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | (3040) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3036) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3041) all_56_15 = e3 & op(e0, e0) = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3041) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3042) op(e0, e0) = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2526), (3042), (function-axioms) are
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3043) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3043) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3044) ~ (all_56_10 = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3045) op(e0, e3) = all_56_10
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3038) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3046) all_56_11 = e3 & op(e2, e2) = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3046) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3047) op(e2, e2) = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (2567), (3047), (function-axioms) are
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3048) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3048) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3049) op(e2, e3) = all_56_3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3039) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3050) all_56_6 = e1 & op(e1, e3) = e1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3050) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3051) op(e1, e3) = e1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (3037), (3051), (function-axioms) are
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #434.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3052) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3052) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3053) ~ (all_56_13 = e3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3054) op(e1, e1) = all_56_13
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3040) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3055) all_56_3 = e2 & op(e2, e3) = e2
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3055) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3056) op(e2, e3) = e2
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (2562), (3056), (function-axioms) are
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #882.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3057) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3057) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3058) ~ (all_56_11 = e3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3059) op(e2, e2) = all_56_11
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10, e3, e0, simplifying with (159), (3045)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3060) all_56_10 = all_52_3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (3032), (3054)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3061) all_56_13 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (2567), (3059)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3062) all_56_11 = e2
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_3, e3, e2, simplifying with (167), (3049)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3063) all_56_3 = all_52_1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_9,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3002), (3035) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3064) all_56_9 = e1
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3044), (3060) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3065) ~ (all_52_3 = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3053), (3061) imply:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3066) ~ (e3 = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3067) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3067) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3068) all_57_0 = e0 & op(e3, e3) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3068) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3069) op(e3, e3) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3002), (3069), (function-axioms) are
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3070) all_57_2 = e0 & op(e2, e3) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3070) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3071) all_57_2 = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3072) op(e2, e3) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3073) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (2567), (3071), (3073),
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #727.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3074) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3074) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3075) all_57_5 = e3 & op(e2, e1) = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3075) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3076) all_57_5 = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (167), (225), (2524), (2567),
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3000), (3076), (function-axioms) are inconsistent
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #440.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3077) all_57_10 = e3 & op(e2, e0) = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3077) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3078) all_57_10 = e3
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3079) all_57_15 = e0 & op(e0, e0) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3079) implies:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3080) op(e0, e0) = e0
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (372), (375), (2539), (2540), (3032),
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3080), (function-axioms) are inconsistent by
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #745.
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3081) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.64 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3081) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3082) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3083) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3082) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3084) all_57_12 = e0 & op(e0, e3) = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3084) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3085) op(e0, e3) = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3065), (3085), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3086) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3086) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3087) all_57_13 = e0 & op(e0, e2) = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3087) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3088) all_57_13 = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3083) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3089) all_57_9 = e0 & op(e3, e0) = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3089) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3090) all_57_9 = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3091) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3091) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3092) all_57_0 = e2 & op(e3, e3) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3092) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3093) op(e3, e3) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3002), (3093), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3094) all_57_1 = e2 & op(e3, e2) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3094) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3095) all_57_1 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3096) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (2565), (3090), (3096),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3097) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3097) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3098) all_57_11 = e2 & op(e1, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3098) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099) all_57_11 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3100) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3100) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3101) all_57_6 = e3 & op(e1, e3) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3101) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102) all_57_6 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3103) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3103) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3104) all_57_0 = e3 & op(e3, e3) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3104) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3105) op(e3, e3) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3002), (3105), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3106) all_57_1 = e3 & op(e3, e2) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3106) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3107) all_57_1 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3095), (3107) imply:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3108) e3 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (219), (375), (3010), (3099),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3102), (3108), (function-axioms) are inconsistent
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #376.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3109) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3109) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3110) all_57_4 = e3 & op(e3, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3110) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3111) all_57_4 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (36), (219), (231), (239), (375),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567), (3002), (3010), (3088), (3090), (3095),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099), (3102), (3111), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #374.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3112) all_57_9 = e3 & op(e3, e0) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (36), (219), (375), (3010), (3090),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3099), (3102), (3112), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #373.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3113) all_57_7 = e3 & op(e1, e2) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3010), (3113) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #586.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3114) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (375), (3099), (3114),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #861.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3115) all_57_15 = e2 & op(e0, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3115) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3116) op(e0, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (2567), (3116),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3117) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3117) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3118) all_57_4 = e2 & op(e3, e1) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3118) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3119) all_57_4 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3120) op(e3, e1) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3121) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (164), (2565), (3090), (3121),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #377.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3122) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3122) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3123) all_57_11 = e2 & op(e1, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3123) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124) all_57_11 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3125) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3125) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3126) all_57_6 = e3 & op(e1, e3) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3126) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127) all_57_6 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3128) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3128) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3129) all_57_0 = e3 & op(e3, e3) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3129) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3130) op(e3, e3) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3002), (3130), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3131) all_57_1 = e3 & op(e3, e2) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3131) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3132) all_57_1 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3133) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3133) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3134) all_57_4 = e3 & op(e3, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3134) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3135) all_57_4 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3119), (3135) imply:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3136) e3 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3136) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3137) e3 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3132), (3137) imply:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3138) all_57_1 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (36), (219), (231), (239), (375),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2567), (3002), (3010), (3088), (3090), (3124),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127), (3135), (3138), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #374.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3139) all_57_5 = e3 & op(e2, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3139) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3140) all_57_5 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (167), (225), (2524), (2567),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3000), (3140), (function-axioms) are inconsistent
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #440.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3141) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3141) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3142) all_57_8 = e3 & op(e1, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3142) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3143) op(e1, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (3143), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3144) all_57_14 = e3 & op(e0, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3144) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3145) op(e0, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (82), (157), (167), (169), (2518), (2519),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2996), (2999), (3072), (3120), (3145),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #369.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3146) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3146) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3147) all_57_4 = e3 & op(e3, e1) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3147) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3148) all_57_4 = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3119), (3148) imply:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3149) e3 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (36), (219), (375), (3010), (3124),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3127), (3149), (function-axioms) are inconsistent
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #376.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3150) all_57_9 = e3 & op(e3, e0) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (36), (219), (375), (3010), (3090),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3124), (3127), (3150), (function-axioms) are
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #373.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3151) all_57_7 = e3 & op(e1, e2) = e3
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3010), (3151) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #586.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3152) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (375), (3124), (3152),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #861.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3153) all_57_15 = e2 & op(e0, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3153) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3154) op(e0, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (2567), (3154),
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3155) all_57_9 = e2 & op(e3, e0) = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3155) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3156) all_57_9 = e2
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3090), (3156) imply:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3157) e2 = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (3157) imply:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3158) $false
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3158) is inconsistent.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3159) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3159) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3160) all_57_10 = e0 & op(e2, e0) = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3160) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3161) all_57_10 = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3078), (3161) are inconsistent by sub-proof
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #935.
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3162) all_57_11 = e0 & op(e1, e0) = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3162) implies:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3163) all_57_11 = e0
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.65 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3164) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3164) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3165) all_57_6 = e3 & op(e1, e3) = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3165) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3166) all_57_6 = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3167) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3167) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3168) all_57_9 = e2 & op(e3, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3168) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3169) all_57_9 = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3170) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (229), (231), (2567),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3088), (3166), (3170), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #719.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3171) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3171) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3172) all_57_8 = e2 & op(e1, e1) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3172) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3173) op(e1, e1) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (3173), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3174) all_57_11 = e2 & op(e1, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3174) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175) all_57_11 = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3176) all_57_15 = e0 & op(e0, e0) = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (372), (375), (2539), (2540),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548), (2549), (2567), (3176), (function-axioms)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #401.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (215), (2526), (3083), (3169),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3175), (function-axioms) are inconsistent by
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #367.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3177) all_57_10 = e2 & op(e2, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3177) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3178) op(e2, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2565), (3178), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3179) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3179) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3180) all_57_11 = e2 & op(e1, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3180) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3181) all_57_11 = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3163), (3181) are inconsistent by sub-proof
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #996.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3182) all_57_15 = e2 & op(e0, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3182) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3183) op(e0, e0) = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (2567), (3183),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #643.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3184) all_57_7 = e3 & op(e1, e2) = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (36), (160), (217),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (372), (2525), (3032), (3163), (3184),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #410.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3185) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3185) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3186) all_57_8 = e3 & op(e1, e1) = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3186) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3187) op(e1, e1) = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (3187), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3188) all_57_11 = e3 & op(e1, e0) = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3188) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3189) all_57_11 = e3
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3163), (3189) are inconsistent by sub-proof
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #858.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3190) all_57_14 = e0 & op(e0, e1) = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3190) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3191) op(e0, e1) = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3029), (3191), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3192) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3192) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3193) all_57_6 = e0 & op(e1, e3) = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3193) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3194) all_57_6 = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (36), (218), (219),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (375), (3010), (3194), (function-axioms)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #453.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3195) all_57_12 = e0 & op(e0, e3) = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3195) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3196) op(e0, e3) = e0
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3065), (3196), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (3197) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3197) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | (3198) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (3011), (3198), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (3199) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (157), (160), (164), (2525), (2540), (2549),
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | (2550), (2565), (3029), (3199), (function-axioms)
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #430.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | (3200) all_57_13 = e1 & op(e0, e2) = e1
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (2521), (3200), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | (3201) all_57_10 = e1 & op(e2, e0) = e1
% 137.71/19.66 | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2524), (3201), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 137.71/19.66 | | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | (3202) all_54_5 = e1 | all_54_5 = e0
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | REF_CLOSE: (268), (2552), (2554), (3202) are inconsistent by
% 137.71/19.66 | | | | | | | | | | | | | | | | sub-proof #641.
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | End of split
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | Case 2:
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | (3203) all_20_2 = e1
% 137.71/19.66 | | | | | | | | | | | | | | (3204) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0
% 137.71/19.66 | | | | | | | | | | | | | | & op(e2, e1) = all_20_1 & $i(all_20_0) &
% 137.71/19.66 | | | | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1)
% 137.71/19.66 | | | | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | COMBINE_EQS: (283), (3203) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3205) all_6_2 = e1
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | SIMP: (3205) implies:
% 137.71/19.66 | | | | | | | | | | | | | | (3206) all_6_2 = e1
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | COMBINE_EQS: (332), (3206) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3207) all_38_2 = e1
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | REDUCE: (348), (3206) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3208) ~ (all_52_1 = e1)
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | REDUCE: (351), (3206) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3209) ~ (all_52_4 = e1)
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | REDUCE: (357), (3206) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3210) ~ (all_52_9 = e1)
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | REDUCE: (373), (3206) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3211) ~ (e3 = e1)
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | REDUCE: (39), (3206) imply:
% 137.71/19.66 | | | | | | | | | | | | | | (3212) op(e2, e2) = e1
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 137.71/19.66 | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | (3213) ~ (all_22_2 = e1)
% 137.71/19.66 | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | REDUCE: (321), (3213) imply:
% 137.71/19.66 | | | | | | | | | | | | | | | (3214) ~ (all_14_2 = e1)
% 137.71/19.66 | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 137.71/19.66 | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | (3215) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 137.71/19.66 | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | BETA: splitting (3215) gives:
% 137.71/19.66 | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.66 | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | (3216) all_57_0 = e1 & op(e3, e3) = e1
% 137.71/19.66 | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | ALPHA: (3216) implies:
% 137.71/19.66 | | | | | | | | | | | | | | | | | (3217) op(e3, e3) = e1
% 137.71/19.66 | | | | | | | | | | | | | | | | |
% 137.71/19.66 | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (3214), (3217), (function-axioms) are
% 137.71/19.66 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #365.
% 137.71/19.66 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | (3218) all_57_2 = e1 & op(e2, e3) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3208), (3218), (function-axioms) are
% 137.71/19.67 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #846.
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | End of split
% 137.71/19.67 | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | Case 2:
% 137.71/19.67 | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | (3219) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 137.71/19.67 | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 137.71/19.67 | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | BETA: splitting (3219) gives:
% 137.71/19.67 | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | (3220) all_57_6 = e1 & op(e1, e3) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | ALPHA: (3220) implies:
% 137.71/19.67 | | | | | | | | | | | | | | | | | (3221) all_57_6 = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | (3222) op(e1, e3) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 137.71/19.67 | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | (3223) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | BETA: splitting (3223) gives:
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | (3224) all_57_0 = e1 & op(e3, e3) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | ALPHA: (3224) implies:
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | (3225) op(e3, e3) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2, e1,
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (51), (3225) gives:
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | (3226) all_14_2 = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (3214), (3226) imply:
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | (3227) $false
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | CLOSE: (3227) is inconsistent.
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | (3228) all_57_1 = e1 & op(e3, e2) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3209), (3228), (function-axioms) are
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #844.
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | End of split
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | Case 2:
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | (3229) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | BETA: splitting (3229) gives:
% 137.71/19.67 | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | Case 1:
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | (3230) all_57_4 = e1 & op(e3, e1) = e1
% 137.71/19.67 | | | | | | | | | | | | | | | | | | |
% 137.71/19.67 | | | | | | | | | | | | | | | | | | | ALPHA: (3230) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3231) all_57_4 = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3232) op(e3, e1) = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (3222) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3233) all_52_2 = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (3232) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3234) all_52_8 = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3233) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3235) ~ (all_52_14 = e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (120), (3234) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3236) ~ (all_52_12 = e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (345), (3234) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3237) ~ (all_14_2 = e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3234) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3238) ~ (all_4_2 = e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | SIMP: (3238) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | (3239) ~ (all_4_2 = e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | (3240) all_54_10 = e3
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (3240) are inconsistent by sub-proof
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | #1112.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | (3241) ~ (all_54_10 = e3)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | (3242) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | BETA: splitting (3242) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | (3243) all_54_10 = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (3243) are inconsistent by sub-proof
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | #1111.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | (3244) ~ (all_54_10 = e2)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | (3245) all_54_10 = e1 | all_54_10 = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3245) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3246) all_54_10 = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (3239), (3246) are inconsistent by
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | sub-proof #378.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3247) all_54_10 = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (3247) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3248) all_4_2 = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | SIMP: (3248) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3249) all_4_2 = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3250) all_48_2 = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3251) ~ (all_52_6 = e0)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3252) ~ (all_52_9 = e0)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3253) ~ (all_52_11 = e0)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3254) ~ (e3 = e0)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3239), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3255) ~ (e1 = e0)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3249) imply:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | (3256) op(e1, e1) = e0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (3257) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3257) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3258) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3258) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3259) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (3222), (3259), (function-axioms) are
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #434.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3260) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3260) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3261) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3262) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3263) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3264) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | (3265) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3264) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3266) all_56_7 = e1 & op(e1, e2) = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3266) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3267) op(e1, e2) = e1
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (3262), (3267), (function-axioms) are
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3268) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3268) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3269) ~ (all_56_13 = e2)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | (3270) op(e1, e1) = all_56_13
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3261) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3271) all_56_15 = e2 & op(e0, e0) = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3271) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3272) op(e0, e0) = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (2539), (2540), (3212), (3272),
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | #526.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3273) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3273) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3274) ~ (all_56_12 = e0)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | (3275) op(e0, e2) = all_56_12
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3262) gives:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3276) all_56_13 = e2 & op(e1, e1) = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3276) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3277) op(e1, e1) = e2
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (3277), (function-axioms) are
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3278) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3278) implies:
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3279) ~ (all_56_7 = e1)
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3280) op(e1, e2) = all_56_7
% 138.31/19.67 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_12, e2, e0, simplifying with (158), (3275)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3281) all_56_12 = all_52_7
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (3256), (3270)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3282) all_56_13 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_7, e2, e1, simplifying with (162), (3280)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3283) all_56_7 = all_52_6
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3274), (3281) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3284) ~ (all_52_7 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3269), (3282) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3285) ~ (e2 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3286) all_57_15 = e0 & op(e0, e0) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3286) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3287) op(e0, e0) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (372), (375), (2539), (2540), (3256),
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3287), (function-axioms) are inconsistent by
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #745.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3288) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3288) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3289) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3290) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3291) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3291) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3292) all_57_1 = e0 & op(e3, e2) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3292) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3293) all_57_1 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3294) op(e3, e2) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3289) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3295) all_57_12 = e0 & op(e0, e3) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3295) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3296) all_57_12 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3297) op(e0, e3) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (3297) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3298) all_52_3 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (3294) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3299) all_52_4 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (3298) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3300) ~ (all_52_1 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (3299) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3301) ~ (all_52_6 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (3299) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3302) ~ (all_52_7 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (3299) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3303) ~ (all_52_12 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3303) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3304) ~ (all_52_12 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (343), (3299) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3305) ~ (all_14_2 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3290) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3306) all_57_9 = e0 & op(e3, e0) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3306) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3307) op(e3, e0) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3304), (3307), (function-axioms) are
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3308) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3308) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3309) all_57_10 = e0 & op(e2, e0) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3309) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3310) all_57_10 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3311) op(e2, e0) = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3265) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3312) all_56_0 = e3 & op(e3, e2) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3312) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3313) op(e3, e2) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (135), (136), (158), (162), (170), (191),
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (248), (258), (2521), (3251), (3274),
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3275), (3279), (3280), (3313), (function-axioms)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #361.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3314) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3314) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3315) ~ (all_56_9 = e2)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3316) op(e3, e3) = all_56_9
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3263) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3317) all_56_9 = e2 & op(e3, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3317) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3318) op(e3, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3315), (3316), (3318), (function-axioms) are
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3319) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3319) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3320) op(e3, e2) = all_56_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (3311) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3321) all_52_13 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (3294), (3320) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3322) all_56_0 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_2,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_9, e3, e3, simplifying with (51), (3316)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3323) all_56_9 = all_14_2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3315), (3323) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3324) ~ (all_14_2 = e2)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3325) all_54_0 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3325) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3326) all_14_2 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (3326) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3327) ~ (all_52_12 = e3)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (51), (3326) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3328) op(e3, e3) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3329) all_54_3 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (3329) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3330) all_52_12 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3327), (3330) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3331) $false
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3331) is inconsistent.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3332) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3333) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3333) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3334) all_57_2 = e3 & op(e2, e3) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3334) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3335) all_57_2 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3336) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3336) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3337) all_57_0 = e2 & op(e3, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3337) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3338) op(e3, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3328), (3338), (function-axioms) are
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3339) all_57_2 = e2 & op(e2, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3335), (3339) are inconsistent by sub-proof
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #635.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3340) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3340) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3341) all_57_6 = e2 & op(e1, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3341) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3342) all_57_6 = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3221), (3342) are inconsistent by sub-proof
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #700.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3343) all_57_12 = e2 & op(e0, e3) = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3343) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3344) all_57_12 = e2
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3296), (3344) are inconsistent by sub-proof
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1025.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3345) all_57_3 = e3 & op(e2, e2) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3345) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3346) op(e2, e2) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (373), (3346), (function-axioms) are
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3347) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3347) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3348) all_57_5 = e3 & op(e2, e1) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3348) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3349) op(e2, e1) = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3350) ~ (all_38_2 = e1)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3207), (3350) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3351) $false
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3351) is inconsistent.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3352) ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e2, e1)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3352) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3353) ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_38_1 & $i(all_38_0) &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3353) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3354) ~ (all_38_0 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3355) op(e2, e1) = all_38_1
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3356) op(all_38_1, e2) = all_38_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3204) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3357) ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e1) = all_20_1 & $i(all_20_0) &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3357) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3358) op(e2, e1) = all_20_1
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3359) op(all_20_1, e2) = all_20_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3332) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, e1, e2, simplifying with (3355), (3358)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3360) all_38_1 = all_20_1
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_1,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (3349), (3355) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3361) all_38_1 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3360), (3361) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3362) all_20_1 = e3
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3356), (3361) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3363) op(e3, e2) = all_38_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3359), (3362) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3364) op(e3, e2) = all_20_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (3294), (3363) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3365) all_38_0 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_0,
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_0, e2, e3, simplifying with (3363), (3364)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3366) all_38_0 = all_20_0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3365), (3366) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3367) all_20_0 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3354), (3365) imply:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3368) $false
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3368) is inconsistent.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3369) all_54_3 = e1 | all_54_3 = e0
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (2523), (3304), (3369) are inconsistent by
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #418.
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3370) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 &
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3370) implies:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3371) op(e2, e1) = all_20_1
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3372) ~ (all_48_2 = e0)
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.68 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3250), (3372) imply:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3373) $false
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3373) is inconsistent.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_20_1,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_38_1, e1, e2, simplifying with (3355), (3371)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3374) all_38_1 = all_20_1
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_38_1,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (3349), (3355) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3375) all_38_1 = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3374), (3375) imply:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3376) all_20_1 = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3356), (3375) imply:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3377) op(e3, e2) = all_38_0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_38_0,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (3294), (3377) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3378) all_38_0 = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3354), (3378) imply:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3379) $false
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3379) is inconsistent.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3380) ~ (all_38_1 = e3) & op(e2, e1) = all_38_1 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_38_1)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3380) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3381) ~ (all_38_1 = e3)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3382) op(e2, e1) = all_38_1
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3204), (3349), (3381), (3382), (function-axioms)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #359.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3383) all_57_10 = e3 & op(e2, e0) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3383) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3384) all_57_10 = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3310), (3384) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #935.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3385) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (2550), (3214), (3324), (3385) are
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3386) all_57_11 = e0 & op(e1, e0) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3386) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3387) all_57_11 = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3388) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3388) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3389) all_57_2 = e0 & op(e2, e3) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (3300), (3389), (function-axioms) are
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1028.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3390) all_57_3 = e0 & op(e2, e2) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3390) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3391) op(e2, e2) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (126), (157),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (160), (162), (164), (165), (167), (169),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (194), (206), (209), (211), (212), (220),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (229), (335), (362), (363), (365), (372),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375), (2524), (2526), (2539), (2540), (2548),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549), (3208), (3209), (3252), (3284), (3391),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #354.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3392) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3392) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3393) all_57_5 = e0 & op(e2, e1) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3393) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3394) op(e2, e1) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3252), (3394), (function-axioms) are
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3395) all_57_10 = e0 & op(e2, e0) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3395) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3396) all_57_10 = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3265) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3397) all_56_0 = e3 & op(e3, e2) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3397) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3398) op(e3, e2) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (135), (136), (158), (162), (170), (191),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (248), (258), (2521), (3251), (3274),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3275), (3279), (3280), (3398), (function-axioms)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #361.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3399) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3399) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3400) ~ (all_56_9 = e2)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401) op(e3, e3) = all_56_9
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3402) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3402) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3403) all_57_9 = e3 & op(e3, e0) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3403) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3404) all_57_9 = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (237), (3231), (3293), (3400),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3401), (3404), (function-axioms) are inconsistent
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #352.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3405) all_57_10 = e3 & op(e2, e0) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3396), (3405) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3406) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3406) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3407) all_57_11 = e3 & op(e1, e0) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3387), (3407) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #957.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3408) all_57_15 = e3 & op(e0, e0) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3408) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3409) op(e0, e0) = e3
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2526), (3409), (function-axioms) are
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3410) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (3253), (3284), (3410),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #885.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3411) all_57_3 = e0 & op(e2, e2) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3411) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3412) op(e2, e2) = e0
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (126), (157),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (160), (162), (164), (165), (167), (169),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (194), (206), (209), (211), (212), (220),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (225), (229), (335), (362), (363), (365), (372),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (375), (2524), (2526), (2539), (2540), (2548),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2549), (3208), (3209), (3252), (3284), (3412),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #354.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3413) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (3251), (3284), (3413),
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #464.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (3414) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3414) gives:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | (3415) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3415) implies:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | (3416) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2549), (3253), (3416), (function-axioms)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #432.
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | (3417) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 138.31/19.69 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3417) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | (3418) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3418) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (3419) all_56_8 = e1 & op(e1, e0) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3419) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (3420) op(e1, e0) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2525), (3420), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (3421) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3421) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | (3422) ~ (all_56_13 = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2540) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (3423) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3423) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3424) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3424) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3425) op(e3, e3) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (2550), (3425), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1125.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3426) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3426) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3427) op(e2, e2) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3212), (3427), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | (3428) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3422), (3428) are inconsistent by sub-proof #947.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3429) all_57_9 = e1 & op(e3, e0) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2523), (3429), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3430) all_57_12 = e1 & op(e0, e3) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2520), (3430), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | (3431) all_22_2 = e1
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | COMBINE_EQS: (321), (3431) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | (3432) all_14_2 = e1
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | REDUCE: (345), (3432) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | (3433) ~ (all_52_8 = e1)
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | REDUCE: (51), (3432) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | (3434) op(e3, e3) = e1
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | (3435) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | BETA: splitting (3435) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3436) all_57_4 = e1 & op(e3, e1) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3433), (3436), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3437) all_57_5 = e1 & op(e2, e1) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3210), (3437), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | (3438) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 138.31/19.70 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | BETA: splitting (3438) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3439) all_57_8 = e1 & op(e1, e1) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | ALPHA: (3439) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3440) op(e1, e1) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2, e1,
% 138.31/19.70 | | | | | | | | | | | | | | | | | e1, e1, simplifying with (36), (3440) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3441) all_4_2 = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | BETA: splitting (2540) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3442) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 138.31/19.70 | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | BETA: splitting (3442) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3443) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | ALPHA: (3443) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3444) op(e3, e3) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3434), (3444), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3445) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | ALPHA: (3445) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3446) op(e2, e2) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3212), (3446), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3447) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 138.31/19.70 | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3440), (3447), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #965.
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3448) all_57_14 = e1 & op(e0, e1) = e1
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2522), (3448), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | End of split
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | (3449) all_16_2 = e0
% 138.31/19.70 | | | | | | | | | | | | | (3450) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0
% 138.31/19.70 | | | | | | | | | | | | | & op(e2, e0) = all_16_1 & $i(all_16_0) &
% 138.31/19.70 | | | | | | | | | | | | | $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0)
% 138.31/19.70 | | | | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | COMBINE_EQS: (328), (3449) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3451) all_6_2 = e0
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | SIMP: (3451) implies:
% 138.31/19.70 | | | | | | | | | | | | | (3452) all_6_2 = e0
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | COMBINE_EQS: (326), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3453) all_18_2 = e0
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (348), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3454) ~ (all_52_1 = e0)
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (351), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3455) ~ (all_52_4 = e0)
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (353), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3456) ~ (all_52_6 = e0)
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (355), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3457) ~ (all_52_7 = e0)
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (357), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3458) ~ (all_52_9 = e0)
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (373), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3459) ~ (e3 = e0)
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | REDUCE: (39), (3452) imply:
% 138.31/19.70 | | | | | | | | | | | | | (3460) op(e2, e2) = e0
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | BETA: splitting (58) gives:
% 138.31/19.70 | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | (3461) ~ (all_18_2 = e0)
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | REDUCE: (3453), (3461) imply:
% 138.31/19.70 | | | | | | | | | | | | | | (3462) $false
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | CLOSE: (3462) is inconsistent.
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | (3463) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0
% 138.31/19.70 | | | | | | | | | | | | | | & op(e2, e0) = all_18_1 & $i(all_18_0) &
% 138.31/19.70 | | | | | | | | | | | | | | $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0)
% 138.31/19.70 | | | | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 138.31/19.70 | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | (3464) ~ (all_22_2 = e1)
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | REDUCE: (321), (3464) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | (3465) ~ (all_14_2 = e1)
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 138.31/19.70 | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | (3466) ~ (all_36_2 = e2)
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | REDUCE: (305), (3466) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | (3467) ~ (all_14_2 = e2)
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3468) all_54_0 = e3
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (3468) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3469) all_14_2 = e3
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REDUCE: (343), (3469) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3470) ~ (all_52_4 = e3)
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REDUCE: (345), (3469) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3471) ~ (all_52_8 = e3)
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REDUCE: (347), (3469) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3472) ~ (all_52_12 = e3)
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | REDUCE: (51), (3469) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | (3473) op(e3, e3) = e3
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3474) ~ (all_48_2 = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (299), (3474) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3475) ~ (all_4_2 = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (51), (194), (335), (372), (375),
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (2540), (2549), (2550), (3475), (function-axioms)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #455.
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3476) all_48_2 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3476) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3477) all_4_2 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (362), (3477) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3478) ~ (all_52_8 = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (365), (3477) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3479) ~ (all_52_11 = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | REDUCE: (36), (3477) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | (3480) op(e1, e1) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3481) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (3455), (3470),
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3471), (3472), (3481), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1101.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | (3482) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | BETA: splitting (3482) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | (3483) all_57_4 = e0 & op(e3, e1) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (3478), (3483), (function-axioms) are
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | (3484) all_57_9 = e0 & op(e3, e0) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | ALPHA: (3484) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | (3485) op(e3, e0) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | (3486) all_57_15 = e0 & op(e0, e0) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3486) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | (3487) op(e0, e0) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (157), (165), (169), (220), (372),
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | (375), (2539), (2540), (3458), (3478), (3479),
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | (3487), (function-axioms) are inconsistent by
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | (3488) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | ALPHA: (3488) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | (3489) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3489) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | (3490) all_57_12 = e0 & op(e0, e3) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3490) implies:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | (3491) all_57_12 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | (3492) op(e0, e3) = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e0,
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (3492) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | (3493) all_52_3 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | e0, e0, e3, simplifying with (168), (3485) gives:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | (3494) all_52_12 = e0
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (3493) imply:
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | (3495) ~ (all_52_7 = e0)
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.70 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (3493) imply:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | (3496) ~ (all_52_11 = e0)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2523), (3494) imply:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | (3497) ~ (e1 = e0)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (3498) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3498) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3499) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3499) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3500) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2526), (3492), (3500), (function-axioms) are
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #346.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3501) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3501) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3502) op(e2, e2) = all_56_11
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3503) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3504) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3505) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3506) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3507) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | (3508) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3508) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (3509) all_56_0 = e3 & op(e3, e2) = e3
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3509) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (3510) op(e3, e2) = e3
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3470), (3510), (function-axioms) are
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (3511) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3511) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (3512) ~ (all_56_9 = e2)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | (3513) op(e3, e3) = all_56_9
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3503) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (3514) all_56_15 = e2 & op(e0, e0) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3514) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (3515) all_56_15 = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (3457), (3505), (3515), (function-axioms)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #976.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (3516) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3516) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (3517) ~ (all_56_12 = e0)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | (3518) op(e0, e2) = all_56_12
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3506) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3519) all_56_9 = e2 & op(e3, e3) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3519) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3520) all_56_9 = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3470), (3508), (3520), (function-axioms)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #345.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3521) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3521) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3522) ~ (all_56_0 = e3)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3523) op(e3, e2) = all_56_0
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3504) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3524) all_56_13 = e2 & op(e1, e1) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3524) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3525) op(e1, e1) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (3525), (function-axioms) are
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3526) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3526) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3527) ~ (all_56_7 = e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3528) op(e1, e2) = all_56_7
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3507) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3529) all_56_7 = e1 & op(e1, e2) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3529) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3530) all_56_7 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3527), (3530) imply:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3531) $false
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (3531) is inconsistent.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3532) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3532) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3533) ~ (all_56_13 = e2)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3534) op(e1, e1) = all_56_13
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_12, e2, e0, simplifying with (158), (3518)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3535) all_56_12 = all_52_7
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (3480), (3534)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3536) all_56_13 = e0
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_7, e2, e1, simplifying with (162), (3528)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3537) all_56_7 = all_52_6
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (3460), (3502)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3538) all_56_11 = e0
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_0, e2, e3, simplifying with (170), (3523)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3539) all_56_0 = all_52_4
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3473), (3513) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3540) all_56_9 = e3
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3527), (3537) imply:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3541) ~ (all_52_6 = e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3533), (3536) imply:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3542) ~ (e2 = e0)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3543) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3543) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3544) all_57_1 = e1 & op(e3, e2) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3544) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3545) op(e3, e2) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3546) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3546) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3547) all_57_6 = e1 & op(e1, e3) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3547) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3548) all_57_6 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3549) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3549) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3550) all_57_0 = e2 & op(e3, e3) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3550) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3551) op(e3, e3) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (128), (135), (136), (158), (162), (170),
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (191), (195), (248), (258), (372), (2521), (3456),
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3504), (3508), (3517), (3518), (3551),
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #344.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3552) all_57_2 = e2 & op(e2, e3) = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3552) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3553) all_57_2 = e2
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3554) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3554) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3555) all_57_2 = e1 & op(e2, e3) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3555) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3556) all_57_2 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3553), (3556) are inconsistent by sub-proof
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #943.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3557) all_57_3 = e1 & op(e2, e2) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3557) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3558) op(e2, e2) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3460), (3558), (function-axioms) are
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3559) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3559) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3560) all_57_5 = e1 & op(e2, e1) = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3560) implies:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3561) all_57_5 = e1
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.71 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3562) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3562) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3563) all_57_2 = e3 & op(e2, e3) = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3563) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3564) all_57_2 = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3553), (3564) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3565) e3 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3540), (3565) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3566) all_56_9 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3470), (3508), (3566), (function-axioms)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #345.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3567) all_57_3 = e3 & op(e2, e2) = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3567) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3568) op(e2, e2) = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3460), (3568), (function-axioms) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3569) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3569) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3570) all_57_5 = e3 & op(e2, e1) = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3561), (3570) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #504.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3571) all_57_10 = e3 & op(e2, e0) = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3571) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3572) op(e2, e0) = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3463) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3573) ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e0) = all_18_1 & $i(all_18_0) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_18_1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3573) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3574) op(e2, e0) = all_18_1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3450), (3545), (3572), (3574), (function-axioms)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #342.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3575) ~ (all_18_1 = e1) & op(e2, e0) = all_18_1 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_18_1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3575) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3576) op(e2, e0) = all_18_1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3450), (3545), (3572), (3576), (function-axioms)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #342.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3577) all_57_10 = e1 & op(e2, e0) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2524), (3577), (function-axioms) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3578) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3578) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3579) all_57_6 = e2 & op(e1, e3) = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3579) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3580) all_57_6 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3548), (3580) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #700.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3581) all_57_12 = e2 & op(e0, e3) = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (167), (168), (169), (170), (232),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (3454), (3470), (3471), (3472), (3548),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3581), (function-axioms) are inconsistent by
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1024.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3582) all_57_7 = e1 & op(e1, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3582) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3583) op(e1, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3541), (3583), (function-axioms) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3584) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (2525), (3480), (3584),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3585) all_57_3 = e1 & op(e2, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3585) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3586) op(e2, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3460), (3586), (function-axioms) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3587) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3587) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3588) all_57_7 = e1 & op(e1, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3588) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3589) op(e1, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3541), (3589), (function-axioms) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3590) all_57_13 = e1 & op(e0, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3590) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3591) all_57_13 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (211),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (2526), (2548), (3457), (3491), (3591),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #356.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (3592) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (160), (2525), (2540), (2549), (3479),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (3492), (3592), (function-axioms) are inconsistent
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #340.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | (3593) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (3457), (3479), (3593),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | #885.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | (3594) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (2550), (3465), (3467), (3594) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | (3595) all_36_2 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | (3596) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 138.31/19.72 | | | | | | | | | | | | | | | | & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 138.31/19.72 | | | | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2)
% 138.31/19.72 | | | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (3595) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | (3597) all_14_2 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | SIMP: (3597) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | (3598) all_14_2 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | COMBINE_EQS: (281), (3598) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | (3599) all_44_2 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | REDUCE: (51), (3598) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | (3600) op(e3, e3) = e2
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | (3601) ~ (all_48_2 = e0)
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | REDUCE: (299), (3601) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | (3602) ~ (all_4_2 = e0)
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | (3603) all_54_10 = e3
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (3603) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | #1112.
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | (3604) ~ (all_54_10 = e3)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | (3605) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | BETA: splitting (3605) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | (3606) all_54_10 = e2
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (3606) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | #1111.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | (3607) ~ (all_54_10 = e2)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | (3608) all_54_10 = e1 | all_54_10 = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | BETA: splitting (3608) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | (3609) all_54_10 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (3609) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | (3610) all_4_2 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | SIMP: (3610) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | (3611) all_4_2 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (375), (3611) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | (3612) ~ (e3 = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3611) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | (3613) ~ (e2 = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (3611) imply:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | (3614) op(e1, e1) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | (3615) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3615) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | (3616) all_57_2 = e1 & op(e2, e3) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3616) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | (3617) all_57_2 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (3618) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3618) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | (3619) all_57_1 = e1 & op(e3, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3619) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | (3620) op(e3, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (3621) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (3454), (3600), (3621),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | #339.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | (3622) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3622) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (3623) all_57_6 = e0 & op(e1, e3) = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3623) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (3624) op(e1, e3) = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (3596), (3599), (3620), (3624),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | #868.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (3625) all_57_12 = e0 & op(e0, e3) = e0
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (128), (135), (136), (139), (140),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (157), (158), (159), (160), (162), (170), (191),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (195), (206), (248), (258), (372), (2521), (2525),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (2526), (2540), (2549), (3456), (3600), (3625),
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | | #338.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | (3626) all_57_3 = e1 & op(e2, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3626) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | (3627) op(e2, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3460), (3627), (function-axioms) are
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | (3628) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3628) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | (3629) all_57_7 = e1 & op(e1, e2) = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3629) implies:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | (3630) all_57_7 = e1
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.72 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (3631) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3631) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3632) all_57_6 = e2 & op(e1, e3) = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3632) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3633) all_57_6 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3634) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (3454), (3600), (3634),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | #339.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (238), (3600), (3617), (3633),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3635), (function-axioms) are inconsistent by
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #403.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3636) all_57_7 = e2 & op(e1, e2) = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3636) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3637) all_57_7 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3630), (3637) are inconsistent by sub-proof
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | (3638) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3638) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3639) all_57_8 = e2 & op(e1, e1) = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3639) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3640) op(e1, e1) = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3614), (3640), (function-axioms) are
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3641) all_57_11 = e2 & op(e1, e0) = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3641) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | (3642) all_57_11 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (2540) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3643) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3643) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3644) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3644) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3645) op(e3, e3) = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3600), (3645), (function-axioms) are
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3646) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3646) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3647) all_56_15 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (2549), (3647) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3648) e2 = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3642), (3648) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3649) all_57_11 = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (162), (216), (218),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (219), (3456), (3614), (3649), (function-axioms)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #806.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3650) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3614), (3650), (function-axioms) are
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #965.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (3651) all_57_13 = e1 & op(e0, e2) = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3651) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (3652) all_57_13 = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (211),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (212), (2526), (2548), (3457), (3652),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | (3653) all_57_3 = e1 & op(e2, e2) = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3653) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | (3654) op(e2, e2) = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3460), (3654), (function-axioms) are
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | (3655) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3655) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | (3656) all_57_5 = e1 & op(e2, e1) = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3656) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | (3657) all_57_5 = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (220), (222),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | (223), (3458), (3614), (3657), (function-axioms)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #336.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | (3658) all_57_10 = e1 & op(e2, e0) = e1
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (2524), (3658), (function-axioms) are
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | (3659) all_54_10 = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (3602), (3659) are inconsistent by
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3660) all_48_2 = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3660) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3661) all_4_2 = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | REDUCE: (362), (3661) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3662) ~ (all_52_8 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | REDUCE: (365), (3661) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3663) ~ (all_52_11 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3664) all_57_15 = e0 & op(e0, e0) = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | ALPHA: (3664) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3665) op(e0, e0) = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (157), (165), (169), (220), (372),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (375), (2539), (2540), (3458), (3662), (3663),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3665), (function-axioms) are inconsistent by
% 138.31/19.73 | | | | | | | | | | | | | | | | | | sub-proof #518.
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3666) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.31/19.73 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | ALPHA: (3666) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3667) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.31/19.73 | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | BETA: splitting (3667) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (3668) all_57_12 = e0 & op(e0, e3) = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (128), (135), (136), (139), (140),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (157), (158), (159), (160), (162), (170), (191),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (195), (206), (248), (258), (372), (2521), (2525),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (2526), (2540), (2549), (3456), (3600), (3668),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | #338.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (3669) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (3457), (3663), (3669),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | #885.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | (3670) all_22_2 = e1
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | COMBINE_EQS: (321), (3670) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | (3671) all_14_2 = e1
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | SIMP: (3671) implies:
% 138.31/19.73 | | | | | | | | | | | | | | | (3672) all_14_2 = e1
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | REDUCE: (337), (3672) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | (3673) ~ (all_52_1 = e1)
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | REDUCE: (343), (3672) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | (3674) ~ (all_52_4 = e1)
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (126), (157),
% 138.31/19.73 | | | | | | | | | | | | | | | (158), (160), (162), (164), (165), (167), (169),
% 138.31/19.73 | | | | | | | | | | | | | | | (170), (194), (206), (209), (211), (212), (220),
% 138.31/19.73 | | | | | | | | | | | | | | | (225), (229), (335), (362), (363), (365), (372),
% 138.31/19.73 | | | | | | | | | | | | | | | (375), (2524), (2526), (2539), (2540), (2548),
% 138.31/19.73 | | | | | | | | | | | | | | | (2549), (3457), (3458), (3460), (3673), (3674),
% 138.31/19.73 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.73 | | | | | | | | | | | | | | | #354.
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | End of split
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | (3675) all_14_2 = e0
% 138.31/19.73 | | | | | | | | | | | | (3676) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0
% 138.31/19.73 | | | | | | | | | | | | & op(e3, e0) = all_14_1 & $i(all_14_0) &
% 138.31/19.73 | | | | | | | | | | | | $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0)
% 138.31/19.73 | | | | | | | | | | | | = all_14_1 & $i(all_14_1))
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | COMBINE_EQS: (315), (3675) imply:
% 138.31/19.73 | | | | | | | | | | | | (3677) all_28_2 = e0
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | REDUCE: (337), (3675) imply:
% 138.31/19.73 | | | | | | | | | | | | (3678) ~ (all_52_1 = e0)
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | REDUCE: (341), (3675) imply:
% 138.31/19.73 | | | | | | | | | | | | (3679) ~ (all_52_3 = e0)
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | REDUCE: (343), (3675) imply:
% 138.31/19.73 | | | | | | | | | | | | (3680) ~ (all_52_4 = e0)
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | REDUCE: (345), (3675) imply:
% 138.31/19.73 | | | | | | | | | | | | (3681) ~ (all_52_8 = e0)
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | REDUCE: (347), (3675) imply:
% 138.31/19.73 | | | | | | | | | | | | (3682) ~ (all_52_12 = e0)
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | BETA: splitting (232) gives:
% 138.31/19.73 | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | (3683) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 138.31/19.73 | | | | | | | | | | | | | & op(e2, e3) = e0)
% 138.31/19.73 | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | BETA: splitting (3683) gives:
% 138.31/19.73 | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | (3684) all_57_0 = e0 & op(e3, e3) = e0
% 138.31/19.73 | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | ALPHA: (3684) implies:
% 138.31/19.73 | | | | | | | | | | | | | | (3685) all_57_0 = e0
% 138.31/19.73 | | | | | | | | | | | | | | (3686) op(e3, e3) = e0
% 138.31/19.73 | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | BETA: splitting (55) gives:
% 138.31/19.73 | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | (3687) ~ (all_16_2 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | REDUCE: (328), (3687) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | (3688) ~ (all_6_2 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | BETA: splitting (61) gives:
% 138.31/19.73 | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | (3689) ~ (all_20_2 = e1)
% 138.31/19.73 | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | REDUCE: (283), (3689) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | (3690) ~ (all_6_2 = e1)
% 138.31/19.73 | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | BETA: splitting (199) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3691) all_54_5 = e3
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3691) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3692) all_6_2 = e3
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | REDUCE: (373), (3692) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3693) $false
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | CLOSE: (3693) is inconsistent.
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3694) ~ (all_54_5 = e3)
% 138.31/19.73 | | | | | | | | | | | | | | | | | (3695) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | BETA: splitting (3695) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3696) all_54_5 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (268), (3696) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3697) all_6_2 = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | REDUCE: (355), (3697) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3698) ~ (all_52_7 = e2)
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | REDUCE: (357), (3697) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3699) ~ (all_52_9 = e2)
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | REDUCE: (359), (3697) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3700) ~ (all_52_13 = e2)
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | REDUCE: (373), (3697) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3701) ~ (e3 = e2)
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | REDUCE: (39), (3697) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | (3702) op(e2, e2) = e2
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (3703) ~ (all_28_2 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | REDUCE: (3677), (3703) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (3704) $false
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | CLOSE: (3704) is inconsistent.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | (3705) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = all_28_1 & $i(all_28_0) &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | (3706) ~ (all_30_2 = e1)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | REDUCE: (2519), (3706) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | (3707) $false
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | CLOSE: (3707) is inconsistent.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | (3708) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | (3709) ~ (all_48_2 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | REDUCE: (299), (3709) imply:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | (3710) ~ (all_4_2 = e0)
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (194), (335), (372), (375),
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | (2540), (2549), (3710), (function-axioms) are
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #333.
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.73 | | | | | | | | | | | | | | | | | | | | | (3711) all_48_2 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | (3712) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = all_48_1 & $i(all_48_0) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (3711) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | (3713) all_4_2 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (360), (3713) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | (3714) ~ (all_52_6 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3713) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | (3715) ~ (all_52_9 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (3713) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | (3716) ~ (all_52_11 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3713) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | (3717) ~ (e2 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | (3718) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (3678), (3702), (3718),
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | #394.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | (3719) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3719) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | (3720) all_57_5 = e0 & op(e2, e1) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3720) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | (3721) op(e2, e1) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (3715), (3721), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | (3722) all_57_10 = e0 & op(e2, e0) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3722) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | (3723) all_57_10 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | (3724) op(e2, e0) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (3725) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (170), (3680), (3702), (3725),
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | #714.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | (3726) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3726) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | (3727) all_57_7 = e0 & op(e1, e2) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3727) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | (3728) op(e1, e2) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (3714), (3728), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | (3729) all_57_13 = e0 & op(e0, e2) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3729) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | (3730) all_57_13 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | (3731) op(e0, e2) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (3732) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (3681), (3715), (3732),
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | #980.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (3733) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3733) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3734) all_57_8 = e0 & op(e1, e1) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3734) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3735) all_57_8 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3736) op(e1, e1) = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (3731) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3737) all_52_7 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (3724) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3738) all_52_13 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (125), (3737) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3739) ~ (all_52_11 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (2524), (3738) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3740) ~ (e1 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3741) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3741) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3742) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3742) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3743) op(e3, e3) = all_56_9
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3744) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3745) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3746) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3747) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3745) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3748) all_56_11 = e3 & op(e2, e2) = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3748) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3749) op(e2, e2) = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3702), (3749), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3750) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3750) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3751) ~ (all_56_3 = e2)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3752) op(e2, e3) = all_56_3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3744) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3753) all_56_13 = e3 & op(e1, e1) = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3753) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3754) op(e1, e1) = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (3754), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3755) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3755) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3756) ~ (all_56_6 = e1)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3757) op(e1, e3) = all_56_6
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3746) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3758) all_56_6 = e1 & op(e1, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3758) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3759) op(e1, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3756), (3757), (3759), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #435.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3760) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3760) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3761) ~ (all_56_13 = e3)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3762) op(e1, e1) = all_56_13
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3747) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3763) all_56_3 = e2 & op(e2, e3) = e2
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3763) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3764) op(e2, e3) = e2
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3751), (3752), (3764), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3765) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3765) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3766) ~ (all_56_11 = e3)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3767) op(e2, e2) = all_56_11
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (3736), (3762)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3768) all_56_13 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6, e3, e1, simplifying with (163), (3757)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3769) all_56_6 = all_52_2
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (3702), (3767)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3770) all_56_11 = e2
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_56_9,
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (3686), (3743) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3771) all_56_9 = e0
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3756), (3769) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3772) ~ (all_52_2 = e1)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3761), (3768) imply:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3773) ~ (e3 = e0)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3774) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3774) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3775) all_57_6 = e1 & op(e1, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3775) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3776) op(e1, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3772), (3776), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3777) all_57_7 = e1 & op(e1, e2) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3777) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3778) all_57_7 = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3779) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3779) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3780) all_57_0 = e1 & op(e3, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3780) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3781) op(e3, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3686), (3781), (function-axioms) are
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3782) all_57_2 = e1 & op(e2, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3782) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3783) all_57_2 = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3784) op(e2, e3) = e1
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3785) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3785) gives:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3786) all_57_2 = e3 & op(e2, e3) = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3786) implies:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3787) all_57_2 = e3
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3783), (3787) are inconsistent by sub-proof
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #701.
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3788) all_57_3 = e3 & op(e2, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3788) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3789) op(e2, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3702), (3789), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3790) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3790) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3791) all_57_5 = e3 & op(e2, e1) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3791) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3792) all_57_5 = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3793) op(e2, e1) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3794) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3794) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3795) all_57_4 = e1 & op(e3, e1) = e1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3795) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3796) all_57_4 = e1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3797) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (165), (3699), (3796), (3797),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #331.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3798) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3798) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3799) all_57_8 = e2 & op(e1, e1) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3799) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3800) op(e1, e1) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (3800), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3801) all_57_14 = e2 & op(e0, e1) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3801) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3802) all_57_14 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3803) op(e0, e1) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3804) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3804) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3805) all_57_0 = e2 & op(e3, e3) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3805) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3806) op(e3, e3) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3686), (3806), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3807) all_57_1 = e2 & op(e3, e2) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3807) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3808) all_57_1 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3809) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3809) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3810) all_57_12 = e3 & op(e0, e3) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3810) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3811) all_57_12 = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3812) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3812) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3813) all_57_1 = e3 & op(e3, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3813) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3814) all_57_1 = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3808), (3814) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3815) e3 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3815) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3816) e3 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3811), (3816) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3817) all_57_12 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3818) all_57_15 = e0 & op(e0, e0) = e0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (36), (372), (375), (2539), (2540),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2548), (2549), (3702), (3818), (function-axioms)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #401.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3819) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3819) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3820) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3820) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3821) all_57_12 = e0 & op(e0, e3) = e0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3817), (3821) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #958.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3822) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3822) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3809) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3811), (3817) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #772.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3823) all_57_13 = e3 & op(e0, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3823) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3824) all_57_13 = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3730), (3824) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #804.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3825) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (2526), (3802), (3825),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #399.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3826) all_57_14 = e0 & op(e0, e1) = e0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (3802), (3826) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #920.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3827) all_57_3 = e3 & op(e2, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3827) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3828) op(e2, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3702), (3828), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3829) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3829) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3830) all_57_7 = e3 & op(e1, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3830) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3831) all_57_7 = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3778), (3831) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3832) e3 = e1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3811), (3832) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3833) all_57_12 = e1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (209),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (212), (372), (375), (2526), (2539),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540), (2548), (2549), (3698), (3702), (3833),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3834) all_57_13 = e3 & op(e0, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3730), (3834) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #600.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3835) all_57_13 = e3 & op(e0, e2) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3730), (3835) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #600.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3836) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3836) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3837) all_57_14 = e3 & op(e0, e1) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (3802), (3837) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #803.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3838) all_57_15 = e3 & op(e0, e0) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3838) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3839) op(e0, e0) = e3
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (210), (211),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (218), (228), (229), (231), (238), (3680), (3685),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3702), (3712), (3730), (3735), (3783), (3793),
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3839), (function-axioms) are inconsistent by
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #647.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3840) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3840) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3841) all_57_4 = e2 & op(e3, e1) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3841) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3842) all_57_4 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (3796), (3842) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1088.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3843) all_57_9 = e2 & op(e3, e0) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3843) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3844) op(e3, e0) = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3705) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3845) ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_28_1 & $i(all_28_0) &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3845) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3846) op(e3, e0) = all_28_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3847) op(all_28_1, e3) = all_28_0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3676) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3848) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_14_1 & $i(all_14_0) &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3848) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3849) ~ (all_14_0 = e1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3850) op(e3, e0) = all_14_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3851) op(all_14_1, e3) = all_14_0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3708) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_28_1,
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (3844), (3846) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3852) all_28_1 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_28_1, e0, e3, simplifying with (3846), (3850)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3853) all_28_1 = all_14_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3852), (3853) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3854) all_14_1 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3847), (3852) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3855) op(e2, e3) = all_28_0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3851), (3854) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3856) op(e2, e3) = all_14_0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3784), (3849), (3855), (3856), (function-axioms)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #329.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3857) ~ (all_30_1 = e2) & op(e0, e1) = all_30_1 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3857) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3858) ~ (all_30_1 = e2)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3859) op(e0, e1) = all_30_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2518), (3803), (3858), (3859), (function-axioms)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #380.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3860) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3844), (3846), (3860), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3861) ~ (all_28_1 = e1) & op(e3, e0) = all_28_1 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3861) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3862) op(e3, e0) = all_28_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3676) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3863) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_14_1 & $i(all_14_0) &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3863) implies:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3864) ~ (all_14_0 = e1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3865) op(e3, e0) = all_14_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3866) op(all_14_1, e3) = all_14_0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_28_1,
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (3844), (3862) gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3867) all_28_1 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_28_1, e0, e3, simplifying with (3862), (3865)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3868) all_28_1 = all_14_1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (3867), (3868) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3869) all_14_1 = e2
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3866), (3869) imply:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3870) op(e2, e3) = all_14_0
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3784), (3864), (3870), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3871) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 &
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3844), (3862), (3871), (function-axioms) are
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3872) all_57_5 = e1 & op(e2, e1) = e1
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (3792), (3872) are inconsistent by sub-proof
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #726.
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.75 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3873) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3873) gives:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3874) all_57_8 = e1 & op(e1, e1) = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3874) implies:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3875) op(e1, e1) = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3736), (3875), (function-axioms) are
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1089.
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3876) all_57_14 = e1 & op(e0, e1) = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2522), (3876), (function-axioms) are
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #347.
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3877) all_57_10 = e3 & op(e2, e0) = e3
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (3723), (3877) are inconsistent by sub-proof
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #351.
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3878) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3878) gives:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3879) all_57_6 = e1 & op(e1, e3) = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3879) implies:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3880) op(e1, e3) = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (3772), (3880), (function-axioms) are
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3881) all_57_12 = e1 & op(e0, e3) = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3881) implies:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3882) all_57_12 = e1
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (209),
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (212), (372), (375), (2526), (2539),
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (2540), (2548), (2549), (3698), (3702), (3882),
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #330.
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3883) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (160), (2525), (3736), (3883),
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #452.
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3884) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (2539), (2540), (3702), (3731),
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3884), (function-axioms) are inconsistent by
% 138.31/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #433.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3885) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3885) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3886) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3886) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3887) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2549), (3716), (3887), (function-axioms)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #432.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3888) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3888) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3889) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3890) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3890) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3891) all_56_5 = e2 & op(e2, e0) = e2
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3891) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3892) op(e2, e0) = e2
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3700), (3892), (function-axioms) are
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3893) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3893) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3894) ~ (all_56_11 = e0)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3895) op(e2, e2) = all_56_11
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3889) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3896) all_56_8 = e1 & op(e1, e0) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3896) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3897) op(e1, e0) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2525), (3897), (function-axioms) are
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3898) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3898) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3899) ~ (all_56_13 = e0)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2540), (2549), (3894), (3895), (3899),
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #326.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3900) all_57_14 = e0 & op(e0, e1) = e0
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3900) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3901) op(e0, e1) = e0
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3716), (3901), (function-axioms) are
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | (3902) all_54_5 = e1 | all_54_5 = e0
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | REF_CLOSE: (268), (3688), (3690), (3902) are inconsistent by
% 138.67/19.76 | | | | | | | | | | | | | | | | | | sub-proof #641.
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | (3903) all_20_2 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (3903) imply:
% 138.67/19.76 | | | | | | | | | | | | | | | | (3904) all_6_2 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | REDUCE: (348), (3904) imply:
% 138.67/19.76 | | | | | | | | | | | | | | | | (3905) ~ (all_52_1 = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | REDUCE: (351), (3904) imply:
% 138.67/19.76 | | | | | | | | | | | | | | | | (3906) ~ (all_52_4 = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | REDUCE: (373), (3904) imply:
% 138.67/19.76 | | | | | | | | | | | | | | | | (3907) ~ (e3 = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | REDUCE: (39), (3904) imply:
% 138.67/19.76 | | | | | | | | | | | | | | | | (3908) op(e2, e2) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | (3909) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (3686), (3905), (3909),
% 138.67/19.76 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.67/19.76 | | | | | | | | | | | | | | | | | #325.
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | (3910) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 138.67/19.76 | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | BETA: splitting (3910) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | (3911) all_57_6 = e1 & op(e1, e3) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | ALPHA: (3911) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | (3912) op(e1, e3) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | (3913) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (3913) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | (3914) all_57_0 = e1 & op(e3, e3) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | ALPHA: (3914) implies:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | (3915) op(e3, e3) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3686), (3915), (function-axioms) are
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | (3916) all_57_1 = e1 & op(e3, e2) = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (3906), (3916), (function-axioms) are
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #844.
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | (3917) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | BETA: splitting (3917) gives:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.76 | | | | | | | | | | | | | | | | | | | | (3918) all_57_4 = e1 & op(e3, e1) = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | ALPHA: (3918) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | (3919) op(e3, e1) = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (3912) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | (3920) all_52_2 = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (3919) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | (3921) all_52_8 = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (3920) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | (3922) ~ (all_52_14 = e1)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (3921) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | (3923) ~ (all_4_2 = e1)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | SIMP: (3923) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | (3924) ~ (all_4_2 = e1)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | (3925) all_54_10 = e3
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (375), (3925) are inconsistent by sub-proof
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | #1112.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | (3926) ~ (all_54_10 = e3)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | (3927) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3927) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | (3928) all_54_10 = e2
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (3928) are inconsistent by sub-proof
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | #1111.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | (3929) ~ (all_54_10 = e2)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | (3930) all_54_10 = e1 | all_54_10 = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3930) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3931) all_54_10 = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (3924), (3931) are inconsistent by
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #378.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3932) all_54_10 = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (3932) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3933) all_4_2 = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (3933) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3934) all_4_2 = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (3934) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3935) ~ (all_52_9 = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (3934) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3936) ~ (all_52_11 = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (3934) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3937) ~ (e2 = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (3924), (3934) imply:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | (3938) ~ (e1 = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (3939) all_57_15 = e0 & op(e0, e0) = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3939) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (3940) op(e0, e0) = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (157), (165), (169), (220), (372),
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (375), (2539), (2540), (3681), (3935), (3936),
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (3940), (function-axioms) are inconsistent by
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #518.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (3941) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3941) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | (3942) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3942) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (3943) all_57_12 = e0 & op(e0, e3) = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3943) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (3944) op(e0, e3) = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (3679), (3944), (function-axioms) are
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | (3945) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3945) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (3946) all_57_13 = e0 & op(e0, e2) = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3946) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | (3947) op(e0, e2) = e0
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3948) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3948) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3949) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3949) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3950) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (375), (3912), (3950), (function-axioms) are
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #434.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3951) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3951) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3952) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3952) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3953) all_56_15 = e2 & op(e0, e0) = e2
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3953) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3954) op(e0, e0) = e2
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (207), (372), (3686),
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3908), (3954), (function-axioms) are inconsistent
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #525.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3955) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3955) implies:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3956) ~ (all_56_12 = e0)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3957) op(e0, e2) = all_56_12
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3947), (3956), (3957), (function-axioms) are
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (3958) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3958) gives:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3959) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 138.67/19.77 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3959) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3960) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (2549), (3936), (3960), (function-axioms)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #432.
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3961) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3961) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3962) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3963) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3964) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3962) gives:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3965) all_56_11 = e0 & op(e2, e2) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3965) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3966) op(e2, e2) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (3908), (3966), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3967) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3967) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3968) ~ (all_56_5 = e2)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (3963) gives:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3969) all_56_8 = e1 & op(e1, e0) = e1
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3969) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3970) op(e1, e0) = e1
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (2525), (3970), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3971) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3971) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (3972) ~ (all_56_13 = e0)
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (2540), (2549), (3964), (3968), (3972),
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #324.
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (3973) all_57_14 = e0 & op(e0, e1) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (3973) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | (3974) op(e0, e1) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (3936), (3974), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #886.
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | (3975) all_57_9 = e1 & op(e3, e0) = e1
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (2523), (3975), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3976) all_57_12 = e1 & op(e0, e3) = e1
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (2520), (3976), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | (3977) all_16_2 = e0
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | COMBINE_EQS: (328), (3977) imply:
% 138.67/19.78 | | | | | | | | | | | | | | | (3978) all_6_2 = e0
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | REDUCE: (359), (3978) imply:
% 138.67/19.78 | | | | | | | | | | | | | | | (3979) ~ (all_52_13 = e0)
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | (3980) all_57_15 = e0 & op(e0, e0) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (2548), (3980) are inconsistent by sub-proof
% 138.67/19.78 | | | | | | | | | | | | | | | | #358.
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | (3981) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.67/19.78 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.67/19.78 | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.67/19.78 | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.67/19.78 | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | ALPHA: (3981) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | (3982) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.67/19.78 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 138.67/19.78 | | | | | | | | | | | | | | | | e0) = e0)
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | BETA: splitting (3982) gives:
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | (3983) all_57_9 = e0 & op(e3, e0) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | ALPHA: (3983) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | (3984) op(e3, e0) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (3682), (3984), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | (3985) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 138.67/19.78 | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | BETA: splitting (3985) gives:
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3986) all_57_10 = e0 & op(e2, e0) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (3979), (3986), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3987) all_57_11 = e0 & op(e1, e0) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | ALPHA: (3987) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3988) op(e1, e0) = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 138.67/19.78 | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (3988) gives:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3989) all_52_14 = e0
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | REDUCE: (367), (3989) imply:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3990) ~ (all_4_2 = e0)
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | SIMP: (3990) implies:
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (3991) ~ (all_4_2 = e0)
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (194), (335), (372), (375),
% 138.67/19.78 | | | | | | | | | | | | | | | | | | (2540), (2549), (3991), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #333.
% 138.67/19.78 | | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | (3992) all_57_2 = e0 & op(e2, e3) = e0
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | REF_CLOSE: (167), (3678), (3992), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | inconsistent by sub-proof #1028.
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | (3993) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 138.67/19.78 | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | BETA: splitting (3993) gives:
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | (3994) all_57_6 = e0 & op(e1, e3) = e0
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | ALPHA: (3994) implies:
% 138.67/19.78 | | | | | | | | | | | | | | (3995) all_57_6 = e0
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (168), (169),
% 138.67/19.78 | | | | | | | | | | | | | | (170), (233), (234), (236), (238), (2520), (3680),
% 138.67/19.78 | | | | | | | | | | | | | | (3681), (3682), (3995), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | inconsistent by sub-proof #321.
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | (3996) all_57_12 = e0 & op(e0, e3) = e0
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | ALPHA: (3996) implies:
% 138.67/19.78 | | | | | | | | | | | | | | (3997) op(e0, e3) = e0
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | REF_CLOSE: (159), (3679), (3997), (function-axioms) are
% 138.67/19.78 | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | End of split
% 138.67/19.78 | | | | | | | | |
% 138.67/19.78 | | | | | | | | End of split
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | End of split
% 138.67/19.78 | | | | | | |
% 138.67/19.78 | | | | | | End of split
% 138.67/19.78 | | | | | |
% 138.67/19.78 | | | | | End of split
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | End of split
% 138.67/19.78 | | | |
% 138.67/19.78 | | | Case 2:
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | (3998) all_8_2 = e3
% 138.67/19.78 | | | | (3999) ( ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 & op(e1, e3) =
% 138.67/19.78 | | | | all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e2) &
% 138.67/19.78 | | | | op(e1, e3) = all_8_1 & $i(all_8_1))
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | COMBINE_EQS: (330), (3998) imply:
% 138.67/19.78 | | | | (4000) all_4_2 = e3
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | SIMP: (4000) implies:
% 138.67/19.78 | | | | (4001) all_4_2 = e3
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | COMBINE_EQS: (317), (4001) imply:
% 138.67/19.78 | | | | (4002) all_12_2 = e3
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | REDUCE: (362), (4001) imply:
% 138.67/19.78 | | | | (4003) ~ (all_52_8 = e3)
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | REDUCE: (363), (4001) imply:
% 138.67/19.78 | | | | (4004) ~ (all_52_9 = e3)
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | REDUCE: (365), (4001) imply:
% 138.67/19.78 | | | | (4005) ~ (all_52_11 = e3)
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | REDUCE: (367), (4001) imply:
% 138.67/19.78 | | | | (4006) ~ (all_52_14 = e3)
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | BETA: splitting (223) gives:
% 138.67/19.78 | | | |
% 138.67/19.78 | | | | Case 1:
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | | (4007) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 138.67/19.78 | | | | | e1) = e3)
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | | REF_CLOSE: (165), (169), (4003), (4004), (4007), (function-axioms) are
% 138.67/19.78 | | | | | inconsistent by sub-proof #319.
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | Case 2:
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | | (4008) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 138.67/19.78 | | | | | e1) = e3)
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | | BETA: splitting (4008) gives:
% 138.67/19.78 | | | | |
% 138.67/19.78 | | | | | Case 1:
% 138.67/19.78 | | | | | |
% 138.67/19.78 | | | | | | (4009) all_57_8 = e3 & op(e1, e1) = e3
% 138.67/19.78 | | | | | |
% 138.67/19.78 | | | | | | ALPHA: (4009) implies:
% 138.67/19.78 | | | | | | (4010) all_57_8 = e3
% 138.67/19.78 | | | | | | (4011) op(e1, e1) = e3
% 138.67/19.78 | | | | | |
% 138.67/19.78 | | | | | | BETA: splitting (46) gives:
% 138.67/19.78 | | | | | |
% 138.67/19.78 | | | | | | Case 1:
% 138.67/19.78 | | | | | | |
% 138.67/19.78 | | | | | | | (4012) ~ (all_10_2 = e1)
% 138.67/19.78 | | | | | | |
% 138.67/19.78 | | | | | | | BETA: splitting (49) gives:
% 138.67/19.78 | | | | | | |
% 138.67/19.78 | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | | (4013) ~ (all_12_2 = e3)
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | | REDUCE: (4002), (4013) imply:
% 138.67/19.78 | | | | | | | | (4014) $false
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | | CLOSE: (4014) is inconsistent.
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | | (4015) ( ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 &
% 138.67/19.78 | | | | | | | | op(e1, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1))
% 138.67/19.78 | | | | | | | | | ( ~ (all_12_1 = e0) & op(e1, e3) = all_12_1 &
% 138.67/19.78 | | | | | | | | $i(all_12_1))
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | | BETA: splitting (52) gives:
% 138.67/19.78 | | | | | | | |
% 138.67/19.78 | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | |
% 138.67/19.78 | | | | | | | | | (4016) ~ (all_14_2 = e0)
% 138.67/19.78 | | | | | | | | |
% 138.67/19.78 | | | | | | | | | BETA: splitting (55) gives:
% 138.67/19.78 | | | | | | | | |
% 138.67/19.78 | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | (4017) ~ (all_16_2 = e0)
% 138.67/19.78 | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | REDUCE: (328), (4017) imply:
% 138.67/19.78 | | | | | | | | | | (4018) ~ (all_6_2 = e0)
% 138.67/19.78 | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | BETA: splitting (61) gives:
% 138.67/19.78 | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | (4019) ~ (all_20_2 = e1)
% 138.67/19.78 | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | REDUCE: (283), (4019) imply:
% 138.67/19.78 | | | | | | | | | | | (4020) ~ (all_6_2 = e1)
% 138.67/19.78 | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | BETA: splitting (199) gives:
% 138.67/19.78 | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | (4021) all_54_5 = e3
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | REF_CLOSE: (268), (373), (4021) are inconsistent by sub-proof
% 138.67/19.78 | | | | | | | | | | | | #318.
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | (4022) ~ (all_54_5 = e3)
% 138.67/19.78 | | | | | | | | | | | | (4023) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | BETA: splitting (4023) gives:
% 138.67/19.78 | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | (4024) all_54_5 = e2
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | COMBINE_EQS: (268), (4024) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4025) all_6_2 = e2
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | SIMP: (4025) implies:
% 138.67/19.78 | | | | | | | | | | | | | (4026) all_6_2 = e2
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (348), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4027) ~ (all_52_1 = e2)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (351), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4028) ~ (all_52_4 = e2)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (355), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4029) ~ (all_52_7 = e2)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (357), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4030) ~ (all_52_9 = e2)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (359), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4031) ~ (all_52_13 = e2)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (373), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4032) ~ (e3 = e2)
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | REDUCE: (39), (4026) imply:
% 138.67/19.78 | | | | | | | | | | | | | (4033) op(e2, e2) = e2
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | BETA: splitting (64) gives:
% 138.67/19.78 | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | Case 1:
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | (4034) ~ (all_22_2 = e1)
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | REDUCE: (321), (4034) imply:
% 138.67/19.78 | | | | | | | | | | | | | | (4035) ~ (all_14_2 = e1)
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (45), (51), (207), (4012),
% 138.67/19.78 | | | | | | | | | | | | | | (4016), (4018), (4033), (4035), (function-axioms)
% 138.67/19.78 | | | | | | | | | | | | | | are inconsistent by sub-proof #314.
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | Case 2:
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | (4036) all_22_2 = e1
% 138.67/19.78 | | | | | | | | | | | | | | (4037) ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0
% 138.67/19.78 | | | | | | | | | | | | | | & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 138.67/19.78 | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e3, e1)
% 138.67/19.78 | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | COMBINE_EQS: (321), (4036) imply:
% 138.67/19.78 | | | | | | | | | | | | | | (4038) all_14_2 = e1
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | SIMP: (4038) implies:
% 138.67/19.78 | | | | | | | | | | | | | | (4039) all_14_2 = e1
% 138.67/19.78 | | | | | | | | | | | | | |
% 138.67/19.78 | | | | | | | | | | | | | | COMBINE_EQS: (313), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4040) all_34_2 = e1
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (337), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4041) ~ (all_52_1 = e1)
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (339), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4042) ~ (all_52_2 = e1)
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (341), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4043) ~ (all_52_3 = e1)
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (343), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4044) ~ (all_52_4 = e1)
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (345), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4045) ~ (all_52_8 = e1)
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (347), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4046) ~ (all_52_12 = e1)
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | REDUCE: (51), (4039) imply:
% 138.67/19.79 | | | | | | | | | | | | | | (4047) op(e3, e3) = e1
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 138.67/19.79 | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | (4048) ~ (all_24_2 = e2)
% 138.67/19.79 | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | REDUCE: (319), (4048) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | (4049) ~ (all_10_2 = e2)
% 138.67/19.79 | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 138.67/19.79 | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | (4050) ~ (all_42_2 = e3)
% 138.67/19.79 | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | REDUCE: (303), (4050) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | (4051) ~ (all_10_2 = e3)
% 138.67/19.79 | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 138.67/19.79 | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | (4052) all_54_15 = e3
% 138.67/19.79 | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4051), (4052) are inconsistent by
% 138.67/19.79 | | | | | | | | | | | | | | | | | sub-proof #755.
% 138.67/19.79 | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.79 | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | (4053) ~ (all_54_15 = e3)
% 138.67/19.79 | | | | | | | | | | | | | | | | | (4054) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | BETA: splitting (4054) gives:
% 138.67/19.79 | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | (4055) all_54_15 = e2
% 138.67/19.79 | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4049), (4055) are inconsistent by
% 138.67/19.79 | | | | | | | | | | | | | | | | | | sub-proof #754.
% 138.67/19.79 | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.79 | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | (4056) ~ (all_54_15 = e2)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | (4057) all_54_15 = e1 | all_54_15 = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | BETA: splitting (4057) gives:
% 138.67/19.79 | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4058) all_54_15 = e1
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4012), (4058) are inconsistent by
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | Case 2:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4059) all_54_15 = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (4059) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4060) all_10_2 = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | SIMP: (4060) implies:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4061) all_10_2 = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (350), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4062) ~ (all_52_3 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (361), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4063) ~ (all_52_7 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (368), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4064) ~ (all_52_11 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (369), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4065) ~ (all_52_12 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (370), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4066) ~ (all_52_13 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (4051), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4067) ~ (e3 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (4049), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4068) ~ (e2 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | REDUCE: (4012), (4061) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | (4069) ~ (e1 = e0)
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | (4070) all_57_15 = e0 & op(e0, e0) = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | ALPHA: (4070) implies:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | (4071) all_57_15 = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | (4072) op(e0, e0) = e0
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | | (4073) all_54_4 = e3
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4073) imply:
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | | (4074) all_52_1 = e3
% 138.67/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | SIMP: (4074) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | (4075) all_52_1 = e3
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (4075) imply:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | (4076) ~ (all_52_13 = e3)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | SIMP: (4076) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | (4077) ~ (all_52_13 = e3)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | (4078) all_54_7 = e3
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4077), (4078) are inconsistent by
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1007.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | (4079) ~ (all_54_7 = e3)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | (4080) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | (4081) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4081) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4082) all_57_6 = e2 & op(e1, e3) = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (51),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (158), (159), (163), (164), (168), (169), (206),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (218), (228), (229), (230),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (237), (238), (239), (372),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4003), (4011), (4012), (4016), (4029), (4031),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4033), (4042), (4043), (4046), (4047), (4049),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4062), (4063), (4065), (4071), (4072), (4082),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | #289.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4083) all_57_7 = e2 & op(e1, e2) = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (229), (231),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4033), (4083), (function-axioms) are inconsistent
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #309.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | (4084) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4084) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4085) all_57_8 = e2 & op(e1, e1) = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4085) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4086) op(e1, e1) = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (4086), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4087) all_57_11 = e2 & op(e1, e0) = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4087) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | (4088) all_57_11 = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4080) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (4089) all_54_7 = e2
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4031), (4089) are inconsistent by
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1006.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (4090) ~ (all_54_7 = e2)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | (4091) all_54_7 = e1 | all_54_7 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | (4092) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4092) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4093) all_57_12 = e3 & op(e0, e3) = e3
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (158),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (167), (168), (169), (206),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (228), (230), (233), (236),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (4003), (4011), (4012), (4016),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4027), (4029), (4031), (4033), (4042), (4043),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4046), (4047), (4049), (4062), (4063), (4065),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4071), (4072), (4093), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #287.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4094) all_57_13 = e3 & op(e0, e2) = e3
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4094) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4095) all_57_13 = e3
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4096) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4096) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4097) all_57_2 = e0 & op(e2, e3) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4097) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4098) all_57_2 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4099) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4099) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4100) all_57_6 = e1 & op(e1, e3) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4100) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4101) op(e1, e3) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4101), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4102) all_57_7 = e1 & op(e1, e2) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4102) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4103) all_57_7 = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (158),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (167), (168), (169), (206),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (220), (222), (223), (228),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (233), (236), (237), (238), (239),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003), (4011), (4012), (4016), (4027), (4029),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4031), (4033), (4042), (4043), (4046), (4047),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4049), (4062), (4063), (4065), (4071), (4072),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4088), (4098), (4103), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #282.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4104) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4011), (4088), (4104),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4105) all_57_3 = e0 & op(e2, e2) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4105) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4106) op(e2, e2) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4033), (4106), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4107) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4107) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4108) all_57_5 = e0 & op(e2, e1) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4108) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4109) all_57_5 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4110) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4110) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4111) all_57_6 = e1 & op(e1, e3) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4111) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4112) op(e1, e3) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4112), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4113) all_57_7 = e1 & op(e1, e2) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4113) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4114) all_57_7 = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4115) op(e1, e2) = e1
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4116) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4116) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4117) all_57_0 = e0 & op(e3, e3) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4117) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4118) op(e3, e3) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4047), (4118), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4119) all_57_2 = e0 & op(e2, e3) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4119) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4120) all_57_2 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (158),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (167), (168), (169), (206),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (220), (222), (223), (228),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (231), (233), (236), (237), (238), (239),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003), (4011), (4012), (4016), (4027), (4029),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4031), (4033), (4042), (4043), (4046), (4047),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4049), (4062), (4063), (4065), (4071), (4072),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4088), (4114), (4120), (function-axioms) are
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #282.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4121) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4121) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4122) all_57_6 = e0 & op(e1, e3) = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4122) implies:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4123) all_57_6 = e0
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4124) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (159), (228),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (4033), (4043), (4063), (4114), (4124),
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #284.
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4125) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4125) gives:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.79 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4126) all_57_14 = e1 & op(e0, e1) = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4126) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4127) all_57_14 = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4128) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4128) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4129) all_57_0 = e3 & op(e3, e3) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4129) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4130) op(e3, e3) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4047), (4130), (function-axioms) are
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4131) all_57_2 = e3 & op(e2, e3) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4131) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4132) all_57_2 = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4133) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (4027), (4047), (4133),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #288.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4134) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4134) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4135) all_57_6 = e2 & op(e1, e3) = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (45), (51),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (159), (163), (164), (168), (169), (206),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (218), (228), (229), (230),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (231), (232), (233), (237), (238), (239), (372),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4003), (4011), (4012), (4016), (4029), (4031),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4033), (4042), (4043), (4046), (4047), (4049),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4062), (4063), (4065), (4071), (4072), (4135),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #289.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4136) all_57_12 = e2 & op(e0, e3) = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4136) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4137) all_57_12 = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4138) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4138) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4139) all_57_9 = e3 & op(e3, e0) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4139) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4140) op(e3, e0) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4091) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4141) all_54_7 = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (4141) imply:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4142) all_52_13 = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4142) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4143) all_52_13 = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (4143) imply:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4144) ~ (all_52_14 = e1)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4144) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4145) ~ (all_52_14 = e1)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4077), (4143) imply:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4146) ~ (e3 = e1)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4031), (4143) imply:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4147) ~ (e2 = e1)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4148) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4148) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4149) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4149) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4150) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4151) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4152) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4153) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4153) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4154) all_57_9 = e1 & op(e3, e0) = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4046), (4154), (function-axioms) are
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4155) all_57_10 = e1 & op(e2, e0) = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4155) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4156) all_57_10 = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4152) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4157) all_56_6 = e1 & op(e1, e3) = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4157) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4158) op(e1, e3) = e1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4158), (function-axioms) are
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4159) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4159) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4160) ~ (all_56_13 = e3)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4150) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4161) all_56_15 = e3 & op(e0, e0) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4161) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4162) op(e0, e0) = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4062), (4151), (4162), (function-axioms)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4163) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4163) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4164) ~ (all_56_10 = e0)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4165) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4165) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4166) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4166) gives:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4167) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_0)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4167) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4168) op(e3, e3) = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (4123), (4132), (4137),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4168), (function-axioms) are inconsistent by
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #281.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4169) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_3)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4169) implies:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4170) op(e3, e3) = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (4123), (4132), (4137),
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4170), (function-axioms) are inconsistent by
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #281.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4171) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4160), (4171) are inconsistent by sub-proof #297.
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4172) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 138.78/19.80 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4172) gives:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4173) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4173) gives:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4174) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4151), (4164), (4174), (function-axioms) are
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #280.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4175) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4175) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4176) op(e2, e2) = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (226), (4109), (4132), (4156),
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4176), (function-axioms) are inconsistent by
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #592.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4177) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4177) gives:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4178) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4178) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4179) op(e2, e2) = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (226), (4109), (4132), (4156),
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4179), (function-axioms) are inconsistent by
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #592.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4180) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4180) gives:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4181) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4181) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4182) op(e0, e0) = e2
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4072), (4182), (function-axioms) are
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4183) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4183) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4184) op(e0, e0) = all_56_15
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4185) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (51), (4012), (4016), (4049), (4184),
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4185), (function-axioms) are inconsistent by
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1114.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4186) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4186) gives:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4187) all_57_11 = e1 & op(e1, e0) = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4187) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4188) op(e1, e0) = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4145), (4188), (function-axioms) are
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4189) all_57_15 = e1 & op(e0, e0) = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4189) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4190) op(e0, e0) = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (163), (207), (4011), (4033),
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4042), (4047), (4150), (4151), (4152), (4190),
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #275.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4191) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4191) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4192) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (4115), (4192), (function-axioms) are
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4193) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4193) gives:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4194) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4194) implies:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4195) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (4047), (4195), (function-axioms)
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295.
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.81 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4196) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4196) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4197) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4197) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4198) all_56_9 = e0 & op(e3, e3) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4198) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4199) op(e3, e3) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (234), (4123), (4132), (4137),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4199), (function-axioms) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #773.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4200) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4200) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4201) ~ (all_56_2 = e3)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4202) op(e3, e0) = all_56_2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4140), (4201), (4202), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4203) all_54_7 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (4066), (4203) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #961.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4204) all_57_10 = e3 & op(e2, e0) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4204) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4205) all_57_10 = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (168), (213), (4046), (4071),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4088), (4205), (function-axioms) are inconsistent
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #273.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4206) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4206) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4207) all_57_11 = e3 & op(e1, e0) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4207) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4208) all_57_11 = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4088), (4208) imply:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4209) e3 = e2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4209) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4210) e3 = e2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4132), (4210) imply:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4211) all_57_2 = e2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (238), (4047), (4123), (4137),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4211), (function-axioms) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #779.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4212) all_57_15 = e3 & op(e0, e0) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4212) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4213) op(e0, e0) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (211), (4063), (4095), (4213), (function-axioms)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #469.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4214) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (158),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (167), (168), (169), (206),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (220), (222), (223), (228),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (230), (233), (236), (237), (239), (4003), (4011),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012), (4016), (4027), (4029), (4031), (4033),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4042), (4043), (4046), (4047), (4049), (4062),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4063), (4065), (4071), (4072), (4088), (4127),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4214), (function-axioms) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #283.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4215) all_57_15 = e1 & op(e0, e0) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4215) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4216) all_57_15 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4071), (4216) are inconsistent by sub-proof
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #291.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4217) all_57_12 = e0 & op(e0, e3) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4217) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4218) op(e0, e3) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4062), (4218), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4219) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4011), (4088), (4219),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4220) all_57_10 = e0 & op(e2, e0) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4066), (4220), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (4221) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4221) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4222) all_57_14 = e3 & op(e0, e1) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4222) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4223) all_57_14 = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4224) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4224) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4225) all_57_6 = e1 & op(e1, e3) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4225) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4226) op(e1, e3) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4226), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4227) all_57_7 = e1 & op(e1, e2) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4227) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4228) all_57_7 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4229) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4229) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4230) all_57_12 = e1 & op(e0, e3) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4043), (4230), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4231) all_57_13 = e1 & op(e0, e2) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4231) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4232) all_57_13 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (9), (158), (228), (231),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4033), (4063), (4228), (4232), (function-axioms)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #285.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4233) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4233) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4234) all_57_14 = e1 & op(e0, e1) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4223), (4234) are inconsistent by sub-proof
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #705.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4235) all_57_15 = e1 & op(e0, e0) = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4235) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4236) all_57_15 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4071), (4236) are inconsistent by sub-proof
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #291.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4237) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4011), (4088), (4237),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #304.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4238) all_57_15 = e3 & op(e0, e0) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4238) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4239) op(e0, e0) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4072), (4239), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | (4240) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4240) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | (4241) all_54_4 = e2
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4027), (4241) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | sub-proof #677.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | (4242) ~ (all_54_4 = e2)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | (4243) all_54_4 = e1 | all_54_4 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | (4244) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4244) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4245) all_57_0 = e3 & op(e3, e3) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4245) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4246) op(e3, e3) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4047), (4246), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4247) all_57_2 = e3 & op(e2, e3) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4247) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4248) all_57_2 = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (4249) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (4033), (4248), (4249),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | #696.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | (4250) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4250) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (4251) all_57_5 = e0 & op(e2, e1) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4251) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (4252) op(e2, e1) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4243) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4253) all_54_4 = e1
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (4041), (4253) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #795.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4254) all_54_4 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4254) imply:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4255) all_52_1 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4255) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4256) all_52_1 = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (4256) imply:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4257) ~ (all_52_9 = e0)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4257) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4258) ~ (all_52_9 = e0)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4252), (4258), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | (4259) all_57_10 = e0 & op(e2, e0) = e0
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4066), (4259), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | (4260) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4260) gives:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4261) all_57_6 = e3 & op(e1, e3) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (163), (216),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (217), (218), (228), (229), (231), (372), (4011),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4033), (4042), (4261), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #302.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4262) all_57_12 = e3 & op(e0, e3) = e3
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (158),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (167), (168), (169), (206),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (213), (214),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (217), (228), (230), (233), (236),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (4003), (4011), (4012), (4016),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4027), (4029), (4031), (4033), (4042), (4043),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4046), (4047), (4049), (4062), (4063), (4065),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | (4071), (4072), (4262), (function-axioms) are
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #287.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | (4263) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | ALPHA: (4263) implies:
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | (4264) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (159), (4062), (4063), (4064),
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | (4264), (function-axioms) are inconsistent by
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | | sub-proof #742.
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | End of split
% 138.78/19.82 | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | Case 2:
% 138.78/19.82 | | | | | | | | | | | | | | | |
% 138.78/19.82 | | | | | | | | | | | | | | | | (4265) all_42_2 = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | (4266) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0
% 138.78/19.83 | | | | | | | | | | | | | | | | & op(e0, e3) = all_42_1 & $i(all_42_0) &
% 138.78/19.83 | | | | | | | | | | | | | | | | $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0, e3)
% 138.78/19.83 | | | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 138.78/19.83 | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (303), (4265) imply:
% 138.78/19.83 | | | | | | | | | | | | | | | | (4267) all_10_2 = e3
% 138.78/19.83 | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | COMBINE_EQS: (297), (4267) imply:
% 138.78/19.83 | | | | | | | | | | | | | | | | (4268) all_46_2 = e3
% 138.78/19.83 | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | REDUCE: (369), (4267) imply:
% 138.78/19.83 | | | | | | | | | | | | | | | | (4269) ~ (all_52_12 = e3)
% 138.78/19.83 | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | REDUCE: (45), (4267) imply:
% 138.78/19.83 | | | | | | | | | | | | | | | | (4270) op(e0, e0) = e3
% 138.78/19.83 | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 138.78/19.83 | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.83 | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | (4271) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 138.78/19.83 | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | BETA: splitting (4271) gives:
% 138.78/19.83 | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4272) all_57_0 = e3 & op(e3, e3) = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (4272) implies:
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4273) op(e3, e3) = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4047), (4273), (function-axioms) are
% 138.78/19.83 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | Case 2:
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4274) all_57_1 = e3 & op(e3, e2) = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | ALPHA: (4274) implies:
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4275) all_57_1 = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4276) op(e3, e2) = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 138.78/19.83 | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (4276) gives:
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4277) all_52_4 = e3
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | REDUCE: (134), (4277) imply:
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4278) ~ (all_52_8 = e3)
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | REDUCE: (133), (4277) imply:
% 138.78/19.83 | | | | | | | | | | | | | | | | | | (4279) ~ (all_52_12 = e3)
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.78/19.83 | | | | | | | | | | | | | | | | | |
% 138.78/19.83 | | | | | | | | | | | | | | | | | | Case 1:
% 138.78/19.83 | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (4280) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | BETA: splitting (4280) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | (4281) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | ALPHA: (4281) implies:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | (4282) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4282) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | (4283) all_56_6 = e1 & op(e1, e3) = e1
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4283) implies:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | (4284) op(e1, e3) = e1
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4284), (function-axioms) are
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | (4285) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4285) implies:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | (4286) ~ (all_56_13 = e3)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (4287) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4287) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (4288) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4047), (4288), (function-axioms) are
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (4289) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4286), (4289) are inconsistent by sub-proof #297.
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (4290) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4290) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (4291) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4291) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (4292) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4292) implies:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (4293) op(e3, e3) = e0
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4047), (4293), (function-axioms) are
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (4294) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4294) implies:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (4295) op(e2, e2) = e1
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4033), (4295), (function-axioms) are
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (4296) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4296) gives:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (4297) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4297) implies:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | (4298) op(e2, e2) = e1
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4033), (4298), (function-axioms) are
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.83 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (4299) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (51), (4012), (4016), (4049), (4299),
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | | #272.
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | | End of split
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.94/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4300) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ALPHA: (4300) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4301) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4047), (4276), (4301), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #296.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.84 | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (4302) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | BETA: splitting (4302) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4303) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ALPHA: (4303) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4304) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (4047), (4304), (function-axioms)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4305) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | ALPHA: (4305) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4306) op(e0, e0) = all_56_15
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4307) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4308) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4309) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4310) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4311) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | (4312) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4307) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | (4313) all_56_13 = e0 & op(e1, e1) = e0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4313) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | (4314) op(e1, e1) = e0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (4314), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | (4315) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4315) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | (4316) ~ (all_56_8 = e1)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | (4317) op(e1, e0) = all_56_8
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4309) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | (4318) all_56_9 = e0 & op(e3, e3) = e0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4318) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | (4319) op(e3, e3) = e0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (168), (207), (372),
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | (4269), (4270), (4312), (4319), (function-axioms)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #530.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | (4320) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4320) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | (4321) ~ (all_56_2 = e3)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | (4322) op(e3, e0) = all_56_2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4310) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | (4323) all_56_8 = e1 & op(e1, e0) = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4323) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | (4324) op(e1, e0) = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4316), (4317), (4324), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | (4325) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4325) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | (4326) ~ (all_56_13 = e0)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | (4327) op(e1, e1) = all_56_13
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4311) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (4328) all_56_5 = e2 & op(e2, e0) = e2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4328) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (4329) op(e2, e0) = e2
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4031), (4329), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (4330) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4330) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (4331) ~ (all_56_11 = e0)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | (4332) op(e2, e2) = all_56_11
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4308) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | (4333) all_56_11 = e0 & op(e2, e2) = e0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4333) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | (4334) op(e2, e2) = e0
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4331), (4332), (4334), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | (4335) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4335) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | (4336) ~ (all_56_5 = e2)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | (4337) op(e2, e0) = all_56_5
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4312) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4338) all_56_2 = e3 & op(e3, e0) = e3
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4338) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4339) op(e3, e0) = e3
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4321), (4322), (4339), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4340) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4340) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4341) ~ (all_56_9 = e0)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4342) op(e3, e3) = all_56_9
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (4270), (4306)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4343) all_56_15 = e3
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e1, simplifying with (160), (4317)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4344) all_56_8 = all_52_14
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (4011), (4327)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4345) all_56_13 = e3
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5, e0, e2, simplifying with (164), (4337)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4346) all_56_5 = all_52_13
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e3, simplifying with (168), (4322)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4347) all_56_2 = all_52_12
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_9,
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (4047), (4342) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4348) all_56_9 = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4316), (4344) imply:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | (4349) ~ (all_52_14 = e1)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4350) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4350) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4351) all_57_6 = e1 & op(e1, e3) = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4351) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4352) op(e1, e3) = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4352), (function-axioms) are
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4353) all_57_7 = e1 & op(e1, e2) = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4353) implies:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4354) all_57_7 = e1
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.84 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4355) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4355) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4356) all_57_1 = e0 & op(e3, e2) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4275), (4356) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #312.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4357) all_57_3 = e0 & op(e2, e2) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4357) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4358) op(e2, e2) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4311), (4336), (4358), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #271.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4359) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4359) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4360) all_57_7 = e0 & op(e1, e2) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4360) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4361) all_57_7 = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4354), (4361) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4362) all_57_13 = e0 & op(e0, e2) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4362) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4363) all_57_13 = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4364) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4364) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4365) all_57_12 = e1 & op(e0, e3) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4043), (4365), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4366) all_57_13 = e1 & op(e0, e2) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4363), (4366) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #805.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4367) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4367) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4368) all_57_14 = e1 & op(e0, e1) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4368) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4369) all_57_14 = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4370) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4370) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4371) all_57_12 = e2 & op(e0, e3) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4371) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4372) op(e0, e3) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4373) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4373) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4374) all_57_9 = e1 & op(e3, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4046), (4374), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4375) all_57_10 = e1 & op(e2, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4375) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4376) op(e2, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (159), (164), (4266), (4268), (4372),
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4376), (function-axioms) are inconsistent by
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #269.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4377) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4377) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4378) all_57_11 = e1 & op(e1, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4378) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4379) op(e1, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (4349), (4379), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4380) all_57_15 = e1 & op(e0, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4380) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4381) op(e0, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4270), (4381), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4382) all_57_13 = e2 & op(e0, e2) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4029), (4382), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4383) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4383) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4384) all_57_14 = e2 & op(e0, e1) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4384) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4385) all_57_14 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4369), (4385) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1048.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4386) all_57_15 = e2 & op(e0, e0) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4386) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4387) op(e0, e0) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4049), (4387), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1115.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4388) all_57_15 = e1 & op(e0, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4388) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4389) op(e0, e0) = e1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4270), (4389), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4390) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (4011), (4349), (4390),
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | | #268.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | (4391) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (4003), (4269), (4391),
% 138.98/19.85 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | #1104.
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | (4392) all_24_2 = e2
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | COMBINE_EQS: (319), (4392) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | (4393) all_10_2 = e2
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | SIMP: (4393) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | (4394) all_10_2 = e2
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | REDUCE: (45), (4394) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | (4395) op(e0, e0) = e2
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 138.98/19.85 | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | (4396) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | BETA: splitting (4396) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | (4397) all_57_6 = e2 & op(e1, e3) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | ALPHA: (4397) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | (4398) op(e1, e3) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | (4399) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | BETA: splitting (4399) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4400) all_57_0 = e2 & op(e3, e3) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | ALPHA: (4400) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4401) op(e3, e3) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4047), (4401), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4402) all_57_1 = e2 & op(e3, e2) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | ALPHA: (4402) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4403) all_57_1 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | (4404) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4404) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4405) all_57_4 = e2 & op(e3, e1) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4405) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4406) all_57_4 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4407) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (4047), (4403), (4407),
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | #817.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4408) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4408) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4409) all_57_4 = e3 & op(e3, e1) = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4409) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4410) op(e3, e1) = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (4410), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4411) all_57_9 = e3 & op(e3, e0) = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4411) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4412) all_57_9 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | (4413) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4413) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (4414) all_57_0 = e0 & op(e3, e3) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4414) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (4415) op(e3, e3) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (207), (4033), (4395), (4415),
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | #642.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (4416) all_57_1 = e0 & op(e3, e2) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4403), (4416) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | #267.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | (4417) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4417) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (4418) all_57_4 = e0 & op(e3, e1) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4406), (4418) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | #1013.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | (4419) all_57_9 = e0 & op(e3, e0) = e0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4412), (4419) are inconsistent by sub-proof
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | | #266.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4420) all_57_5 = e2 & op(e2, e1) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4420) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4421) op(e2, e1) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4030), (4421), (function-axioms) are
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | (4422) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | (212), (372), (4395), (4422), (function-axioms)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | (4423) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | BETA: splitting (4423) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4424) all_57_4 = e2 & op(e3, e1) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | ALPHA: (4424) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4425) all_57_4 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4426) op(e3, e1) = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e2,
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (4398) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4427) all_52_2 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (4426) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4428) all_52_8 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | REDUCE: (144), (4427) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4429) ~ (all_52_3 = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | SIMP: (4429) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | (4430) ~ (all_52_3 = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | (4431) ~ (all_34_2 = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | REDUCE: (4040), (4431) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | (4432) $false
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | CLOSE: (4432) is inconsistent.
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | (4433) ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | $i(all_34_1)) | ( ~ (all_34_1 = e0) & op(e3, e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4037) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4434) ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 &
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_22_1 & $i(all_22_0) &
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4434) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4435) ~ (all_22_0 = e0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4436) op(e3, e1) = all_22_1
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4437) op(all_22_1, e3) = all_22_0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_22_1,
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (4426), (4436) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4438) all_22_1 = e2
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4437), (4438) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | (4439) op(e2, e3) = all_22_0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | all_22_0, e3, e2, simplifying with (167), (4439)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4440) all_52_1 = all_22_0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4440) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4441) all_54_4 = all_22_0
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4440) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4442) ~ (all_52_3 = all_22_0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4442) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4443) ~ (all_52_3 = all_22_0)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4027), (4440) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4444) ~ (all_22_0 = e2)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4041), (4440) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | (4445) ~ (all_22_0 = e1)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4446) all_54_4 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4441), (4446) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4447) all_22_0 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4447) implies:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4448) all_22_0 = e3
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4443), (4448) imply:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | (4449) ~ (all_52_3 = e3)
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.85 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | (4450) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4450) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4451) all_57_9 = e3 & op(e3, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4451) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4452) op(e3, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (140), (158), (159), (169), (192),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (206), (207), (249), (4003), (4033), (4043),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4047), (4395), (4430), (4449), (4452),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | #265.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4453) all_57_10 = e3 & op(e2, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4453) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4454) all_57_10 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4455) all_54_12 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4455) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4456) all_52_3 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4449), (4456) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4457) $false
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4457) is inconsistent.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4458) ~ (all_54_12 = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4459) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4459) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4460) all_54_12 = e2
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4460) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4461) all_52_3 = e2
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4430), (4461) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4462) $false
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4462) is inconsistent.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4463) ~ (all_54_12 = e2)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4464) all_54_12 = e1 | all_54_12 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4464) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4465) all_54_12 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (4043), (4465) are inconsistent by
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #662.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4466) all_54_12 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4466) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4467) all_52_3 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4467) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4468) all_52_3 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (4468) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4469) ~ (all_52_11 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4469) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4470) ~ (all_52_11 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4449), (4468) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4471) ~ (e3 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4430), (4468) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4472) ~ (e2 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4043), (4468) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4473) ~ (e1 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4474) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (4033), (4041), (4474),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #442.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4475) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4475) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4476) all_57_5 = e1 & op(e2, e1) = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4476) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4477) all_57_5 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4478) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4478) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4479) all_57_4 = e0 & op(e3, e1) = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4479) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4480) all_57_4 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4425), (4480) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1050.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4481) all_57_5 = e0 & op(e2, e1) = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4477), (4481) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #264.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4482) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (4011), (4470), (4482),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4483) all_57_10 = e1 & op(e2, e0) = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4483) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4484) all_57_10 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4454), (4484) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | (4485) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4485) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4486) all_57_11 = e3 & op(e1, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4486) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4487) all_57_11 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (140), (158), (159), (163),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (169), (192), (206), (207), (217), (228), (239),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (249), (372), (4003), (4011), (4033), (4042),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4043), (4047), (4395), (4430), (4449), (4487),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | #262.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4488) all_57_15 = e3 & op(e0, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4488) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4489) op(e0, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4395), (4489), (function-axioms) are
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | (4490) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4435), (4441), (4444), (4445), (4490) are
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #261.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4491) ~ (all_34_1 = e0) & op(e3, e1) = all_34_1 &
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4491) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4492) ~ (all_34_1 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4493) op(e3, e1) = all_34_1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | all_22_0, e3, e2, simplifying with (167), (4439)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4494) all_52_1 = all_22_0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (4494) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4495) all_54_4 = all_22_0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (4494) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4496) ~ (all_52_3 = all_22_0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | SIMP: (4496) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4497) ~ (all_52_3 = all_22_0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4027), (4494) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4498) ~ (all_22_0 = e2)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4041), (4494) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4499) ~ (all_22_0 = e1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | (4500) all_54_4 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4495), (4500) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | (4501) all_22_0 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4501) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | (4502) all_22_0 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4497), (4502) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | (4503) ~ (all_52_3 = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | (4504) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4504) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4505) all_57_9 = e3 & op(e3, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4505) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4506) op(e3, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9), (140), (158), (159), (169), (192),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (206), (207), (249), (4003), (4033), (4043),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4047), (4395), (4430), (4503), (4506),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | #265.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4507) all_57_10 = e3 & op(e2, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4507) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4508) all_57_10 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4509) all_54_12 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4509) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4510) all_52_3 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4503), (4510) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4511) $false
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4511) is inconsistent.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4512) ~ (all_54_12 = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | (4513) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4513) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4514) all_54_12 = e2
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4514) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4515) all_52_3 = e2
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4430), (4515) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4516) $false
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4516) is inconsistent.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4517) all_54_12 = e1 | all_54_12 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4517) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4518) all_54_12 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (4043), (4518) are inconsistent by
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #662.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4519) all_54_12 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (4519) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4520) all_52_3 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4520) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4521) all_52_3 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (139), (4521) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4522) ~ (all_52_11 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4522) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4523) ~ (all_52_11 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4503), (4521) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4524) ~ (e3 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4043), (4521) imply:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4525) ~ (e1 = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4526) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (4033), (4041), (4526),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #442.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4527) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4527) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4528) all_57_5 = e1 & op(e2, e1) = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4528) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4529) all_57_5 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4530) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4530) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4531) all_57_4 = e0 & op(e3, e1) = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4531) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4532) op(e3, e1) = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4492), (4493), (4532), (function-axioms) are
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #260.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4533) all_57_5 = e0 & op(e2, e1) = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4529), (4533) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #264.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4534) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (157), (4011), (4523), (4534),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #263.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4535) all_57_10 = e1 & op(e2, e0) = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4535) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4536) all_57_10 = e1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4508), (4536) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | (4537) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4537) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4538) all_57_11 = e3 & op(e1, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4538) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4539) all_57_11 = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (36), (140), (158), (159), (163),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (169), (192), (206), (207), (217), (228), (239),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (249), (372), (4003), (4011), (4033), (4042),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4043), (4047), (4395), (4430), (4503), (4539),
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | #262.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4540) all_57_15 = e3 & op(e0, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4540) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | (4541) op(e0, e0) = e3
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4395), (4541), (function-axioms) are
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | (4542) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4435), (4495), (4498), (4499), (4542) are
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #261.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | (4543) ~ (all_22_1 = e2) & op(e3, e1) = all_22_1 &
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4543) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | (4544) ~ (all_22_1 = e2)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | (4545) op(e3, e1) = all_22_1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4433) gives:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4546) ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 &
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_34_1 & $i(all_34_0) &
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4546) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4547) op(e3, e1) = all_34_1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4426), (4544), (4545), (4547), (function-axioms)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #370.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4548) ~ (all_34_1 = e0) & op(e3, e1) = all_34_1 &
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4548) implies:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | (4549) op(e3, e1) = all_34_1
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4426), (4544), (4545), (4549), (function-axioms)
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #370.
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.86 | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.86 | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | (4550) all_57_9 = e2 & op(e3, e0) = e2
% 138.98/19.86 | | | | | | | | | | | | | | | | | | |
% 138.98/19.86 | | | | | | | | | | | | | | | | | | | ALPHA: (4550) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | (4551) all_57_9 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (4552) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4552) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4553) all_57_4 = e2 & op(e3, e1) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4553) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4554) all_57_4 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | (4555) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4555) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4556) all_57_0 = e0 & op(e3, e3) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4556) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4557) op(e3, e3) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (207), (4033), (4395), (4557),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | #642.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4558) all_57_1 = e0 & op(e3, e2) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4558) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4559) all_57_1 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (239), (4003), (4047),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4551), (4559), (function-axioms) are inconsistent
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #259.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | (4560) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4560) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4561) all_57_4 = e0 & op(e3, e1) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4554), (4561) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | #1013.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4562) all_57_9 = e0 & op(e3, e0) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4551), (4562) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | #368.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4563) all_57_5 = e2 & op(e2, e1) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4563) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4564) op(e2, e1) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4030), (4564), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (4565) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (212), (372), (4395), (4565), (function-axioms)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | (4566) all_57_7 = e2 & op(e1, e2) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (229), (231),
% 138.98/19.87 | | | | | | | | | | | | | | | | | (4033), (4566), (function-axioms) are inconsistent
% 138.98/19.87 | | | | | | | | | | | | | | | | | by sub-proof #309.
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | (4567) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 138.98/19.87 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 138.98/19.87 | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | BETA: splitting (4567) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | (4568) all_57_8 = e2 & op(e1, e1) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | ALPHA: (4568) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | (4569) op(e1, e1) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (4569), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | (4570) all_57_11 = e2 & op(e1, e0) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | ALPHA: (4570) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | (4571) all_57_11 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | (4572) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (167), (4027), (4047), (4572),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | #288.
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | (4573) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | BETA: splitting (4573) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | (4574) all_57_6 = e2 & op(e1, e3) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | ALPHA: (4574) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | (4575) all_57_6 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (4576) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4576) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4577) all_57_6 = e0 & op(e1, e3) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4575), (4577) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | #994.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4578) all_57_7 = e0 & op(e1, e2) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4578) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4579) all_57_7 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | (4580) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4580) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4581) all_57_9 = e1 & op(e3, e0) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4046), (4581), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4582) all_57_10 = e1 & op(e2, e0) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4582) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4583) all_57_10 = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | (4584) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4584) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4585) all_57_2 = e3 & op(e2, e3) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4585) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4586) all_57_2 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (165), (169),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (170), (207), (213), (215), (217), (219), (221),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (222), (224), (226), (229), (231), (233), (372),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4010), (4011), (4030), (4033), (4044), (4045),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4395), (4571), (4579), (4583), (4586),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | #254.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4587) all_57_3 = e3 & op(e2, e2) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4587) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4588) op(e2, e2) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4033), (4588), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | (4589) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4589) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4590) all_57_5 = e3 & op(e2, e1) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4590) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4591) all_57_5 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (4592) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4592) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4593) all_57_4 = e1 & op(e3, e1) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4045), (4593), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4594) all_57_5 = e1 & op(e2, e1) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4591), (4594) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | #726.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (4595) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4595) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4596) all_57_8 = e1 & op(e1, e1) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4596) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4597) op(e1, e1) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4011), (4597), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4598) all_57_14 = e1 & op(e0, e1) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4598) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4599) all_57_14 = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4600) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4600) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4601) all_57_4 = e0 & op(e3, e1) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4601) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4602) all_57_4 = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (165), (222), (372), (4030),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4599), (4602), (function-axioms) are inconsistent
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #256.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4603) all_57_5 = e0 & op(e2, e1) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4591), (4603) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #729.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4604) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4604) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4605) all_57_8 = e0 & op(e1, e1) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4605) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4606) op(e1, e1) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (4606), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4607) all_57_14 = e0 & op(e0, e1) = e0
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4599), (4607) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #786.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4608) all_57_10 = e3 & op(e2, e0) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4608) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4609) all_57_10 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4583), (4609) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | (4610) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4395), (4571), (4610), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #853.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (4611) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (4011), (4571), (4611),
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | #307.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | (4612) all_57_12 = e2 & op(e0, e3) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | ALPHA: (4612) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | (4613) all_57_12 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | (4614) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4614) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4615) all_57_6 = e1 & op(e1, e3) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4615) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4616) op(e1, e3) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4042), (4616), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4617) all_57_7 = e1 & op(e1, e2) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4617) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | (4618) all_57_7 = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | (4619) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4619) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4620) all_57_4 = e2 & op(e3, e1) = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4620) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | (4621) all_57_4 = e2
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | (4622) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4622) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4623) all_57_9 = e1 & op(e3, e0) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4046), (4623), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4624) all_57_10 = e1 & op(e2, e0) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4624) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | (4625) all_57_10 = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | (4626) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4626) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4627) all_57_0 = e3 & op(e3, e3) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4627) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4628) op(e3, e3) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4047), (4628), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4629) all_57_2 = e3 & op(e2, e3) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4629) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4630) all_57_2 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4631) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4631) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4632) all_57_12 = e3 & op(e0, e3) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4632) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4633) all_57_12 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4613), (4633) are inconsistent by sub-proof
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #772.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4634) all_57_13 = e3 & op(e0, e2) = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4634) implies:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4635) all_57_13 = e3
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4636) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4636) gives:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4637) all_57_12 = e1 & op(e0, e3) = e1
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4043), (4637), (function-axioms) are
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.87 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4638) all_57_13 = e1 & op(e0, e2) = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4635), (4638) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1014.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4639) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4639) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4640) all_57_14 = e1 & op(e0, e1) = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4640) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4641) all_57_14 = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4642) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4642) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4643) all_57_9 = e3 & op(e3, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4643) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4644) all_57_9 = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4645) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4645) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4646) all_57_4 = e0 & op(e3, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4646) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4647) all_57_4 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (165), (222), (372), (4030),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4641), (4647), (function-axioms) are inconsistent
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #256.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4648) all_57_5 = e0 & op(e2, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4648) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4649) all_57_5 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4650) all_57_15 = e0 & op(e0, e0) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4650) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4651) op(e0, e0) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4395), (4651), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4652) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4652) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4653) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4653) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4654) all_57_12 = e0 & op(e0, e3) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4654) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4655) all_57_12 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4613), (4655) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4656) e2 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4656) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4657) e2 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4621), (4657) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4658) all_57_4 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (36), (165), (222), (372), (4030),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4641), (4658), (function-axioms) are inconsistent
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #256.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4659) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4659) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4660) all_57_13 = e0 & op(e0, e2) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4660) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4661) all_57_13 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4635), (4661) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4662) e3 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (4395),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4571), (4644), (4662), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4663) all_57_14 = e0 & op(e0, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4663) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4664) all_57_14 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4641), (4664) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4665) e1 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4665) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4666) e1 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4618), (4666) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4667) all_57_7 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (165), (169),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (207), (213), (215), (217), (219), (221),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (226), (229), (231), (233), (372), (4010),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011), (4030), (4033), (4044), (4045), (4395),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4571), (4625), (4630), (4649), (4667),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #255.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4668) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4668) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4669) all_57_8 = e0 & op(e1, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4669) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4670) op(e1, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (4670), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4671) all_57_14 = e0 & op(e0, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4671) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4672) all_57_14 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4641), (4672) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4673) e1 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4673) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4674) e1 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4618), (4674) imply:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4675) all_57_7 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (165), (169),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (207), (213), (215), (217), (219), (221),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (224), (226), (229), (231), (233), (372),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4010), (4011), (4030), (4033), (4044), (4045),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4395), (4571), (4625), (4630), (4675),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #254.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4676) all_57_10 = e3 & op(e2, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4676) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4677) all_57_10 = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4625), (4677) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4678) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4678) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4679) all_57_11 = e3 & op(e1, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4679) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4680) all_57_11 = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4571), (4680) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1055.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4681) all_57_15 = e3 & op(e0, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4681) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4682) op(e0, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (210), (211),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4635), (4682), (function-axioms) are inconsistent
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #252.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4683) all_57_15 = e1 & op(e0, e0) = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4683) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4684) op(e0, e0) = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4395), (4684), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4685) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4685) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4686) all_57_14 = e3 & op(e0, e1) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4686) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4687) all_57_14 = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4688) all_57_15 = e0 & op(e0, e0) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4688) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4689) op(e0, e0) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4395), (4689), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4690) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4690) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4691) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4691) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4692) all_57_12 = e0 & op(e0, e3) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4613), (4692) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #958.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4693) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4693) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4694) all_57_13 = e0 & op(e0, e2) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4694) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4695) all_57_13 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4696) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4696) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4697) all_57_12 = e1 & op(e0, e3) = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4043), (4697), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4698) all_57_13 = e1 & op(e0, e2) = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4698) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4699) all_57_13 = e1
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4695), (4699) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #721.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4700) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4395), (4687), (4700),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #251.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4701) all_57_14 = e0 & op(e0, e1) = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4701) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4702) all_57_14 = e0
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4687), (4702) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1067.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4703) all_57_15 = e3 & op(e0, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4703) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4704) op(e0, e0) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4395), (4704), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | (4705) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4705) gives:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4706) all_57_6 = e3 & op(e1, e3) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4706) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4707) all_57_6 = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (4011), (4571), (4618),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4707), (function-axioms) are inconsistent by
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #306.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4708) all_57_12 = e3 & op(e0, e3) = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4708) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4709) all_57_12 = e3
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4613), (4709) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | | #772.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | (4710) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4395), (4571), (4710), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #853.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | (4711) all_57_5 = e2 & op(e2, e1) = e2
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4711) implies:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | (4712) op(e2, e1) = e2
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4030), (4712), (function-axioms) are
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | (4713) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | (212), (372), (4395), (4713), (function-axioms)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | (4714) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (4011), (4571), (4714),
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | | #304.
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | (4715) all_54_5 = e1 | all_54_5 = e0
% 138.98/19.88 | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | | REF_CLOSE: (268), (4018), (4020), (4715) are inconsistent by
% 138.98/19.88 | | | | | | | | | | | | | sub-proof #641.
% 138.98/19.88 | | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | End of split
% 138.98/19.88 | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | Case 2:
% 138.98/19.88 | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | (4716) all_20_2 = e1
% 138.98/19.88 | | | | | | | | | | | (4717) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0
% 138.98/19.88 | | | | | | | | | | | & op(e2, e1) = all_20_1 & $i(all_20_0) &
% 138.98/19.88 | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1)
% 138.98/19.88 | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 138.98/19.88 | | | | | | | | | | |
% 138.98/19.88 | | | | | | | | | | | COMBINE_EQS: (283), (4716) imply:
% 138.98/19.89 | | | | | | | | | | | (4718) all_6_2 = e1
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | SIMP: (4718) implies:
% 138.98/19.89 | | | | | | | | | | | (4719) all_6_2 = e1
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | COMBINE_EQS: (332), (4719) imply:
% 138.98/19.89 | | | | | | | | | | | (4720) all_38_2 = e1
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | REDUCE: (355), (4719) imply:
% 138.98/19.89 | | | | | | | | | | | (4721) ~ (all_52_7 = e1)
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | REDUCE: (359), (4719) imply:
% 138.98/19.89 | | | | | | | | | | | (4722) ~ (all_52_13 = e1)
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | REDUCE: (39), (4719) imply:
% 138.98/19.89 | | | | | | | | | | | (4723) op(e2, e2) = e1
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | BETA: splitting (64) gives:
% 138.98/19.89 | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | (4724) ~ (all_22_2 = e1)
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | REDUCE: (321), (4724) imply:
% 138.98/19.89 | | | | | | | | | | | | (4725) ~ (all_14_2 = e1)
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | BETA: splitting (207) gives:
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | (4726) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.98/19.89 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.98/19.89 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.98/19.89 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.98/19.89 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.98/19.89 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 138.98/19.89 | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 138.98/19.89 | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 138.98/19.89 | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 138.98/19.89 | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 138.98/19.89 | | | | | | | | | | | | | $i(all_56_6))
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | BETA: splitting (4726) gives:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4727) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.98/19.89 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.98/19.89 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.98/19.89 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.98/19.89 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.98/19.89 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | REF_CLOSE: (39), (373), (4727), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | inconsistent by sub-proof #1128.
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4728) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 138.98/19.89 | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 138.98/19.89 | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 138.98/19.89 | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 138.98/19.89 | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | REF_CLOSE: (51), (4725), (4728), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | inconsistent by sub-proof #316.
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | End of split
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | (4729) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.98/19.89 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.98/19.89 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.98/19.89 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.98/19.89 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 138.98/19.89 | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 138.98/19.89 | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 138.98/19.89 | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 138.98/19.89 | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 138.98/19.89 | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 138.98/19.89 | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 138.98/19.89 | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 138.98/19.89 | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 138.98/19.89 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 138.98/19.89 | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 138.98/19.89 | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 138.98/19.89 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.89 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.98/19.89 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.89 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | BETA: splitting (4729) gives:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4730) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.98/19.89 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.98/19.89 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.98/19.89 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.98/19.89 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | REF_CLOSE: (36), (51), (372), (4016), (4730),
% 138.98/19.89 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.89 | | | | | | | | | | | | | | #1123.
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4731) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 138.98/19.89 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 138.98/19.89 | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 138.98/19.89 | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 138.98/19.89 | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 138.98/19.89 | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 138.98/19.89 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 138.98/19.89 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.98/19.89 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 138.98/19.89 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 138.98/19.89 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.98/19.89 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.89 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.98/19.89 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.89 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (45), (51), (372), (4012),
% 138.98/19.89 | | | | | | | | | | | | | | (4016), (4018), (4723), (4731), (function-axioms)
% 138.98/19.89 | | | | | | | | | | | | | | are inconsistent by sub-proof #249.
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | End of split
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | End of split
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | (4732) all_22_2 = e1
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | COMBINE_EQS: (321), (4732) imply:
% 138.98/19.89 | | | | | | | | | | | | (4733) all_14_2 = e1
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | REDUCE: (337), (4733) imply:
% 138.98/19.89 | | | | | | | | | | | | (4734) ~ (all_52_1 = e1)
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | REDUCE: (341), (4733) imply:
% 138.98/19.89 | | | | | | | | | | | | (4735) ~ (all_52_3 = e1)
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | REDUCE: (347), (4733) imply:
% 138.98/19.89 | | | | | | | | | | | | (4736) ~ (all_52_12 = e1)
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | REDUCE: (51), (4733) imply:
% 138.98/19.89 | | | | | | | | | | | | (4737) op(e3, e3) = e1
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | BETA: splitting (213) gives:
% 138.98/19.89 | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | (4738) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 138.98/19.89 | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | BETA: splitting (4738) gives:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4739) all_57_9 = e1 & op(e3, e0) = e1
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | REF_CLOSE: (168), (4736), (4739), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4740) all_57_10 = e1 & op(e2, e0) = e1
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | REF_CLOSE: (164), (4722), (4740), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | End of split
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | (4741) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 138.98/19.89 | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | BETA: splitting (4741) gives:
% 138.98/19.89 | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | (4742) all_57_11 = e1 & op(e1, e0) = e1
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | ALPHA: (4742) implies:
% 138.98/19.89 | | | | | | | | | | | | | | (4743) all_57_11 = e1
% 138.98/19.89 | | | | | | | | | | | | | | (4744) op(e1, e0) = e1
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 138.98/19.89 | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | (4745) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 138.98/19.89 | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | BETA: splitting (4745) gives:
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | (4746) all_57_12 = e1 & op(e0, e3) = e1
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (4735), (4746), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | (4747) all_57_13 = e1 & op(e0, e2) = e1
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4721), (4747), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | End of split
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | (4748) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 138.98/19.89 | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | BETA: splitting (4748) gives:
% 138.98/19.89 | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | (4749) all_57_14 = e1 & op(e0, e1) = e1
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | ALPHA: (4749) implies:
% 138.98/19.89 | | | | | | | | | | | | | | | | (4750) all_57_14 = e1
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 138.98/19.89 | | | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (4744) gives:
% 138.98/19.89 | | | | | | | | | | | | | | | | (4751) all_52_14 = e1
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | REDUCE: (141), (4751) imply:
% 138.98/19.89 | | | | | | | | | | | | | | | | (4752) ~ (all_52_2 = e1)
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | REDUCE: (371), (4751) imply:
% 138.98/19.89 | | | | | | | | | | | | | | | | (4753) ~ (all_10_2 = e1)
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | REDUCE: (4006), (4751) imply:
% 138.98/19.89 | | | | | | | | | | | | | | | | (4754) ~ (e3 = e1)
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 138.98/19.89 | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | (4755) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.98/19.89 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 138.98/19.89 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 138.98/19.89 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 138.98/19.89 | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | BETA: splitting (4755) gives:
% 138.98/19.89 | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | (4756) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 138.98/19.89 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 138.98/19.89 | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 138.98/19.89 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 138.98/19.89 | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 138.98/19.89 | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 138.98/19.89 | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 138.98/19.89 | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | ALPHA: (4756) implies:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | (4757) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 138.98/19.89 | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.98/19.89 | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | BETA: splitting (4757) gives:
% 138.98/19.89 | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | (4758) all_56_6 = e1 & op(e1, e3) = e1
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | ALPHA: (4758) implies:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | (4759) op(e1, e3) = e1
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4752), (4759), (function-axioms) are
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | (4760) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | ALPHA: (4760) implies:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | (4761) ~ (all_56_13 = e3)
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | |
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.89 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4762) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4762) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4763) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4737), (4763), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4764) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4761), (4764) are inconsistent by sub-proof #297.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4765) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4765) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4766) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (372), (4737), (4766),
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | #248.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4767) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (36), (39), (45), (51), (372), (4012),
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4016), (4018), (4723), (4767), (function-axioms)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #249.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.90 | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4768) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 138.98/19.90 | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | ALPHA: (4768) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4769) op(e2, e2) = all_56_11
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4770) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4771) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4772) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4773) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4774) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 138.98/19.90 | | | | | | | | | | | | | | | | | | (4775) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 138.98/19.90 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 138.98/19.90 | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | BETA: splitting (4774) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | (4776) all_56_7 = e1 & op(e1, e2) = e1
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | ALPHA: (4776) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | (4777) op(e1, e2) = e1
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (4771), (4777), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | (4778) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | ALPHA: (4778) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | (4779) ~ (all_56_13 = e2)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | (4780) op(e1, e1) = all_56_13
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | BETA: splitting (4773) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4781) all_56_9 = e2 & op(e3, e3) = e2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (4781) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4782) op(e3, e3) = e2
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (4737), (4782), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4783) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | ALPHA: (4783) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4784) ~ (all_56_0 = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | (4785) op(e3, e2) = all_56_0
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4775) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4786) all_56_0 = e3 & op(e3, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4786) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4787) op(e3, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4784), (4785), (4787), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4788) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4788) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4789) ~ (all_56_9 = e2)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4790) op(e3, e3) = all_56_9
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (4011), (4780)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4791) all_56_13 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (4723), (4769)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4792) all_56_11 = e1
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | all_56_0, e2, e3, simplifying with (170), (4785)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4793) all_56_0 = all_52_4
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_9,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (4737), (4790) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4794) all_56_9 = e1
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4784), (4793) imply:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4795) ~ (all_52_4 = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | REDUCE: (4789), (4794) imply:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | (4796) ~ (e2 = e1)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | (4797) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4797) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4798) all_57_1 = e3 & op(e3, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4798) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4799) op(e3, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4795), (4799), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4800) all_57_3 = e3 & op(e2, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4800) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4801) op(e2, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (373), (4801), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | End of split
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | (4802) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4802) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4803) all_57_7 = e3 & op(e1, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4803) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4804) all_57_7 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (36), (216), (218),
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (372), (4011), (4743), (4804), (function-axioms)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #245.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4805) all_57_13 = e3 & op(e0, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4805) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4806) all_57_13 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | (4807) op(e0, e2) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | (4808) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (170), (4737), (4795), (4808),
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | #244.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | (4809) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4809) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4810) all_57_4 = e3 & op(e3, e1) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4810) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4811) op(e3, e1) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (4811), (function-axioms) are
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4812) all_57_9 = e3 & op(e3, e0) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4812) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4813) all_57_9 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4814) op(e3, e0) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e3,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (4807) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4815) all_52_7 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (4814) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | (4816) all_52_12 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | (4817) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4817) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4818) all_57_2 = e3 & op(e2, e3) = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4818) implies:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4819) all_57_2 = e3
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4772) gives:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.90 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4820) all_56_12 = e0 & op(e0, e2) = e0
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4820) implies:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4821) op(e0, e2) = e0
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4807), (4821), (function-axioms) are
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #243.
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4822) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4822) implies:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4823) ~ (all_56_15 = e2)
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4824) op(e0, e0) = all_56_15
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4770) gives:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4825) all_56_15 = e2 & op(e0, e0) = e2
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4825) implies:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4826) all_56_15 = e2
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4823), (4826) imply:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4827) $false
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4827) is inconsistent.
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4828) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4828) implies:
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4829) ~ (all_56_12 = e0)
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4830) op(e0, e2) = all_56_12
% 138.98/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (45), (88), (214), (224),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4717), (4720), (4723), (4743), (4807), (4813),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4819), (4823), (4824), (4829), (4830),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #240.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4831) all_57_3 = e3 & op(e2, e2) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4831) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4832) op(e2, e2) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (373), (4832), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | (4833) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4833) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4834) all_57_5 = e3 & op(e2, e1) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4834) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4835) all_57_5 = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4772) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4836) all_56_12 = e0 & op(e0, e2) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4836) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4837) op(e0, e2) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4807), (4837), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #243.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4838) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4838) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4839) ~ (all_56_15 = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4840) op(e0, e0) = all_56_15
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4770) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4841) all_56_15 = e2 & op(e0, e0) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4841) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4842) all_56_15 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4839), (4842) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4843) $false
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (4843) is inconsistent.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4844) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4844) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4845) ~ (all_56_12 = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4846) op(e0, e2) = all_56_12
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4847) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4847) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4848) all_57_4 = e2 & op(e3, e1) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4848) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4849) all_57_4 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4850) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4850) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4851) all_57_0 = e0 & op(e3, e3) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4851) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4852) op(e3, e3) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4737), (4852), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4853) all_57_1 = e0 & op(e3, e2) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4853) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854) all_57_1 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4855) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4855) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4856) all_57_1 = e2 & op(e3, e2) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4854), (4856) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4857) all_57_3 = e2 & op(e2, e2) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4857) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4858) op(e2, e2) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (164), (167), (225), (4722), (4734),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4835), (4858), (function-axioms) are inconsistent
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #440.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4859) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4859) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4860) all_57_7 = e2 & op(e1, e2) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4860) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4861) all_57_7 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4862) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4862) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4863) all_57_6 = e0 & op(e1, e3) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4863) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4864) all_57_6 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4865) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4865) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4866) all_57_0 = e3 & op(e3, e3) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4866) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4867) op(e3, e3) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4737), (4867), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4868) all_57_2 = e3 & op(e2, e3) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4868) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4869) all_57_2 = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (45), (88), (214), (224),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4717), (4720), (4723), (4743), (4807), (4813),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4839), (4840), (4845), (4846), (4869),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #240.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4870) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4870) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4871) all_57_6 = e3 & op(e1, e3) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4871) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4872) all_57_6 = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4862) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4863), (4872) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #603.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4873) all_57_7 = e0 & op(e1, e2) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4873) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4874) all_57_7 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4861), (4874) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #578.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4875) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (4011), (4743), (4875),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #239.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4876) all_57_12 = e3 & op(e0, e3) = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4876) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4877) all_57_12 = e3
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4878) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4878) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4879) all_57_0 = e2 & op(e3, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4879) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4880) op(e3, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4789), (4790), (4880), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4881) all_57_2 = e2 & op(e2, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4881) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4882) all_57_2 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4883) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4883) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4884) all_57_4 = e0 & op(e3, e1) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4884) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4885) all_57_4 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4849), (4885) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4886) e2 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4882), (4886) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4887) all_57_2 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4878) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4888) all_57_0 = e2 & op(e3, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4888) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4889) op(e3, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4789), (4790), (4889), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #391.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4882), (4887) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4890) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4890) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4891) all_57_6 = e2 & op(e1, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4864), (4891) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #783.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4892) all_57_12 = e2 & op(e0, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4892) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4893) all_57_12 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4877), (4893) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4894) e3 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (4894) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4895) e3 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4813), (4895) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4896) all_57_9 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (239), (4003), (4737),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854), (4896), (function-axioms) are inconsistent
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #259.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4897) all_57_5 = e0 & op(e2, e1) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (88), (4717), (4720), (4807), (4897),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #241.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4898) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4898) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4899) all_57_8 = e0 & op(e1, e1) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4899) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4900) op(e1, e1) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (4900), (function-axioms) are
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4901) all_57_14 = e0 & op(e0, e1) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4901) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4902) all_57_14 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4750), (4902) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1071.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4903) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4903) gives:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4904) all_57_6 = e2 & op(e1, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4864), (4904) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #783.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4905) all_57_12 = e2 & op(e0, e3) = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4905) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4906) all_57_12 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4877), (4906) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4907) e3 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4813), (4907) imply:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4908) all_57_9 = e2
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (239), (4003), (4737),
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854), (4908), (function-axioms) are inconsistent
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #259.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4909) all_57_7 = e0 & op(e1, e2) = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4909) implies:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4910) all_57_7 = e0
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4861), (4910) are inconsistent by sub-proof
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #578.
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4911) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.28/19.91 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (4011), (4743), (4911),
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #239.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4912) all_57_13 = e2 & op(e0, e2) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4912) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4913) all_57_13 = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4806), (4913) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4914) e3 = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4813), (4914) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4915) all_57_9 = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (169), (239), (4003), (4737),
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4854), (4915), (function-axioms) are inconsistent
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #259.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4916) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4916) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4917) all_57_4 = e0 & op(e3, e1) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4917) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4918) all_57_4 = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4849), (4918) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1050.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4919) all_57_9 = e0 & op(e3, e0) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4919) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4920) all_57_9 = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4813), (4920) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #863.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4921) all_57_5 = e2 & op(e2, e1) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4921) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4922) all_57_5 = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4835), (4922) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #936.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4923) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (36), (372), (4750), (4923),
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #257.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4924) all_57_10 = e3 & op(e2, e0) = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4924) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4925) all_57_10 = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4926) all_57_15 = e0 & op(e0, e0) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4926) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4927) all_57_15 = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4928) op(e0, e0) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4929) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4929) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4930) all_57_9 = e2 & op(e3, e0) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4813), (4930) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #598.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4931) all_57_10 = e2 & op(e2, e0) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4925), (4931) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #694.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4932) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4932) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4933) all_57_11 = e2 & op(e1, e0) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4933) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4934) all_57_11 = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (168), (213), (4736), (4925),
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4927), (4934), (function-axioms) are inconsistent
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #273.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4935) all_57_15 = e2 & op(e0, e0) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4935) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4936) op(e0, e0) = e2
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4928), (4936), (function-axioms) are
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4937) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4937) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4938) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4938) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4939) all_57_9 = e0 & op(e3, e0) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4813), (4939) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #266.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4940) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (4940) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4941) all_57_10 = e0 & op(e2, e0) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4925), (4941) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #692.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4942) all_57_11 = e0 & op(e1, e0) = e0
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4743), (4942) are inconsistent by sub-proof
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #808.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4943) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.28/19.92 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.28/19.92 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.92 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.28/19.92 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.28/19.92 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.28/19.92 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.28/19.92 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.28/19.92 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.28/19.92 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.92 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.28/19.92 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.28/19.92 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.28/19.92 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.28/19.92 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.28/19.92 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (169), (4003), (4011), (4737), (4744),
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4943), (function-axioms) are inconsistent by
% 139.28/19.92 | | | | | | | | | | | | | | | | | sub-proof #293.
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | (4944) all_57_15 = e1 & op(e0, e0) = e1
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | ALPHA: (4944) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | (4945) op(e0, e0) = e1
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (4012), (4945), (function-axioms) are
% 139.28/19.92 | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | (4946) all_57_15 = e1 & op(e0, e0) = e1
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | ALPHA: (4946) implies:
% 139.28/19.92 | | | | | | | | | | | | | | (4947) op(e0, e0) = e1
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | REF_CLOSE: (45), (4012), (4947), (function-axioms) are
% 139.28/19.92 | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | End of split
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | (4948) all_16_2 = e0
% 139.28/19.92 | | | | | | | | | | (4949) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0
% 139.28/19.92 | | | | | | | | | | & op(e2, e0) = all_16_1 & $i(all_16_0) &
% 139.28/19.92 | | | | | | | | | | $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0)
% 139.28/19.92 | | | | | | | | | | = all_16_1 & $i(all_16_1))
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | COMBINE_EQS: (328), (4948) imply:
% 139.28/19.92 | | | | | | | | | | (4950) all_6_2 = e0
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | SIMP: (4950) implies:
% 139.28/19.92 | | | | | | | | | | (4951) all_6_2 = e0
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | COMBINE_EQS: (326), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4952) all_18_2 = e0
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (348), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4953) ~ (all_52_1 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (351), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4954) ~ (all_52_4 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (353), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4955) ~ (all_52_6 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (355), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4956) ~ (all_52_7 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (357), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4957) ~ (all_52_9 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (359), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4958) ~ (all_52_13 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | REDUCE: (373), (4951) imply:
% 139.28/19.92 | | | | | | | | | | (4959) ~ (e3 = e0)
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | BETA: splitting (228) gives:
% 139.28/19.92 | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | (4960) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.28/19.92 | | | | | | | | | | | & op(e2, e2) = e0)
% 139.28/19.92 | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | BETA: splitting (4960) gives:
% 139.28/19.92 | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | (4961) all_57_1 = e0 & op(e3, e2) = e0
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | REF_CLOSE: (170), (4954), (4961), (function-axioms) are
% 139.28/19.92 | | | | | | | | | | | | inconsistent by sub-proof #1102.
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | (4962) all_57_3 = e0 & op(e2, e2) = e0
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | ALPHA: (4962) implies:
% 139.28/19.92 | | | | | | | | | | | | (4963) all_57_3 = e0
% 139.28/19.92 | | | | | | | | | | | | (4964) op(e2, e2) = e0
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | BETA: splitting (58) gives:
% 139.28/19.92 | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | (4965) ~ (all_18_2 = e0)
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | REDUCE: (4952), (4965) imply:
% 139.28/19.92 | | | | | | | | | | | | | (4966) $false
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | CLOSE: (4966) is inconsistent.
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | (4967) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0
% 139.28/19.92 | | | | | | | | | | | | | & op(e2, e0) = all_18_1 & $i(all_18_0) &
% 139.28/19.92 | | | | | | | | | | | | | $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0)
% 139.28/19.92 | | | | | | | | | | | | | = all_18_1 & $i(all_18_1))
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | BETA: splitting (64) gives:
% 139.28/19.92 | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | (4968) ~ (all_22_2 = e1)
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | REDUCE: (321), (4968) imply:
% 139.28/19.92 | | | | | | | | | | | | | | (4969) ~ (all_14_2 = e1)
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 139.28/19.92 | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | (4970) ~ (all_24_2 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | REDUCE: (319), (4970) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4971) ~ (all_10_2 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (4012), (4016),
% 139.28/19.92 | | | | | | | | | | | | | | | (4964), (4969), (4971), (function-axioms) are
% 139.28/19.92 | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | (4972) all_24_2 = e2
% 139.28/19.92 | | | | | | | | | | | | | | | (4973) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0
% 139.28/19.92 | | | | | | | | | | | | | | | & op(e0, e2) = all_24_1 & $i(all_24_0) &
% 139.28/19.92 | | | | | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2)
% 139.28/19.92 | | | | | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | COMBINE_EQS: (319), (4972) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4974) all_10_2 = e2
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | SIMP: (4974) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | (4975) all_10_2 = e2
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | COMBINE_EQS: (307), (4975) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4976) all_40_2 = e2
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | REDUCE: (350), (4975) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4977) ~ (all_52_3 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | REDUCE: (369), (4975) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4978) ~ (all_52_12 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | REDUCE: (370), (4975) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4979) ~ (all_52_13 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | REDUCE: (45), (4975) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | (4980) op(e0, e0) = e2
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | BETA: splitting (85) gives:
% 139.28/19.92 | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | (4981) ~ (all_36_2 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | REDUCE: (305), (4981) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | (4982) ~ (all_14_2 = e2)
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4983) all_54_0 = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (4983) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4984) all_14_2 = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | REDUCE: (343), (4984) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4985) ~ (all_52_4 = e3)
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | REDUCE: (347), (4984) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4986) ~ (all_52_12 = e3)
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | REDUCE: (51), (4984) imply:
% 139.28/19.92 | | | | | | | | | | | | | | | | | (4987) op(e3, e3) = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | (4988) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.28/19.92 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.28/19.92 | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | BETA: splitting (4988) gives:
% 139.28/19.92 | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | (4989) all_57_9 = e3 & op(e3, e0) = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | ALPHA: (4989) implies:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | (4990) op(e3, e0) = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (4986), (4990), (function-axioms) are
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1105.
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.92 | | | | | | | | | | | | | | | | | | | (4991) all_57_10 = e3 & op(e2, e0) = e3
% 139.28/19.92 | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (91), (113),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (117), (120), (135), (144), (148), (149), (158),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (159), (163), (164), (165), (167), (168), (169),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (170), (192), (200), (201), (206), (209), (210),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (212), (216), (217), (218), (222), (231), (233),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (235), (239), (249), (269), (270), (372), (4003),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (4011), (4949), (4953), (4954), (4956), (4958),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (4964), (4967), (4973), (4976), (4977), (4978),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (4979), (4980), (4985), (4987), (4991),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | #220.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | (4992) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.28/19.93 | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | BETA: splitting (4992) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (4993) all_57_11 = e3 & op(e1, e0) = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | ALPHA: (4993) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | (4994) all_57_11 = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | (4995) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | BETA: splitting (4995) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | (4996) all_57_6 = e0 & op(e1, e3) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | ALPHA: (4996) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | (4997) all_57_6 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | (4998) all_57_15 = e0 & op(e0, e0) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (4998) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | (4999) op(e0, e0) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4980), (4999), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | (5000) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5000) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | (5001) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5001) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | (5002) all_57_9 = e0 & op(e3, e0) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5002) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | (5003) all_57_9 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | (5004) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5004) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5005) all_57_2 = e3 & op(e2, e3) = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5005) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5006) all_57_2 = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (5007) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5007) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5008) all_57_2 = e2 & op(e2, e3) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5008) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5009) all_57_2 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5006), (5009) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5010) e3 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4994), (5010) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5011) all_57_11 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (4980),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5003), (5011), (function-axioms) are inconsistent
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #851.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5012) all_57_3 = e2 & op(e2, e2) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5012) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5013) op(e2, e2) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4964), (5013), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (5014) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (117), (144), (148), (149), (158),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (165), (167), (192), (200),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (249), (269), (4004), (4011), (4953),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (4956), (4964), (4977), (4979), (4980), (5014),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | #219.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5015) all_57_3 = e3 & op(e2, e2) = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5015) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5016) op(e2, e2) = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4964), (5016), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | (5017) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5017) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5018) all_57_5 = e3 & op(e2, e1) = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5018) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5019) all_57_5 = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (5020) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5020) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5021) all_57_6 = e2 & op(e1, e3) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5021) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5022) all_57_6 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (4997), (5022) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | #811.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5023) all_57_7 = e2 & op(e1, e2) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5023) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5024) all_57_7 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5025) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5025) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5026) all_57_4 = e2 & op(e3, e1) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5026) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5027) all_57_4 = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5028) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5028) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5029) all_57_4 = e0 & op(e3, e1) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5029) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5030) all_57_4 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5025) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5027), (5030) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1050.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5031) all_57_5 = e2 & op(e2, e1) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (117), (144), (148), (149), (158),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (165), (167), (192), (200),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (249), (269), (4004), (4011), (4953),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956), (4964), (4977), (4980), (5031),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #228.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5032) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (372), (4980), (5032), (function-axioms)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5033) all_57_5 = e0 & op(e2, e1) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5033) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5034) op(e2, e1) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (4957), (5034), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5035) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5035) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5036) all_57_8 = e0 & op(e1, e1) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5036) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5037) op(e1, e1) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5037), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5038) all_57_14 = e0 & op(e0, e1) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5038) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5039) all_57_14 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5040) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5040) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5041) all_57_6 = e1 & op(e1, e3) = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5041) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5042) all_57_6 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4997), (5042) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5043) e1 = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (4), (5043) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5044) $false
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5044) is inconsistent.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5045) all_57_7 = e1 & op(e1, e2) = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5045) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5046) all_57_7 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5024), (5046) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5047) e2 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5047) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5048) e2 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5027), (5048) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5049) all_57_4 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (117), (144),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (148), (149), (158), (159), (163), (164), (165),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (192), (200), (206), (209), (210), (212),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (249), (269), (372), (4004), (4011),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4953), (4956), (4964), (4977), (4980), (5049),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #227.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5050) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5050) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5051) all_57_8 = e1 & op(e1, e1) = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5051) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5052) op(e1, e1) = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (4011), (5052), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5053) all_57_11 = e1 & op(e1, e0) = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5053) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5054) all_57_11 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4994), (5054) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5055) e3 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5055) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5056) e3 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (4010), (5056) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5057) all_57_8 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5019), (5056) imply:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5058) all_57_5 = e1
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (222), (223), (5039),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5057), (5058) are inconsistent by sub-proof #494.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5059) all_57_5 = e2 & op(e2, e1) = e2
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (117), (144), (148), (149), (158),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (165), (167), (192), (200),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (206), (249), (269), (4004), (4011), (4953),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4956), (4964), (4977), (4980), (5059),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #228.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5060) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (372), (4980), (5060), (function-axioms)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #766.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (5061) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (36), (213), (215),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | (372), (4980), (5003), (5061), (function-axioms)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #765.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (5062) all_57_10 = e3 & op(e2, e0) = e3
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (91), (113),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (117), (120), (135), (144), (148), (149), (158),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (159), (163), (164), (165), (167), (168), (169),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (170), (192), (200), (201), (206), (209), (210),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (212), (216), (217), (218), (222), (231), (233),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (235), (239), (249), (269), (270), (372), (4003),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (4011), (4949), (4953), (4954), (4956), (4958),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (4964), (4967), (4973), (4976), (4977), (4978),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (4979), (4980), (4985), (4987), (5062),
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | | #220.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | (5063) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5063) gives:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | (5064) all_57_10 = e0 & op(e2, e0) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (4958), (5064), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | (5065) all_57_11 = e0 & op(e1, e0) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4994), (5065) are inconsistent by sub-proof
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | | #584.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | (5066) all_57_7 = e0 & op(e1, e2) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5066) implies:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | (5067) op(e1, e2) = e0
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (4955), (5067), (function-axioms) are
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.93 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5068) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5068) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (5069) all_57_8 = e0 & op(e1, e1) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5069) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (5070) op(e1, e1) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5070), (function-axioms) are
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (5071) all_57_11 = e0 & op(e1, e0) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5071) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (5072) all_57_11 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4994), (5072) are inconsistent by sub-proof
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | #858.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | (5073) all_57_15 = e3 & op(e0, e0) = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | ALPHA: (5073) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | (5074) op(e0, e0) = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (4980), (5074), (function-axioms) are
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | (5075) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (4016), (4969), (4982), (5075) are
% 139.28/19.94 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | (5076) all_36_2 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | COMBINE_EQS: (305), (5076) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | (5077) all_14_2 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | REDUCE: (337), (5077) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | (5078) ~ (all_52_1 = e2)
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | (5079) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (4964), (5078), (5079),
% 139.28/19.94 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.94 | | | | | | | | | | | | | | | | | #881.
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | (5080) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.28/19.94 | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (117), (144), (148), (149), (158),
% 139.28/19.94 | | | | | | | | | | | | | | | | | (159), (163), (164), (165), (167), (192), (200),
% 139.28/19.94 | | | | | | | | | | | | | | | | | (206), (249), (269), (4004), (4011), (4953),
% 139.28/19.94 | | | | | | | | | | | | | | | | | (4956), (4964), (4977), (4979), (4980), (5080),
% 139.28/19.94 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.94 | | | | | | | | | | | | | | | | | #219.
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | (5081) all_22_2 = e1
% 139.28/19.94 | | | | | | | | | | | | | | (5082) ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0
% 139.28/19.94 | | | | | | | | | | | | | | & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 139.28/19.94 | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e3, e1)
% 139.28/19.94 | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | COMBINE_EQS: (321), (5081) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5083) all_14_2 = e1
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | SIMP: (5083) implies:
% 139.28/19.94 | | | | | | | | | | | | | | (5084) all_14_2 = e1
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | COMBINE_EQS: (313), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5085) all_34_2 = e1
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | REDUCE: (337), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5086) ~ (all_52_1 = e1)
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | REDUCE: (339), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5087) ~ (all_52_2 = e1)
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | REDUCE: (341), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5088) ~ (all_52_3 = e1)
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | REDUCE: (343), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5089) ~ (all_52_4 = e1)
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | REDUCE: (347), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5090) ~ (all_52_12 = e1)
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | REDUCE: (51), (5084) imply:
% 139.28/19.94 | | | | | | | | | | | | | | (5091) op(e3, e3) = e1
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 139.28/19.94 | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | (5092) ~ (all_24_2 = e2)
% 139.28/19.94 | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | REDUCE: (319), (5092) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | (5093) ~ (all_10_2 = e2)
% 139.28/19.94 | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 139.28/19.94 | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | (5094) ~ (all_34_2 = e1)
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | REDUCE: (5085), (5094) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | (5095) $false
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | CLOSE: (5095) is inconsistent.
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | (5096) ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 139.28/19.94 | | | | | | | | | | | | | | | | $i(all_34_1)) | ( ~ (all_34_1 = e0) & op(e3, e1)
% 139.28/19.94 | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | (5097) ~ (all_42_2 = e3)
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | REDUCE: (303), (5097) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | (5098) ~ (all_10_2 = e3)
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | (5099) all_54_15 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5098), (5099) are inconsistent by
% 139.28/19.94 | | | | | | | | | | | | | | | | | | sub-proof #755.
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | (5100) ~ (all_54_15 = e3)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | (5101) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | BETA: splitting (5101) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | (5102) all_54_15 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5093), (5102) are inconsistent by
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | (5103) ~ (all_54_15 = e2)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | (5104) all_54_15 = e1 | all_54_15 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | BETA: splitting (5104) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5105) all_54_15 = e1
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4012), (5105) are inconsistent by
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5106) all_54_15 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5106) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5107) all_10_2 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | SIMP: (5107) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5108) all_10_2 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (5108) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5109) ~ (all_52_3 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (5108) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5110) ~ (all_52_12 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (5093), (5108) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5111) ~ (e2 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | REDUCE: (4012), (5108) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | (5112) ~ (e1 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (5113) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (4953), (5091), (5113),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | #839.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | (5114) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5114) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | (5115) all_57_6 = e0 & op(e1, e3) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5115) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | (5116) all_57_6 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | (5117) op(e1, e3) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | (5118) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5118) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5119) all_57_0 = e0 & op(e3, e3) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5119) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5120) all_57_0 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5121) op(e3, e3) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (234), (236),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (238), (5088), (5116), (5120), (5121),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | #322.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5122) all_57_1 = e0 & op(e3, e2) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (4954), (5122), (function-axioms) are
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1102.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | (5123) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5123) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5124) all_57_4 = e0 & op(e3, e1) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5124) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5125) all_57_4 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5126) op(e3, e1) = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e0,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (5117) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5127) all_52_2 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e0,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (5126) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5128) all_52_8 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (5127) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5129) ~ (all_52_3 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (5128) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | (5130) ~ (all_52_9 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5096) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | (5131) ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 &
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_34_1 & $i(all_34_0) &
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5131) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | (5132) ~ (all_34_0 = e2)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | (5133) op(e3, e1) = all_34_1
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | (5134) op(all_34_1, e3) = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5082) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5135) ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 &
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_22_1 & $i(all_22_0) &
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5135) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5136) op(e3, e1) = all_22_1
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5137) op(all_22_1, e3) = all_22_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_34_1,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (5126), (5133) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5138) all_34_1 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_1, e1, e3, simplifying with (5133), (5136)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5139) all_34_1 = all_22_1
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5138), (5139) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5140) all_22_1 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5134), (5138) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5141) op(e0, e3) = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5137), (5140) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5142) op(e0, e3) = all_22_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_22_0, e3, e0, simplifying with (159), (5142)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5143) all_52_3 = all_22_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_0, e3, e0, simplifying with (159), (5141)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5144) all_52_3 = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5143), (5144) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5145) all_34_0 = all_22_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5143) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5146) all_54_12 = all_22_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5143) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5147) ~ (all_52_1 = all_22_0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5109), (5143) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5148) ~ (all_22_0 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5132), (5145) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5149) ~ (all_22_0 = e2)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5150) all_54_12 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5146), (5150) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5151) all_22_0 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5151) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5152) all_22_0 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5147), (5152) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5153) ~ (all_52_1 = e3)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (45), (117), (145), (146), (164),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (169), (170), (198), (200), (206),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (212), (213), (214), (222), (233),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (261), (269), (372), (4003), (4004),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012), (4953), (4954), (4957), (4964), (5086),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5091), (5125), (5153), (function-axioms) are
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5154) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5154) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5155) all_54_12 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5146), (5155) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5156) all_22_0 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5156) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5157) all_22_0 = e2
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5149), (5157) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5158) $false
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5158) is inconsistent.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5159) all_54_12 = e1 | all_54_12 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5088), (5109), (5159) are inconsistent by
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #661.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5160) ~ (all_22_1 = e2) & op(e3, e1) = all_22_1 &
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5160) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5161) op(e3, e1) = all_22_1
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_34_1,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (5126), (5133) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5162) all_34_1 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_22_1,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_1, e1, e3, simplifying with (5133), (5161)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5163) all_34_1 = all_22_1
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5162), (5163) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5164) all_22_1 = e0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5134), (5162) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5165) op(e0, e3) = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | all_34_0, e3, e0, simplifying with (159), (5165)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5166) all_52_3 = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (5166) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5167) all_54_12 = all_34_0
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (5166) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5168) ~ (all_52_1 = all_34_0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5109), (5166) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | (5169) ~ (all_34_0 = e0)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5170) all_54_12 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5167), (5170) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5171) all_34_0 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5171) implies:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5172) all_34_0 = e3
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5168), (5172) imply:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5173) ~ (all_52_1 = e3)
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (45), (117), (145), (146), (164),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (167), (169), (170), (198), (200), (206),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (212), (213), (214), (222), (233),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (239), (261), (269), (372), (4003), (4004),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (4012), (4953), (4954), (4957), (4964), (5086),
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5091), (5125), (5173), (function-axioms) are
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #218.
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.94 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5174) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5174) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5175) all_54_12 = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5167), (5175) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5176) all_34_0 = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5176) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5177) all_34_0 = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5132), (5177) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5178) $false
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5178) is inconsistent.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5179) all_54_12 = e1 | all_54_12 = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (249), (5088), (5109), (5179) are inconsistent by
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #661.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5180) ~ (all_34_1 = e0) & op(e3, e1) = all_34_1 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5180) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5181) ~ (all_34_1 = e0)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5182) op(e3, e1) = all_34_1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5126), (5181), (5182), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #260.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (5183) all_57_9 = e0 & op(e3, e0) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5183) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (5184) op(e3, e0) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5110), (5184), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #941.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5185) all_57_12 = e0 & op(e0, e3) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5185) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5186) op(e0, e3) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (5109), (5186), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | (5187) all_42_2 = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | COMBINE_EQS: (303), (5187) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | (5188) all_10_2 = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | REDUCE: (369), (5188) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | (5189) ~ (all_52_12 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | REDUCE: (45), (5188) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | (5190) op(e0, e0) = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | (5191) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | BETA: splitting (5191) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | (5192) all_57_1 = e3 & op(e3, e2) = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | ALPHA: (5192) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | (5193) op(e3, e2) = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (5193) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | (5194) all_52_4 = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | REDUCE: (134), (5194) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | (5195) ~ (all_52_8 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | REDUCE: (133), (5194) imply:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | (5196) ~ (all_52_12 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (5197) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5197) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5198) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5198) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5199) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5200) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5201) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5200) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5202) all_56_10 = e0 & op(e0, e3) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5202) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5203) op(e0, e3) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5201) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5204) all_56_6 = e1 & op(e1, e3) = e1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5204) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5205) op(e1, e3) = e1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5087), (5205), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5206) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5206) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5207) ~ (all_56_13 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (5208) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5208) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5209) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5091), (5209), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5210) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5207), (5210) are inconsistent by sub-proof #297.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (5211) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5211) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5212) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4964), (5091), (5212), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #217.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5213) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5213) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (5214) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5214) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (5215) op(e2, e2) = e1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (4964), (5215), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (5216) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5216) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5217) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5217) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5218) op(e0, e0) = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5199), (5203), (5218), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #953.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5219) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5219) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5220) op(e0, e0) = all_56_15
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5221) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (51), (4012), (4016), (5093), (5220),
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5221), (function-axioms) are inconsistent by
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1114.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5222) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5222) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5223) ~ (all_56_15 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5224) op(e0, e0) = all_56_15
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5190), (5223), (5224), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #740.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5225) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5225) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5226) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5091), (5193), (5226), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #296.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (5227) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5227) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5228) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5228) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5229) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (5091), (5229), (function-axioms)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5230) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5230) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5231) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5232) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5233) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | (5234) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5231) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5235) all_56_13 = e0 & op(e1, e1) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5235) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5236) op(e1, e1) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5236), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5237) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5237) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5238) ~ (all_56_8 = e1)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | (5239) op(e1, e0) = all_56_8
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5232) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5240) all_56_9 = e0 & op(e3, e3) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5240) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5241) op(e3, e3) = e0
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (168), (207), (372),
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5189), (5190), (5234), (5241), (function-axioms)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #530.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5242) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5242) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5243) ~ (all_56_2 = e3)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | (5244) op(e3, e0) = all_56_2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5233) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (5245) all_56_5 = e2 & op(e2, e0) = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5245) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | (5246) op(e2, e0) = e2
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5234) gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5247) all_56_2 = e3 & op(e3, e0) = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5247) implies:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5248) op(e3, e0) = e3
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5243), (5244), (5248), (function-axioms) are
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e1, simplifying with (160), (5239)
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | (5249) all_56_8 = all_52_14
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.28/19.95 | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (5246) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | (5250) all_52_13 = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e3, simplifying with (168), (5244)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | (5251) all_56_2 = all_52_12
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5238), (5249) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | (5252) ~ (all_52_14 = e1)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (5250) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | (5253) ~ (all_52_12 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (110), (5250) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | (5254) ~ (all_52_14 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5254) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | (5255) ~ (all_52_14 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (193) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (5256) all_54_11 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (4006), (5256) are inconsistent by
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #216.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | (5257) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5258) all_54_3 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5189), (5258) are inconsistent by
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #439.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5259) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5257) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5260) all_54_11 = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (5255), (5260) are inconsistent by
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #215.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5261) all_54_11 = e1 | all_54_11 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5261) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5262) all_54_11 = e1
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (250), (5252), (5262) are inconsistent by
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #942.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5263) all_54_11 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (250), (5263) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5264) all_52_14 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5264) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5265) all_52_14 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (5265) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5266) ~ (all_52_12 = e0)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5259) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5267) all_54_3 = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5253), (5267) are inconsistent by
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #983.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5268) all_54_3 = e1 | all_54_3 = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5090), (5266), (5268) are inconsistent by
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #418.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | (5269) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5269) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | (5270) ~ (all_56_11 = e0)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | (5271) op(e2, e2) = all_56_11
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4964), (5270), (5271), (function-axioms) are
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5272) all_57_3 = e3 & op(e2, e2) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | ALPHA: (5272) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5273) op(e2, e2) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4964), (5273), (function-axioms) are
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5274) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | BETA: splitting (5274) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5275) all_57_7 = e3 & op(e1, e2) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | ALPHA: (5275) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5276) all_57_7 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | (5277) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5277) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | (5278) all_57_0 = e3 & op(e3, e3) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5278) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | (5279) op(e3, e3) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5091), (5279), (function-axioms) are
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | (5280) all_57_1 = e3 & op(e3, e2) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5280) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | (5281) all_57_1 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (229), (230), (4963),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | | (5276), (5281) are inconsistent by sub-proof #515.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | (5282) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (4003), (5189), (5282),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | | #1104.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5283) all_57_13 = e3 & op(e0, e2) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | ALPHA: (5283) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5284) all_57_13 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (211), (4956), (5190), (5284), (function-axioms)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #469.
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | (5285) all_24_2 = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | COMBINE_EQS: (319), (5285) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5286) all_10_2 = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | SIMP: (5286) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | (5287) all_10_2 = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (368), (5287) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5288) ~ (all_52_11 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (370), (5287) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5289) ~ (all_52_13 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (45), (5287) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5290) op(e0, e0) = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | (5291) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.28/19.96 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.28/19.96 | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | BETA: splitting (5291) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | (5292) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.28/19.96 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.28/19.96 | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.28/19.96 | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.28/19.96 | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (4011), (5087), (5292), (function-axioms)
% 139.28/19.96 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #214.
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | (5293) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.28/19.96 | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.28/19.96 | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.28/19.96 | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.28/19.96 | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | ALPHA: (5293) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | (5294) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_12))
% 139.28/19.96 | | | | | | | | | | | | | | | | | (5295) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (4956), (5290), (5294), (5295),
% 139.28/19.96 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.96 | | | | | | | | | | | | | | | | | #975.
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | (5296) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.28/19.96 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.28/19.96 | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (118), (121), (123), (157), (164),
% 139.28/19.96 | | | | | | | | | | | | | | | | (165), (169), (190), (198), (247), (261), (4957),
% 139.28/19.96 | | | | | | | | | | | | | | | | (4964), (5091), (5288), (5289), (5290), (5296),
% 139.28/19.96 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.96 | | | | | | | | | | | | | | | | #213.
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | (5297) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.28/19.96 | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | REF_CLOSE: (158), (162), (4955), (4956), (5297),
% 139.28/19.96 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.96 | | | | | | | | | | | #464.
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | (5298) all_14_2 = e0
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | REDUCE: (337), (5298) imply:
% 139.28/19.96 | | | | | | | | | (5299) ~ (all_52_1 = e0)
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | REDUCE: (339), (5298) imply:
% 139.28/19.96 | | | | | | | | | (5300) ~ (all_52_2 = e0)
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | REDUCE: (341), (5298) imply:
% 139.28/19.96 | | | | | | | | | (5301) ~ (all_52_3 = e0)
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | REDUCE: (343), (5298) imply:
% 139.28/19.96 | | | | | | | | | (5302) ~ (all_52_4 = e0)
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | REDUCE: (345), (5298) imply:
% 139.28/19.96 | | | | | | | | | (5303) ~ (all_52_8 = e0)
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | REDUCE: (347), (5298) imply:
% 139.28/19.96 | | | | | | | | | (5304) ~ (all_52_12 = e0)
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | BETA: splitting (232) gives:
% 139.28/19.96 | | | | | | | | |
% 139.28/19.96 | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | (5305) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 139.28/19.96 | | | | | | | | | | & op(e2, e3) = e0)
% 139.28/19.96 | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | BETA: splitting (5305) gives:
% 139.28/19.96 | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | (5306) all_57_0 = e0 & op(e3, e3) = e0
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | ALPHA: (5306) implies:
% 139.28/19.96 | | | | | | | | | | | (5307) all_57_0 = e0
% 139.28/19.96 | | | | | | | | | | | (5308) op(e3, e3) = e0
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | BETA: splitting (55) gives:
% 139.28/19.96 | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | (5309) ~ (all_16_2 = e0)
% 139.28/19.96 | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | REDUCE: (328), (5309) imply:
% 139.28/19.96 | | | | | | | | | | | | (5310) ~ (all_6_2 = e0)
% 139.28/19.96 | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | BETA: splitting (61) gives:
% 139.28/19.96 | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | (5311) ~ (all_20_2 = e1)
% 139.28/19.96 | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | REDUCE: (283), (5311) imply:
% 139.28/19.96 | | | | | | | | | | | | | (5312) ~ (all_6_2 = e1)
% 139.28/19.96 | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | BETA: splitting (199) gives:
% 139.28/19.96 | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | (5313) all_54_5 = e3
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | REF_CLOSE: (268), (373), (5313) are inconsistent by sub-proof
% 139.28/19.96 | | | | | | | | | | | | | | #318.
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | (5314) ~ (all_54_5 = e3)
% 139.28/19.96 | | | | | | | | | | | | | | (5315) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | BETA: splitting (5315) gives:
% 139.28/19.96 | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | (5316) all_54_5 = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | COMBINE_EQS: (268), (5316) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5317) all_6_2 = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | SIMP: (5317) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | (5318) all_6_2 = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (348), (5318) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5319) ~ (all_52_1 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (351), (5318) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5320) ~ (all_52_4 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (357), (5318) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5321) ~ (all_52_9 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (359), (5318) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5322) ~ (all_52_13 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (373), (5318) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5323) ~ (e3 = e2)
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | REDUCE: (39), (5318) imply:
% 139.28/19.96 | | | | | | | | | | | | | | | (5324) op(e2, e2) = e2
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.28/19.96 | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | (5325) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.28/19.96 | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.28/19.96 | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.28/19.96 | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.28/19.96 | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.28/19.96 | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (5308), (5325), (function-axioms) are
% 139.28/19.96 | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | (5326) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.28/19.96 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.28/19.96 | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.28/19.96 | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.28/19.96 | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.28/19.96 | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.28/19.96 | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.28/19.96 | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.28/19.96 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | BETA: splitting (5326) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | (5327) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.28/19.96 | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | BETA: splitting (5327) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5328) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | ALPHA: (5328) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5329) op(e0, e0) = e3
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (51),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (118), (121), (123), (133), (134), (157), (159),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (168), (169), (170),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (190), (202), (206), (207), (209), (210), (211),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (212), (213), (214), (216), (217), (218), (219),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (220), (222), (223), (224), (225), (227), (228),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (229), (231), (234), (235), (236), (238), (239),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (247), (271), (345), (372), (373), (3999), (4003),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (4005), (4010), (4011), (4015), (5299), (5300),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5301), (5302), (5303), (5304), (5307), (5308),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5319), (5320), (5321), (5322), (5324), (5329),
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.96 | | | | | | | | | | | | | | | | | | #203.
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5330) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | ALPHA: (5330) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5331) op(e2, e2) = e1
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5324), (5331), (function-axioms) are
% 139.28/19.96 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | End of split
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | (5332) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.28/19.96 | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.28/19.96 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.28/19.96 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | BETA: splitting (5332) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5333) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | ALPHA: (5333) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5334) op(e2, e2) = e1
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5324), (5334), (function-axioms) are
% 139.28/19.96 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (5335) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.28/19.96 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.28/19.96 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.28/19.96 | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.28/19.96 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.28/19.96 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | BETA: splitting (5335) gives:
% 139.28/19.96 | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5336) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | ALPHA: (5336) implies:
% 139.28/19.96 | | | | | | | | | | | | | | | | | | | (5337) op(e0, e0) = e2
% 139.28/19.96 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (207), (5308), (5324), (5337),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | #642.
% 139.28/19.97 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | (5338) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.28/19.97 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | ALPHA: (5338) implies:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | (5339) op(e0, e0) = all_56_15
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | (5340) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.28/19.97 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (5340) gives:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | (5341) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5341) gives:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5342) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5342) implies:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5343) all_56_15 = e3
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5339), (5343) imply:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5344) op(e0, e0) = e3
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (39), (51),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (118), (121), (123), (133), (134), (157), (159),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (168), (169), (170),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (190), (202), (206), (207), (209), (210), (211),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (212), (213), (214), (216), (217), (218), (219),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (220), (222), (223), (224), (225), (227), (228),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (229), (231), (234), (235), (236), (238), (239),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (247), (271), (345), (372), (373), (3999), (4003),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (4005), (4010), (4011), (4015), (5299), (5300),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5301), (5302), (5303), (5304), (5307), (5308),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5319), (5320), (5321), (5322), (5324), (5344),
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | #203.
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5345) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5345) implies:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | (5346) op(e2, e2) = e0
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5324), (5346), (function-axioms) are
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | (5347) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5347), (function-axioms) are
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #279.
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | Case 2:
% 139.28/19.97 | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | (5348) all_54_5 = e1 | all_54_5 = e0
% 139.28/19.97 | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | | REF_CLOSE: (268), (5310), (5312), (5348) are inconsistent by
% 139.28/19.97 | | | | | | | | | | | | | | | sub-proof #641.
% 139.28/19.97 | | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | End of split
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | Case 2:
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | (5349) all_20_2 = e1
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | COMBINE_EQS: (283), (5349) imply:
% 139.28/19.97 | | | | | | | | | | | | | (5350) all_6_2 = e1
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | REDUCE: (351), (5350) imply:
% 139.28/19.97 | | | | | | | | | | | | | (5351) ~ (all_52_4 = e1)
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | REDUCE: (39), (5350) imply:
% 139.28/19.97 | | | | | | | | | | | | | (5352) op(e2, e2) = e1
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | BETA: splitting (67) gives:
% 139.28/19.97 | | | | | | | | | | | | |
% 139.28/19.97 | | | | | | | | | | | | | Case 1:
% 139.28/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | (5353) ~ (all_24_2 = e2)
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | REDUCE: (319), (5353) imply:
% 139.51/19.97 | | | | | | | | | | | | | | (5354) ~ (all_10_2 = e2)
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | (5355) ~ (all_42_2 = e3)
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | REDUCE: (303), (5355) imply:
% 139.51/19.97 | | | | | | | | | | | | | | | (5356) ~ (all_10_2 = e3)
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | (5357) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/19.97 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/19.97 | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/19.97 | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/19.97 | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.51/19.97 | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.51/19.97 | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.51/19.97 | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.51/19.97 | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (5308), (5357), (function-axioms) are
% 139.51/19.97 | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | (5358) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/19.97 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/19.97 | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/19.97 | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/19.97 | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.51/19.97 | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.51/19.97 | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.51/19.97 | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.51/19.97 | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.51/19.97 | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.51/19.97 | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | BETA: splitting (5358) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5359) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/19.97 | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | BETA: splitting (5359) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5360) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ALPHA: (5360) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5361) op(e0, e0) = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (189), (246), (4012), (5354), (5356),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5361), (function-axioms) are inconsistent by
% 139.51/19.97 | | | | | | | | | | | | | | | | | | sub-proof #201.
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5362) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ALPHA: (5362) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5363) op(e1, e1) = e2
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (5363), (function-axioms) are
% 139.51/19.97 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5364) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.51/19.97 | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.51/19.97 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.51/19.97 | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | BETA: splitting (5364) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5365) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ALPHA: (5365) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5366) op(e1, e1) = e2
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (5366), (function-axioms) are
% 139.51/19.97 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5367) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.51/19.97 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.51/19.97 | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.51/19.97 | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | BETA: splitting (5367) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5368) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ALPHA: (5368) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5369) op(e0, e0) = e2
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (207), (372), (5308),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5352), (5369), (function-axioms) are inconsistent
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | by sub-proof #525.
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5370) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ALPHA: (5370) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5371) op(e0, e0) = all_56_15
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5372) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | (5373) all_54_15 = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5356), (5373) are inconsistent by
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | sub-proof #755.
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | (5374) ~ (all_54_15 = e3)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | (5375) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (246), (4011), (4012), (5352),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | (5354), (5356), (5371), (5372), (5375),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | | #200.
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | (5376) all_42_2 = e3
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (5376) imply:
% 139.51/19.97 | | | | | | | | | | | | | | | (5377) all_10_2 = e3
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | REDUCE: (45), (5377) imply:
% 139.51/19.97 | | | | | | | | | | | | | | | (5378) op(e0, e0) = e3
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | (5379) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | BETA: splitting (5379) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5380) all_57_1 = e3 & op(e3, e2) = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | ALPHA: (5380) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5381) op(e3, e2) = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e3,
% 139.51/19.97 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (5381) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5382) all_52_4 = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | REDUCE: (133), (5382) imply:
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5383) ~ (all_52_12 = e3)
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | SIMP: (5383) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5384) ~ (all_52_12 = e3)
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5385) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/19.97 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (5301), (5308), (5378), (5381),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5385), (function-axioms) are inconsistent by
% 139.51/19.97 | | | | | | | | | | | | | | | | | | sub-proof #212.
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (5386) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/19.97 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | BETA: splitting (5386) gives:
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5387) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ALPHA: (5387) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5388) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5389) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5390) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5391) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5392) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (118), (121), (123), (157), (165),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (169), (190), (202), (247), (271), (4005), (5303),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5308), (5352), (5378), (5388), (5389), (5390),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5391), (5392), (function-axioms) are inconsistent
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | by sub-proof #532.
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5393) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | ALPHA: (5393) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5394) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (168), (207), (372),
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | (5308), (5378), (5384), (5394), (function-axioms)
% 139.51/19.97 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #530.
% 139.51/19.97 | | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5395) all_57_3 = e3 & op(e2, e2) = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | ALPHA: (5395) implies:
% 139.51/19.97 | | | | | | | | | | | | | | | | | (5396) op(e2, e2) = e3
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (373), (5396), (function-axioms) are
% 139.51/19.97 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1129.
% 139.51/19.97 | | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | (5397) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 139.51/19.97 | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 139.51/19.97 | | | | | | | | | | | | | | | | (211), (216), (217), (218), (372), (4011), (5378),
% 139.51/19.97 | | | | | | | | | | | | | | | | (5397), (function-axioms) are inconsistent by
% 139.51/19.97 | | | | | | | | | | | | | | | | sub-proof #208.
% 139.51/19.97 | | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | (5398) all_24_2 = e2
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (9), (36), (45), (207), (319), (372),
% 139.51/19.97 | | | | | | | | | | | | | | (4012), (5308), (5352), (5398), (function-axioms)
% 139.51/19.97 | | | | | | | | | | | | | | are inconsistent by sub-proof #524.
% 139.51/19.97 | | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | End of split
% 139.51/19.97 | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | Case 2:
% 139.51/19.97 | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | (5399) all_16_2 = e0
% 139.51/19.97 | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | COMBINE_EQS: (328), (5399) imply:
% 139.51/19.97 | | | | | | | | | | | | (5400) all_6_2 = e0
% 139.51/19.97 | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | REDUCE: (353), (5400) imply:
% 139.51/19.97 | | | | | | | | | | | | (5401) ~ (all_52_6 = e0)
% 139.51/19.97 | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | REDUCE: (357), (5400) imply:
% 139.51/19.97 | | | | | | | | | | | | (5402) ~ (all_52_9 = e0)
% 139.51/19.97 | | | | | | | | | | | |
% 139.51/19.97 | | | | | | | | | | | | REDUCE: (373), (5400) imply:
% 139.51/19.98 | | | | | | | | | | | | (5403) ~ (e3 = e0)
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | REDUCE: (39), (5400) imply:
% 139.51/19.98 | | | | | | | | | | | | (5404) op(e2, e2) = e0
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | (5405) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.51/19.98 | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | REF_CLOSE: (162), (163), (5300), (5401), (5405),
% 139.51/19.98 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.98 | | | | | | | | | | | | | #199.
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | (5406) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.51/19.98 | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | BETA: splitting (5406) gives:
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | (5407) all_57_8 = e0 & op(e1, e1) = e0
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | ALPHA: (5407) implies:
% 139.51/19.98 | | | | | | | | | | | | | | (5408) op(e1, e1) = e0
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5408), (function-axioms) are
% 139.51/19.98 | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | (5409) all_57_11 = e0 & op(e1, e0) = e0
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | ALPHA: (5409) implies:
% 139.51/19.98 | | | | | | | | | | | | | | (5410) op(e1, e0) = e0
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | (5411) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.51/19.98 | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (5303), (5402), (5411),
% 139.51/19.98 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.98 | | | | | | | | | | | | | | | #980.
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | (5412) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.51/19.98 | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | BETA: splitting (5412) gives:
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | (5413) all_57_8 = e0 & op(e1, e1) = e0
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | ALPHA: (5413) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5414) op(e1, e1) = e0
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5414), (function-axioms) are
% 139.51/19.98 | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | (5415) all_57_14 = e0 & op(e0, e1) = e0
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | ALPHA: (5415) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5416) all_57_14 = e0
% 139.51/19.98 | | | | | | | | | | | | | | | | (5417) op(e0, e1) = e0
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.51/19.98 | | | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (5417) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5418) all_52_11 = e0
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.51/19.98 | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (5410) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5419) all_52_14 = e0
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | REDUCE: (125), (5418) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5420) ~ (all_52_7 = e0)
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | REDUCE: (371), (5419) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5421) ~ (all_10_2 = e0)
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | SIMP: (5421) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | (5422) ~ (all_10_2 = e0)
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5423) ~ (all_24_2 = e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | REDUCE: (319), (5423) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5424) ~ (all_10_2 = e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5425) all_54_15 = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5425) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5426) all_10_2 = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | REDUCE: (369), (5426) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5427) ~ (all_52_12 = e3)
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | REDUCE: (45), (5426) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5428) op(e0, e0) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5429) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (5429) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5430) all_57_1 = e3 & op(e3, e2) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (5430) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5431) op(e3, e2) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (5432) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (159), (5301), (5308), (5428), (5431),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (5432), (function-axioms) are inconsistent by
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | sub-proof #212.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (5433) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5433) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (5434) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5434) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (5435) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5417), (5428), (5435), (function-axioms) are
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #664.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (5436) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5436) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (5437) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (168), (207), (372),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | (5308), (5427), (5428), (5437), (function-axioms)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #530.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5438) all_57_3 = e3 & op(e2, e2) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (5438) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5439) op(e2, e2) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5404), (5439), (function-axioms) are
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5440) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | BETA: splitting (5440) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5441) all_57_7 = e3 & op(e1, e2) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (216), (217),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (218), (372), (4011), (5441), (function-axioms)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #233.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5442) all_57_13 = e3 & op(e0, e2) = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | ALPHA: (5442) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5443) all_57_13 = e3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (210), (211), (5416),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | (5428), (5443), (function-axioms) are inconsistent
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | | by sub-proof #666.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5444) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (4012), (5422), (5424), (5444) are
% 139.51/19.98 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #198.
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5445) all_24_2 = e2
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | COMBINE_EQS: (319), (5445) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5446) all_10_2 = e2
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | SIMP: (5446) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5447) all_10_2 = e2
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | REDUCE: (350), (5447) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5448) ~ (all_52_3 = e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | REDUCE: (370), (5447) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5449) ~ (all_52_13 = e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | REDUCE: (45), (5447) imply:
% 139.51/19.98 | | | | | | | | | | | | | | | | | (5450) op(e0, e0) = e2
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5451) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | BETA: splitting (5451) gives:
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5452) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | ALPHA: (5452) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5453) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5454) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5455) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5456) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (144), (148), (149), (159), (163),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (167), (192), (200), (249), (269), (4011), (5299),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5404), (5448), (5450), (5453), (5454), (5455),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5456), (function-axioms) are inconsistent by
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | sub-proof #229.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5457) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | ALPHA: (5457) implies:
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5458) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (5459) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5420), (5450), (5458), (5459),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.98 | | | | | | | | | | | | | | | | | | | #975.
% 139.51/19.98 | | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5460) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/19.98 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/19.98 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (5404), (5417), (5449), (5450),
% 139.51/19.98 | | | | | | | | | | | | | | | | | | (5460), (function-axioms) are inconsistent by
% 139.51/19.98 | | | | | | | | | | | | | | | | | | sub-proof #197.
% 139.51/19.98 | | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | (5461) all_57_2 = e0 & op(e2, e3) = e0
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | REF_CLOSE: (167), (5299), (5461), (function-axioms) are
% 139.51/19.98 | | | | | | | | | | | inconsistent by sub-proof #1028.
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | (5462) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 139.51/19.98 | | | | | | | | | | e0 & op(e0, e3) = e0)
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | REF_CLOSE: (159), (163), (5300), (5301), (5462),
% 139.51/19.98 | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.98 | | | | | | | | | | #196.
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | End of split
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | End of split
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | End of split
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | Case 2:
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | (5463) all_10_2 = e1
% 139.51/19.98 | | | | | | | (5464) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 139.51/19.98 | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) |
% 139.51/19.98 | | | | | | | ( ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 139.51/19.98 | | | | | | | $i(all_10_1))
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | COMBINE_EQS: (309), (5463) imply:
% 139.51/19.98 | | | | | | | (5465) all_30_2 = e1
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | REDUCE: (350), (5463) imply:
% 139.51/19.98 | | | | | | | (5466) ~ (all_52_3 = e1)
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | REDUCE: (361), (5463) imply:
% 139.51/19.98 | | | | | | | (5467) ~ (all_52_7 = e1)
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | REDUCE: (368), (5463) imply:
% 139.51/19.98 | | | | | | | (5468) ~ (all_52_11 = e1)
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | REDUCE: (371), (5463) imply:
% 139.51/19.98 | | | | | | | (5469) ~ (all_52_14 = e1)
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | BETA: splitting (210) gives:
% 139.51/19.98 | | | | | | |
% 139.51/19.98 | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | | (5470) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 139.51/19.98 | | | | | | | | op(e0, e2) = e1)
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | | BETA: splitting (5470) gives:
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | (5471) all_57_12 = e1 & op(e0, e3) = e1
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | REF_CLOSE: (159), (5466), (5471), (function-axioms) are
% 139.51/19.98 | | | | | | | | | inconsistent by sub-proof #350.
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | (5472) all_57_13 = e1 & op(e0, e2) = e1
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | REF_CLOSE: (158), (5467), (5472), (function-axioms) are
% 139.51/19.98 | | | | | | | | | inconsistent by sub-proof #366.
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | End of split
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | | (5473) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 139.51/19.98 | | | | | | | | op(e0, e0) = e1)
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | | BETA: splitting (5473) gives:
% 139.51/19.98 | | | | | | | |
% 139.51/19.98 | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | (5474) all_57_14 = e1 & op(e0, e1) = e1
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | REF_CLOSE: (157), (5468), (5474), (function-axioms) are
% 139.51/19.98 | | | | | | | | | inconsistent by sub-proof #347.
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | (5475) all_57_15 = e1 & op(e0, e0) = e1
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | ALPHA: (5475) implies:
% 139.51/19.98 | | | | | | | | | (5476) all_57_15 = e1
% 139.51/19.98 | | | | | | | | | (5477) op(e0, e0) = e1
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | BETA: splitting (52) gives:
% 139.51/19.98 | | | | | | | | |
% 139.51/19.98 | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | (5478) ~ (all_14_2 = e0)
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | BETA: splitting (55) gives:
% 139.51/19.98 | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | (5479) ~ (all_16_2 = e0)
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | REDUCE: (328), (5479) imply:
% 139.51/19.98 | | | | | | | | | | | (5480) ~ (all_6_2 = e0)
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | BETA: splitting (61) gives:
% 139.51/19.98 | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | (5481) ~ (all_20_2 = e1)
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | REDUCE: (283), (5481) imply:
% 139.51/19.98 | | | | | | | | | | | | (5482) ~ (all_6_2 = e1)
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | BETA: splitting (199) gives:
% 139.51/19.98 | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | (5483) all_54_5 = e3
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | COMBINE_EQS: (268), (5483) imply:
% 139.51/19.98 | | | | | | | | | | | | | (5484) all_6_2 = e3
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | REDUCE: (373), (5484) imply:
% 139.51/19.98 | | | | | | | | | | | | | (5485) $false
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | CLOSE: (5485) is inconsistent.
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | Case 2:
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | (5486) ~ (all_54_5 = e3)
% 139.51/19.98 | | | | | | | | | | | | | (5487) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | BETA: splitting (5487) gives:
% 139.51/19.98 | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | Case 1:
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | (5488) all_54_5 = e2
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | COMBINE_EQS: (268), (5488) imply:
% 139.51/19.98 | | | | | | | | | | | | | | (5489) all_6_2 = e2
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | REDUCE: (355), (5489) imply:
% 139.51/19.98 | | | | | | | | | | | | | | (5490) ~ (all_52_7 = e2)
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.98 | | | | | | | | | | | | | | REDUCE: (357), (5489) imply:
% 139.51/19.98 | | | | | | | | | | | | | | (5491) ~ (all_52_9 = e2)
% 139.51/19.98 | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | REDUCE: (359), (5489) imply:
% 139.51/19.99 | | | | | | | | | | | | | | (5492) ~ (all_52_13 = e2)
% 139.51/19.99 | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | REDUCE: (373), (5489) imply:
% 139.51/19.99 | | | | | | | | | | | | | | (5493) ~ (e3 = e2)
% 139.51/19.99 | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | REDUCE: (39), (5489) imply:
% 139.51/19.99 | | | | | | | | | | | | | | (5494) op(e2, e2) = e2
% 139.51/19.99 | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 139.51/19.99 | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | (5495) ~ (all_22_2 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | REDUCE: (321), (5495) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | (5496) ~ (all_14_2 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | (5497) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/19.99 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/19.99 | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/19.99 | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/19.99 | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.51/19.99 | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.51/19.99 | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.51/19.99 | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.51/19.99 | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.51/19.99 | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | BETA: splitting (5497) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5498) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/19.99 | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5494), (5498), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #317.
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5499) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.51/19.99 | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (5496), (5499), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #316.
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | End of split
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | (5500) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/19.99 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/19.99 | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/19.99 | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/19.99 | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.51/19.99 | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.51/19.99 | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.51/19.99 | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.51/19.99 | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.51/19.99 | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.51/19.99 | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.51/19.99 | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.51/19.99 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.51/19.99 | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.51/19.99 | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.51/19.99 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.99 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/19.99 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.99 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | BETA: splitting (5500) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5501) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/19.99 | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | BETA: splitting (5501) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (5502) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | ALPHA: (5502) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (5503) op(e0, e0) = e3
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5477), (5503), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (5504) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | ALPHA: (5504) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (5505) op(e2, e2) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5494), (5505), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | End of split
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5506) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.51/19.99 | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.51/19.99 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (4011), (5477), (5494), (5506),
% 139.51/19.99 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.99 | | | | | | | | | | | | | | | | | #276.
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | End of split
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | End of split
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | (5507) all_22_2 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | (5508) ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0
% 139.51/19.99 | | | | | | | | | | | | | | | & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 139.51/19.99 | | | | | | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e3, e1)
% 139.51/19.99 | | | | | | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | COMBINE_EQS: (321), (5507) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | (5509) all_14_2 = e1
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | SIMP: (5509) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | (5510) all_14_2 = e1
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | COMBINE_EQS: (313), (5510) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | (5511) all_34_2 = e1
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | REDUCE: (343), (5510) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | (5512) ~ (all_52_4 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | REDUCE: (345), (5510) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | (5513) ~ (all_52_8 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | REDUCE: (51), (5510) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | (5514) op(e3, e3) = e1
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.51/19.99 | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | (5515) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | BETA: splitting (5515) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5516) all_57_4 = e1 & op(e3, e1) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5513), (5516), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #349.
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5517) all_57_5 = e1 & op(e2, e1) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | ALPHA: (5517) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5518) all_57_5 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | (5519) op(e2, e1) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (5520) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (170), (5494), (5512), (5520),
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.99 | | | | | | | | | | | | | | | | | | #379.
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | (5521) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | BETA: splitting (5521) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5522) all_57_7 = e1 & op(e1, e2) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | ALPHA: (5522) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5523) all_57_7 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5524) op(e1, e2) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (5524) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5525) all_52_6 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (5519) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5526) all_52_9 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | REDUCE: (143), (5525) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5527) ~ (all_52_2 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | REDUCE: (128), (5525) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5528) ~ (all_52_7 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (5525) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5529) ~ (all_52_14 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | REDUCE: (4004), (5526) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5530) ~ (e3 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | REDUCE: (5491), (5526) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | (5531) ~ (e2 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (5532) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5532) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5533) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5533) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5534) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5535) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5536) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (163), (207), (4011), (5477),
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5494), (5514), (5527), (5534), (5535), (5536),
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | #275.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5537) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5537) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5538) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (5524), (5538), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (5539) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5539) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5540) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5540) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5541) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (5514), (5541), (function-axioms)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5542) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5542) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5543) op(e0, e0) = all_56_15
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5544) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5545) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5546) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5547) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5548) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | (5549) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5546) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | (5550) all_56_9 = e0 & op(e3, e3) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5550) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | (5551) op(e3, e3) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5514), (5551), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | (5552) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5552) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | (5553) ~ (all_56_2 = e3)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | (5554) op(e3, e0) = all_56_2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5547) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | (5555) all_56_8 = e1 & op(e1, e0) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5555) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | (5556) op(e1, e0) = e1
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5469), (5556), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | (5557) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5557) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | (5558) ~ (all_56_13 = e0)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | (5559) op(e1, e1) = all_56_13
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5548) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | (5560) all_56_5 = e2 & op(e2, e0) = e2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5560) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | (5561) op(e2, e0) = e2
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5492), (5561), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | (5562) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5562) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | (5563) ~ (all_56_11 = e0)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | (5564) op(e2, e2) = all_56_11
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5549) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | (5565) all_56_2 = e3 & op(e3, e0) = e3
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5565) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | (5566) all_56_2 = e3
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5553), (5566) imply:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | (5567) $false
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5567) is inconsistent.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | (5568) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5568) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | (5569) ~ (all_56_9 = e0)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | (5570) op(e3, e3) = all_56_9
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5544) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (5571) all_56_13 = e0 & op(e1, e1) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5571) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (5572) op(e1, e1) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5572), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (5573) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5573) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (5574) ~ (all_56_8 = e1)
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | (5575) op(e1, e0) = all_56_8
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5545) gives:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5576) all_56_11 = e0 & op(e2, e2) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5576) implies:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5577) op(e2, e2) = e0
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5563), (5564), (5577), (function-axioms) are
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5578) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/19.99 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5578) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5579) ~ (all_56_5 = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5580) op(e2, e0) = all_56_5
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (5477), (5543)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5581) all_56_15 = e1
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e1, simplifying with (160), (5575)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5582) all_56_8 = all_52_14
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (4011), (5559)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5583) all_56_13 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5, e0, e2, simplifying with (164), (5580)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5584) all_56_5 = all_52_13
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (5494), (5564)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5585) all_56_11 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e3, simplifying with (168), (5554)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5586) all_56_2 = all_52_12
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_9,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (5514), (5570) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5587) all_56_9 = e1
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5553), (5586) imply:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5588) ~ (all_52_12 = e3)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5589) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5589) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5590) all_57_0 = e3 & op(e3, e3) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5590) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5591) op(e3, e3) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5514), (5591), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5592) all_57_1 = e3 & op(e3, e2) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5592) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5593) all_57_1 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5594) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5594) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5595) all_57_9 = e3 & op(e3, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5595) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5596) op(e3, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (5588), (5596), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1105.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5597) all_57_10 = e3 & op(e2, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5597) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5598) all_57_10 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5599) op(e2, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5600) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5600) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5601) all_57_1 = e0 & op(e3, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5593), (5601) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #312.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5602) all_57_3 = e0 & op(e2, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5602) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5603) op(e2, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5563), (5564), (5603), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5604) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5604) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5605) all_57_7 = e0 & op(e1, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5605) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5606) all_57_7 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5523), (5606) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5607) all_57_13 = e0 & op(e0, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5607) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5608) all_57_13 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5609) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5609) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5610) all_57_2 = e0 & op(e2, e3) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5610) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5611) op(e2, e3) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5612) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5612) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5613) all_57_12 = e3 & op(e0, e3) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5613) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5614) all_57_12 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5615) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5615) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5616) all_57_12 = e2 & op(e0, e3) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5616) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5617) all_57_12 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5614), (5617) imply:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5618) e3 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (160),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (217), (218), (228), (229), (231), (372),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011), (5467), (5469), (5494), (5593), (5618),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #195.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5619) all_57_13 = e2 & op(e0, e2) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5490), (5619), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5620) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5620) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5621) all_57_14 = e2 & op(e0, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5621) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5622) op(e0, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e1, e0, simplifying with (157), (5622) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5623) all_52_11 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e2, simplifying with (164), (5599) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5624) all_52_13 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5625) ~ (all_30_2 = e1)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5465), (5625) imply:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5626) $false
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5626) is inconsistent.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5627) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5464) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5628) ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) &
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5628) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5629) op(e0, e1) = all_10_1
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5464), (5599), (5622), (5627), (5629),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #194.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5630) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5630) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5631) op(e0, e1) = all_10_1
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5464), (5599), (5622), (5627), (5631),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #194.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5632) all_57_15 = e2 & op(e0, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5632) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5633) op(e0, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5477), (5633), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5634) all_57_13 = e3 & op(e0, e2) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5634) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5635) all_57_13 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5608), (5635) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #804.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5636) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5636) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5637) all_57_14 = e3 & op(e0, e1) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5637) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5638) all_57_14 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5639) op(e0, e1) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5640) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5640) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5641) all_57_4 = e2 & op(e3, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5641) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5642) op(e3, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (76), (82), (157), (167), (169), (5464), (5465),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5508), (5511), (5611), (5639), (5642),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #369.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5643) all_57_5 = e2 & op(e2, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5643) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5644) op(e2, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5491), (5644), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5645) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5645) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5646) all_57_8 = e2 & op(e1, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5646) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5647) op(e1, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (5647), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5648) all_57_14 = e2 & op(e0, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5648) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5649) all_57_14 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5638), (5649) imply:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5650) e3 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5650) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5651) e3 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (160),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (217), (218), (228), (229), (231), (372),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011), (5467), (5469), (5494), (5593), (5651),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #195.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5652) all_57_15 = e3 & op(e0, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5652) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5653) op(e0, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (213), (214),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5598), (5653), (function-axioms) are inconsistent
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #650.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5654) all_57_3 = e0 & op(e2, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5654) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5655) op(e2, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5563), (5564), (5655), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5656) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5656) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5657) all_57_5 = e0 & op(e2, e1) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5518), (5657) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #264.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5658) all_57_10 = e0 & op(e2, e0) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5658) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5659) all_57_10 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5598), (5659) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #935.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5660) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5660) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5661) all_57_11 = e3 & op(e1, e0) = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5661) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5662) all_57_11 = e3
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5663) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5663) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5664) all_57_9 = e2 & op(e3, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5664) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5665) all_57_9 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5666) all_57_15 = e0 & op(e0, e0) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5476), (5666) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #358.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5667) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5667) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5668) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5668) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5669) all_57_9 = e0 & op(e3, e0) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5669) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5670) all_57_9 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5665), (5670) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1018.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5671) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5671) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5672) all_57_10 = e0 & op(e2, e0) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5672) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5673) all_57_10 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5674) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5674) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5675) all_57_6 = e0 & op(e1, e3) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5675) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5676) all_57_6 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5677) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5677) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5678) all_57_6 = e2 & op(e1, e3) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5676), (5678) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #783.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5679) all_57_7 = e2 & op(e1, e2) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5679) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5680) all_57_7 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5681) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (228), (231),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5494), (5680), (5681), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #415.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5521) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5522), (5680) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #864.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5682) all_57_13 = e1 & op(e0, e2) = e1
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5467), (5682), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5683) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5683) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5684) all_57_8 = e2 & op(e1, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5684) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5685) op(e1, e1) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (5685), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5686) all_57_11 = e2 & op(e1, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5686) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5687) all_57_11 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (215), (5477), (5665), (5673),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5687), (function-axioms) are inconsistent by
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #392.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5688) all_57_7 = e0 & op(e1, e2) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5688) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5689) all_57_7 = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5523), (5689) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5690) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5690) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5691) all_57_8 = e0 & op(e1, e1) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5691) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5692) op(e1, e1) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (4011), (5692), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #308.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5693) all_57_11 = e0 & op(e1, e0) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5662), (5693) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #584.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5694) all_57_11 = e0 & op(e1, e0) = e0
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5662), (5694) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #584.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5695) all_57_10 = e2 & op(e2, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5695) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5696) op(e2, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5492), (5696), (function-axioms) are
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5697) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5697) gives:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5698) all_57_11 = e2 & op(e1, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5698) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5699) all_57_11 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5662), (5699) imply:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5700) e3 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5700) implies:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5701) e3 = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (160),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (216), (217), (218), (228), (229), (231), (372),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (4011), (5467), (5469), (5494), (5593), (5701),
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #195.
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5702) all_57_15 = e2 & op(e0, e0) = e2
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.00 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5702) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5703) op(e0, e0) = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5477), (5703), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5704) all_57_15 = e3 & op(e0, e0) = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5704) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5705) op(e0, e0) = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5477), (5705), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5706) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (4003), (5588), (5706),
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1104.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5707) all_57_13 = e1 & op(e0, e2) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5467), (5707), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | (5708) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.51/20.01 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (4011), (5468), (5708),
% 139.51/20.01 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | | | #193.
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5709) all_54_5 = e1 | all_54_5 = e0
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (268), (5480), (5482), (5709) are inconsistent by
% 139.51/20.01 | | | | | | | | | | | | | | sub-proof #641.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | (5710) all_20_2 = e1
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | COMBINE_EQS: (283), (5710) imply:
% 139.51/20.01 | | | | | | | | | | | | (5711) all_6_2 = e1
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | REDUCE: (357), (5711) imply:
% 139.51/20.01 | | | | | | | | | | | | (5712) ~ (all_52_9 = e1)
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | REDUCE: (373), (5711) imply:
% 139.51/20.01 | | | | | | | | | | | | (5713) ~ (e3 = e1)
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | (5714) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.51/20.01 | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | BETA: splitting (5714) gives:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5715) all_57_4 = e1 & op(e3, e1) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | ALPHA: (5715) implies:
% 139.51/20.01 | | | | | | | | | | | | | | (5716) op(e3, e1) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (36), (39), (51), (169), (207), (345),
% 139.51/20.01 | | | | | | | | | | | | | | (372), (373), (4003), (4011), (5477), (5716),
% 139.51/20.01 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | #204.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5717) all_57_5 = e1 & op(e2, e1) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (165), (5712), (5717), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | (5718) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.51/20.01 | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | REF_CLOSE: (8), (157), (4011), (5468), (5718),
% 139.51/20.01 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | #193.
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | (5719) all_16_2 = e0
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | COMBINE_EQS: (328), (5719) imply:
% 139.51/20.01 | | | | | | | | | | | (5720) all_6_2 = e0
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (351), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5721) ~ (all_52_4 = e0)
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (353), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5722) ~ (all_52_6 = e0)
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (355), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5723) ~ (all_52_7 = e0)
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (357), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5724) ~ (all_52_9 = e0)
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (359), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5725) ~ (all_52_13 = e0)
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (373), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5726) ~ (e3 = e0)
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | REDUCE: (39), (5720) imply:
% 139.51/20.01 | | | | | | | | | | | (5727) op(e2, e2) = e0
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | BETA: splitting (64) gives:
% 139.51/20.01 | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | (5728) ~ (all_22_2 = e1)
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | REDUCE: (321), (5728) imply:
% 139.51/20.01 | | | | | | | | | | | | (5729) ~ (all_14_2 = e1)
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | (5730) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.01 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.01 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.01 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.51/20.01 | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.51/20.01 | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.51/20.01 | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.51/20.01 | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.51/20.01 | | | | | | | | | | | | | $i(all_56_6))
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | BETA: splitting (5730) gives:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5731) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.01 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.01 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.01 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (7), (5727), (5731), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | inconsistent by sub-proof #1118.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5732) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.51/20.01 | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.51/20.01 | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.51/20.01 | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.51/20.01 | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (51), (5729), (5732), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | inconsistent by sub-proof #316.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | (5733) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.01 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/20.01 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.51/20.01 | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.51/20.01 | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.51/20.01 | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.51/20.01 | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.51/20.01 | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.51/20.01 | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.51/20.01 | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.51/20.01 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.51/20.01 | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.51/20.01 | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.51/20.01 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/20.01 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | BETA: splitting (5733) gives:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5734) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.01 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/20.01 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (5477), (5727), (5734),
% 139.51/20.01 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | #192.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5735) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.51/20.01 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.51/20.01 | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.51/20.01 | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.51/20.01 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.51/20.01 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.51/20.01 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.51/20.01 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.51/20.01 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.51/20.01 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/20.01 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (4011), (5477), (5727),
% 139.51/20.01 | | | | | | | | | | | | | | (5735), (function-axioms) are inconsistent by
% 139.51/20.01 | | | | | | | | | | | | | | sub-proof #191.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | (5736) all_22_2 = e1
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | COMBINE_EQS: (321), (5736) imply:
% 139.51/20.01 | | | | | | | | | | | | (5737) all_14_2 = e1
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | SIMP: (5737) implies:
% 139.51/20.01 | | | | | | | | | | | | (5738) all_14_2 = e1
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | REDUCE: (339), (5738) imply:
% 139.51/20.01 | | | | | | | | | | | | (5739) ~ (all_52_2 = e1)
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | REDUCE: (51), (5738) imply:
% 139.51/20.01 | | | | | | | | | | | | (5740) op(e3, e3) = e1
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | BETA: splitting (217) gives:
% 139.51/20.01 | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | (5741) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 139.51/20.01 | | | | | | | | | | | | | & op(e1, e2) = e1)
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | BETA: splitting (5741) gives:
% 139.51/20.01 | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5742) all_57_6 = e1 & op(e1, e3) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | ALPHA: (5742) implies:
% 139.51/20.01 | | | | | | | | | | | | | | (5743) op(e1, e3) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | REF_CLOSE: (163), (5739), (5743), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | (5744) all_57_7 = e1 & op(e1, e2) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | ALPHA: (5744) implies:
% 139.51/20.01 | | | | | | | | | | | | | | (5745) all_57_7 = e1
% 139.51/20.01 | | | | | | | | | | | | | | (5746) op(e1, e2) = e1
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.51/20.01 | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | (5747) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.51/20.01 | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.51/20.01 | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | BETA: splitting (5747) gives:
% 139.51/20.01 | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | (5748) all_57_4 = e1 & op(e3, e1) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | ALPHA: (5748) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5749) all_57_4 = e1
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | (5750) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.51/20.01 | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5721), (5740), (5750),
% 139.51/20.01 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | | | | #819.
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | (5751) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.51/20.01 | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | BETA: splitting (5751) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5752) all_57_4 = e0 & op(e3, e1) = e0
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5749), (5752) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | | | | | #1100.
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5753) all_57_9 = e0 & op(e3, e0) = e0
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | ALPHA: (5753) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5754) all_57_9 = e0
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5755) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (5755) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5756) all_57_0 = e2 & op(e3, e3) = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (5756) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5757) op(e3, e3) = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5740), (5757), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5758) all_57_1 = e2 & op(e3, e2) = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (5758) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5759) all_57_1 = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (239), (5740), (5749), (5754),
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5759), (function-axioms) are inconsistent by
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | sub-proof #375.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5760) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (5760) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5761) all_57_4 = e2 & op(e3, e1) = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (5761) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5762) all_57_4 = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5749), (5762) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | #1088.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5763) all_57_9 = e2 & op(e3, e0) = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (5763) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5764) all_57_9 = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5754), (5764) are inconsistent by sub-proof
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | #1018.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | (5765) all_57_5 = e1 & op(e2, e1) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | ALPHA: (5765) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5766) all_57_5 = e1
% 139.51/20.01 | | | | | | | | | | | | | | | | (5767) op(e2, e1) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (5746) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5768) all_52_6 = e1
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (5767) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5769) all_52_9 = e1
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | REDUCE: (126), (5768) imply:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5770) ~ (all_52_14 = e1)
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | REDUCE: (117), (5769) imply:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5771) ~ (all_52_13 = e1)
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | SIMP: (5771) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5772) ~ (all_52_13 = e1)
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | REDUCE: (4004), (5769) imply:
% 139.51/20.01 | | | | | | | | | | | | | | | | (5773) ~ (e3 = e1)
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | (5774) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/20.01 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/20.01 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | BETA: splitting (5774) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5775) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | ALPHA: (5775) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5776) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5777) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | (5778) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 139.51/20.01 | | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | BETA: splitting (5778) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5779) all_56_6 = e1 & op(e1, e3) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | ALPHA: (5779) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5780) op(e1, e3) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (5739), (5780), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5781) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | ALPHA: (5781) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | (5782) ~ (all_56_13 = e3)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | BETA: splitting (5776) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5783) all_56_15 = e3 & op(e0, e0) = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (5783) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5784) op(e0, e0) = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5477), (5784), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5785) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | ALPHA: (5785) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | (5786) ~ (all_56_10 = e0)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (5787) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5787) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (5788) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5740), (5788), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (5789) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5782), (5789) are inconsistent by sub-proof #297.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (5790) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5790) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (5791) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5791) gives:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | (5792) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5777), (5786), (5792), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #280.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | (5793) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5793) implies:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | (5794) op(e2, e2) = e1
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5727), (5794), (function-axioms) are
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (5795) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (4011), (5477), (5727),
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | (5795), (function-axioms) are inconsistent by
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | | sub-proof #191.
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.01 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.01 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5796) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.51/20.02 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ALPHA: (5796) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5797) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (5746), (5797), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | (5798) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/20.02 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/20.02 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/20.02 | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | BETA: splitting (5798) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5799) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ALPHA: (5799) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5800) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (4003), (5740), (5800), (function-axioms)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #295.
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5801) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | ALPHA: (5801) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5802) op(e0, e0) = all_56_15
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5803) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5804) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5805) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5806) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.51/20.02 | | | | | | | | | | | | | | | | | | (5807) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/20.02 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | BETA: splitting (5804) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | (5808) all_56_9 = e0 & op(e3, e3) = e0
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | ALPHA: (5808) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | (5809) op(e3, e3) = e0
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5740), (5809), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | (5810) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | ALPHA: (5810) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | (5811) ~ (all_56_2 = e3)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | (5812) op(e3, e0) = all_56_2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | BETA: splitting (5806) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | (5813) all_56_5 = e2 & op(e2, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (5813) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | (5814) op(e2, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5807) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | (5815) all_56_2 = e3 & op(e3, e0) = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5815) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | (5816) all_56_2 = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5811), (5816) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | (5817) $false
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | CLOSE: (5817) is inconsistent.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | (5818) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | ALPHA: (5818) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | (5819) ~ (all_56_9 = e0)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | (5820) op(e3, e3) = all_56_9
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5805) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | (5821) all_56_8 = e1 & op(e1, e0) = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5821) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | (5822) op(e1, e0) = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (5469), (5822), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #459.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | (5823) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5823) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | (5824) ~ (all_56_13 = e0)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | (5825) op(e1, e1) = all_56_13
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5803) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5826) all_56_11 = e0 & op(e2, e2) = e0
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (5477), (5802)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5827) all_56_15 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (4011), (5825)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5828) all_56_13 = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (5814) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5829) all_52_13 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e3, simplifying with (168), (5812)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5830) all_56_2 = all_52_12
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_9,
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (5740), (5820) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5831) all_56_9 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5811), (5830) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5832) ~ (all_52_12 = e3)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (5829) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5833) ~ (all_52_1 = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | (5834) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5834) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5835) all_57_2 = e3 & op(e2, e3) = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5835) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5836) all_57_2 = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (5837) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5837) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5838) all_57_9 = e2 & op(e3, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5838) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5839) all_57_9 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5840) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (5727), (5833), (5840),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #881.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5841) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5841) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5842) all_57_5 = e2 & op(e2, e1) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5842) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5843) all_57_5 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5766), (5843) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5844) e2 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (5844) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5845) e2 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5839), (5845) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5846) all_57_9 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (233), (237),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (5721), (5740), (5846), (function-axioms)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #812.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5847) all_57_10 = e2 & op(e2, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (168), (169), (209), (210), (211), (212),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (220), (222), (230), (238),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (372), (4003), (4011), (5476), (5477),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5722), (5723), (5724), (5727), (5740), (5745),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766), (5832), (5836), (5847), (function-axioms)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #186.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5848) all_57_10 = e2 & op(e2, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (158), (162),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (168), (169), (209), (210), (211), (212),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (216), (218), (220), (222), (230), (238),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (372), (4003), (4011), (5476), (5477),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5722), (5723), (5724), (5727), (5740), (5745),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5766), (5832), (5836), (5848), (function-axioms)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #186.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (5849) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5849) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5850) all_57_11 = e2 & op(e1, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5850) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5851) all_57_11 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (167), (168), (215), (226),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5477), (5727), (5766), (5832), (5833), (5851),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | #185.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5852) all_57_15 = e2 & op(e0, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5852) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5853) op(e0, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5477), (5853), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5854) all_57_3 = e3 & op(e2, e2) = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5854) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5855) op(e2, e2) = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5727), (5855), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | (5856) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5856) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5857) all_57_5 = e3 & op(e2, e1) = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5766), (5857) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | #504.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5858) all_57_10 = e3 & op(e2, e0) = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5858) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | (5859) all_57_10 = e3
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (5860) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5860) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5861) all_57_9 = e2 & op(e3, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5861) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5862) all_57_9 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5863) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (5727), (5833), (5863),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #881.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5864) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5864) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5865) all_57_5 = e2 & op(e2, e1) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5865) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5866) all_57_5 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5766), (5866) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5867) e2 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5862), (5867) imply:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5868) all_57_9 = e1
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (170), (233), (237),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (5721), (5740), (5868), (function-axioms)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #812.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5869) all_57_10 = e2 & op(e2, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5869) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5870) all_57_10 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5859), (5870) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #492.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5871) all_57_10 = e2 & op(e2, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5871) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5872) all_57_10 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5859), (5872) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | #492.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | (5873) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5873) gives:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5874) all_57_11 = e2 & op(e1, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5874) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5875) all_57_11 = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (8), (9), (167), (168), (215), (226),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5477), (5727), (5766), (5832), (5833), (5875),
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | #185.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5876) all_57_15 = e2 & op(e0, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5876) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5877) op(e0, e0) = e2
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5477), (5877), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5878) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5878) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | (5879) ~ (all_56_5 = e2)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5727), (5806), (5879), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #271.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | (5880) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | ALPHA: (5880) implies:
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | (5881) ~ (all_56_11 = e0)
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | (5882) op(e2, e2) = all_56_11
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5727), (5881), (5882), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | (5883) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.51/20.02 | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.51/20.02 | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | | REF_CLOSE: (8), (157), (4011), (5468), (5883),
% 139.51/20.02 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | | | #193.
% 139.51/20.02 | | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | (5884) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 139.51/20.02 | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 139.51/20.02 | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | | REF_CLOSE: (8), (160), (4011), (5469), (5884),
% 139.51/20.02 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.02 | | | | | | | | | | | | | #268.
% 139.51/20.02 | | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | (5885) all_14_2 = e0
% 139.51/20.02 | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | REDUCE: (51), (5885) imply:
% 139.51/20.02 | | | | | | | | | | (5886) op(e3, e3) = e0
% 139.51/20.02 | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | BETA: splitting (207) gives:
% 139.51/20.02 | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | Case 1:
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | (5887) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.02 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.02 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.02 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.02 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.02 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.51/20.02 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.51/20.02 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.51/20.02 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.51/20.02 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.51/20.02 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.51/20.02 | | | | | | | | | | | $i(all_56_6))
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | REF_CLOSE: (4), (5), (5886), (5887), (function-axioms) are
% 139.51/20.02 | | | | | | | | | | | inconsistent by sub-proof #752.
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | Case 2:
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | (5888) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.02 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/20.02 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/20.02 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/20.02 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/20.02 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.51/20.02 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.51/20.02 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.51/20.02 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.51/20.02 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.51/20.02 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.51/20.02 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.51/20.02 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.51/20.02 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.51/20.02 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.51/20.02 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.51/20.02 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.51/20.02 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.51/20.02 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.02 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/20.02 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/20.02 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.02 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/20.02 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (36), (372), (4011), (5477),
% 139.51/20.02 | | | | | | | | | | | (5888), (function-axioms) are inconsistent by
% 139.51/20.02 | | | | | | | | | | | sub-proof #211.
% 139.51/20.02 | | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | | |
% 139.51/20.02 | | | | | | | | | End of split
% 139.51/20.02 | | | | | | | | |
% 139.51/20.02 | | | | | | | | End of split
% 139.51/20.02 | | | | | | | |
% 139.51/20.02 | | | | | | | End of split
% 139.51/20.02 | | | | | | |
% 139.51/20.02 | | | | | | End of split
% 139.51/20.02 | | | | | |
% 139.51/20.02 | | | | | Case 2:
% 139.51/20.02 | | | | | |
% 139.51/20.02 | | | | | | (5889) all_57_14 = e3 & op(e0, e1) = e3
% 139.51/20.02 | | | | | |
% 139.51/20.02 | | | | | | REF_CLOSE: (157), (4005), (5889), (function-axioms) are inconsistent
% 139.51/20.02 | | | | | | by sub-proof #184.
% 139.51/20.02 | | | | | |
% 139.51/20.02 | | | | | End of split
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | End of split
% 139.51/20.02 | | | |
% 139.51/20.02 | | | End of split
% 139.51/20.02 | | |
% 139.51/20.02 | | Case 2:
% 139.51/20.02 | | |
% 139.51/20.02 | | | (5890) all_6_2 = e3
% 139.51/20.02 | | | (5891) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) =
% 139.51/20.02 | | | all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) &
% 139.51/20.02 | | | op(e2, e3) = all_6_1 & $i(all_6_1))
% 139.51/20.02 | | |
% 139.51/20.02 | | | COMBINE_EQS: (331), (5890) imply:
% 139.51/20.02 | | | (5892) all_26_2 = e3
% 139.51/20.02 | | |
% 139.51/20.02 | | | REDUCE: (348), (5890) imply:
% 139.51/20.02 | | | (5893) ~ (all_52_1 = e3)
% 139.51/20.02 | | |
% 139.51/20.02 | | | REDUCE: (351), (5890) imply:
% 139.51/20.02 | | | (5894) ~ (all_52_4 = e3)
% 139.51/20.02 | | |
% 139.51/20.02 | | | REDUCE: (353), (5890) imply:
% 139.51/20.02 | | | (5895) ~ (all_52_6 = e3)
% 139.51/20.02 | | |
% 139.51/20.02 | | | REDUCE: (355), (5890) imply:
% 139.51/20.02 | | | (5896) ~ (all_52_7 = e3)
% 139.51/20.02 | | |
% 139.51/20.02 | | | REDUCE: (357), (5890) imply:
% 139.51/20.02 | | | (5897) ~ (all_52_9 = e3)
% 139.51/20.02 | | |
% 139.51/20.02 | | | REDUCE: (359), (5890) imply:
% 139.51/20.02 | | | (5898) ~ (all_52_13 = e3)
% 139.51/20.02 | | |
% 139.51/20.02 | | | BETA: splitting (227) gives:
% 139.51/20.02 | | |
% 139.51/20.02 | | | Case 1:
% 139.51/20.02 | | | |
% 139.51/20.02 | | | | (5899) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 139.51/20.02 | | | | e2) = e3)
% 139.51/20.02 | | | |
% 139.51/20.02 | | | | BETA: splitting (5899) gives:
% 139.51/20.02 | | | |
% 139.51/20.02 | | | | Case 1:
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | | (5900) all_57_2 = e3 & op(e2, e3) = e3
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | | REF_CLOSE: (167), (5893), (5900), (function-axioms) are inconsistent
% 139.51/20.02 | | | | | by sub-proof #183.
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | Case 2:
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | | (5901) all_57_3 = e3 & op(e2, e2) = e3
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | | ALPHA: (5901) implies:
% 139.51/20.02 | | | | | (5902) all_57_3 = e3
% 139.51/20.02 | | | | | (5903) op(e2, e2) = e3
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | | BETA: splitting (43) gives:
% 139.51/20.02 | | | | |
% 139.51/20.02 | | | | | Case 1:
% 139.51/20.02 | | | | | |
% 139.51/20.02 | | | | | | (5904) ~ (all_8_2 = e3)
% 139.51/20.02 | | | | | |
% 139.51/20.02 | | | | | | REDUCE: (330), (5904) imply:
% 139.51/20.03 | | | | | | (5905) ~ (all_4_2 = e3)
% 139.51/20.03 | | | | | |
% 139.51/20.03 | | | | | | BETA: splitting (46) gives:
% 139.51/20.03 | | | | | |
% 139.51/20.03 | | | | | | Case 1:
% 139.51/20.03 | | | | | | |
% 139.51/20.03 | | | | | | | (5906) ~ (all_10_2 = e1)
% 139.51/20.03 | | | | | | |
% 139.51/20.03 | | | | | | | BETA: splitting (52) gives:
% 139.51/20.03 | | | | | | |
% 139.51/20.03 | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | |
% 139.51/20.03 | | | | | | | | (5907) ~ (all_14_2 = e0)
% 139.51/20.03 | | | | | | | |
% 139.51/20.03 | | | | | | | | BETA: splitting (64) gives:
% 139.51/20.03 | | | | | | | |
% 139.51/20.03 | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | |
% 139.51/20.03 | | | | | | | | | (5908) ~ (all_22_2 = e1)
% 139.51/20.03 | | | | | | | | |
% 139.51/20.03 | | | | | | | | | REDUCE: (321), (5908) imply:
% 139.51/20.03 | | | | | | | | | (5909) ~ (all_14_2 = e1)
% 139.51/20.03 | | | | | | | | |
% 139.51/20.03 | | | | | | | | | BETA: splitting (67) gives:
% 139.51/20.03 | | | | | | | | |
% 139.51/20.03 | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | (5910) ~ (all_24_2 = e2)
% 139.51/20.03 | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | REDUCE: (319), (5910) imply:
% 139.51/20.03 | | | | | | | | | | (5911) ~ (all_10_2 = e2)
% 139.51/20.03 | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | BETA: splitting (70) gives:
% 139.51/20.03 | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | (5912) ~ (all_26_2 = e3)
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | REDUCE: (5892), (5912) imply:
% 139.51/20.03 | | | | | | | | | | | (5913) $false
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | CLOSE: (5913) is inconsistent.
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | (5914) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0
% 139.51/20.03 | | | | | | | | | | | & op(e2, e3) = all_26_1 & $i(all_26_0) &
% 139.51/20.03 | | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3)
% 139.51/20.03 | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | BETA: splitting (85) gives:
% 139.51/20.03 | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | (5915) ~ (all_36_2 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (305), (5915) imply:
% 139.51/20.03 | | | | | | | | | | | | (5916) ~ (all_14_2 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | (5917) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.03 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.03 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.03 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.03 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.51/20.03 | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.51/20.03 | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.51/20.03 | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.51/20.03 | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.51/20.03 | | | | | | | | | | | | | $i(all_56_6))
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | BETA: splitting (5917) gives:
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | (5918) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.03 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.51/20.03 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.51/20.03 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.51/20.03 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | BETA: splitting (5918) gives:
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | (5919) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.51/20.03 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0 &
% 139.51/20.03 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_0)
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | ALPHA: (5919) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | (5920) op(e3, e3) = e2
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | REF_CLOSE: (51), (204), (279), (5907), (5909), (5916),
% 139.51/20.03 | | | | | | | | | | | | | | | (5920), (function-axioms) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | sub-proof #182.
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | (5921) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 =
% 139.51/20.03 | | | | | | | | | | | | | | | e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 &
% 139.51/20.03 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_3)
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | ALPHA: (5921) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | (5922) op(e3, e3) = e2
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | REF_CLOSE: (51), (204), (279), (5907), (5909), (5916),
% 139.51/20.03 | | | | | | | | | | | | | | | (5922), (function-axioms) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | sub-proof #182.
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | End of split
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | (5923) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.51/20.03 | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.51/20.03 | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.51/20.03 | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.51/20.03 | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (5923), (function-axioms) are
% 139.51/20.03 | | | | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | End of split
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | (5924) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.51/20.03 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.51/20.03 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.51/20.03 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.51/20.03 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.51/20.03 | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.51/20.03 | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.51/20.03 | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.51/20.03 | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.51/20.03 | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.51/20.03 | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.51/20.03 | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.51/20.03 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.51/20.03 | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.51/20.03 | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.51/20.03 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.03 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.51/20.03 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.51/20.03 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | REF_CLOSE: (36), (45), (51), (372), (5906), (5907), (5911),
% 139.51/20.03 | | | | | | | | | | | | | (5924), (function-axioms) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | sub-proof #181.
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | End of split
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | (5925) all_36_2 = e2
% 139.51/20.03 | | | | | | | | | | | | (5926) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 139.51/20.03 | | | | | | | | | | | | & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 139.51/20.03 | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2)
% 139.51/20.03 | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | COMBINE_EQS: (305), (5925) imply:
% 139.51/20.03 | | | | | | | | | | | | (5927) all_14_2 = e2
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | SIMP: (5927) implies:
% 139.51/20.03 | | | | | | | | | | | | (5928) all_14_2 = e2
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | COMBINE_EQS: (281), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5929) all_44_2 = e2
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (337), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5930) ~ (all_52_1 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (339), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5931) ~ (all_52_2 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (341), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5932) ~ (all_52_3 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (343), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5933) ~ (all_52_4 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (345), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5934) ~ (all_52_8 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (347), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5935) ~ (all_52_12 = e2)
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | REDUCE: (51), (5928) imply:
% 139.51/20.03 | | | | | | | | | | | | (5936) op(e3, e3) = e2
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | BETA: splitting (97) gives:
% 139.51/20.03 | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | (5937) ~ (all_44_2 = e2)
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | REDUCE: (5929), (5937) imply:
% 139.51/20.03 | | | | | | | | | | | | | (5938) $false
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | CLOSE: (5938) is inconsistent.
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | (5939) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0
% 139.51/20.03 | | | | | | | | | | | | | & op(e3, e2) = all_44_1 & $i(all_44_0) &
% 139.51/20.03 | | | | | | | | | | | | | $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3, e2)
% 139.51/20.03 | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | BETA: splitting (94) gives:
% 139.51/20.03 | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | (5940) ~ (all_42_2 = e3)
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | REDUCE: (303), (5940) imply:
% 139.51/20.03 | | | | | | | | | | | | | | (5941) ~ (all_10_2 = e3)
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.51/20.03 | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | (5942) all_54_15 = e3
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | REF_CLOSE: (246), (5941), (5942) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | sub-proof #755.
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | (5943) ~ (all_54_15 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | (5944) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | BETA: splitting (5944) gives:
% 139.51/20.03 | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | (5945) all_54_15 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5911), (5945) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | | sub-proof #754.
% 139.51/20.03 | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | (5946) ~ (all_54_15 = e2)
% 139.51/20.03 | | | | | | | | | | | | | | | | (5947) all_54_15 = e1 | all_54_15 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | BETA: splitting (5947) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5948) all_54_15 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5906), (5948) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5949) all_54_15 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (5949) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5950) all_10_2 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | SIMP: (5950) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5951) all_10_2 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (350), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5952) ~ (all_52_3 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (361), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5953) ~ (all_52_7 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (368), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5954) ~ (all_52_11 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (370), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5955) ~ (all_52_13 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (5941), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5956) ~ (e3 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (5911), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5957) ~ (e2 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | REDUCE: (5906), (5951) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | (5958) ~ (e1 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | (5959) ~ (all_48_2 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | REDUCE: (299), (5959) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | (5960) ~ (all_4_2 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | (5961) all_54_10 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (5905), (5961) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | sub-proof #1112.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | (5962) ~ (all_54_10 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | (5963) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | BETA: splitting (5963) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | (5964) all_54_10 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (5964) are inconsistent by sub-proof
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | #1111.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | (5965) ~ (all_54_10 = e2)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | (5966) all_54_10 = e1 | all_54_10 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | BETA: splitting (5966) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5967) all_54_10 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (5967) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5968) all_4_2 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | SIMP: (5968) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5969) all_4_2 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5970) ~ (all_52_2 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (362), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5971) ~ (all_52_8 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5972) ~ (all_52_9 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5973) ~ (all_52_11 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (5905), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5974) ~ (e3 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (372), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5975) ~ (e2 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (5969) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | (5976) op(e1, e1) = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (190) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | (5977) all_54_14 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (5977) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | (5978) all_52_11 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (5978) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | (5979) ~ (all_52_8 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | (5980) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (5897), (5979), (5980),
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | #319.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | (5981) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5981) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | (5982) all_57_8 = e3 & op(e1, e1) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5982) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | (5983) op(e1, e1) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5976), (5983), (function-axioms) are
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | (5984) all_57_14 = e3 & op(e0, e1) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5984) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | (5985) all_57_14 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | (5986) all_54_2 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (271), (5979), (5986) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #538.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | (5987) ~ (all_54_2 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | (5988) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | (5989) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5989) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5990) all_57_4 = e2 & op(e3, e1) = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5990) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5991) all_57_4 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (235), (239),
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5936), (5991), (function-axioms) are inconsistent
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #407.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5992) all_57_5 = e2 & op(e2, e1) = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (5992) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5993) all_57_5 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5994) op(e2, e1) = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5988) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5995) all_54_2 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (5995) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5996) all_52_8 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5934), (5996) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5997) $false
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (5997) is inconsistent.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5998) ~ (all_54_2 = e2)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5999) all_54_2 = e1 | all_54_2 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5999) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6000) all_54_2 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (6000) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6001) all_52_8 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5971), (6001) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6002) $false
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6002) is inconsistent.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6003) all_54_2 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (6003) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6004) all_52_8 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (6004) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6005) ~ (all_52_4 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (6004) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6006) ~ (all_52_9 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6006) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6007) ~ (all_52_9 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (6004) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6008) ~ (all_52_12 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6008) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6009) ~ (all_52_12 = e0)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6010) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6010) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6011) all_57_0 = e3 & op(e3, e3) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6011) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6012) op(e3, e3) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5936), (6012), (function-axioms) are
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6013) all_57_2 = e3 & op(e2, e3) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6013) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6014) all_57_2 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6015) all_54_1 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6015) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6016) all_52_4 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5894), (6016) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6017) $false
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6017) is inconsistent.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6018) ~ (all_54_1 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6019) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6019) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6020) all_54_1 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6020) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6021) all_52_4 = e2
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5933), (6021) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6022) $false
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6022) is inconsistent.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6023) ~ (all_54_1 = e2)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6024) all_54_1 = e1 | all_54_1 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6025) all_54_6 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (5897), (6025) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6026) ~ (all_54_6 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6027) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6028) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (5894), (5936), (6028),
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6029) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6029) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6030) all_57_4 = e3 & op(e3, e1) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6030) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6031) op(e3, e1) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5979), (6031), (function-axioms) are
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6032) all_57_9 = e3 & op(e3, e0) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6032) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6033) all_57_9 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6024) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6034) all_54_1 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6034) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6035) all_52_4 = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6035) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6036) ~ (all_52_6 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6036) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6037) ~ (all_52_6 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (6035) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6038) ~ (all_52_7 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6038) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6039) ~ (all_52_7 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (6035) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6040) ~ (all_52_12 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6040) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6041) ~ (all_52_12 = e1)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (170), (6035) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6042) op(e3, e2) = e1
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6043) all_54_3 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6043) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6044) all_52_12 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6044) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6045) all_52_12 = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (6045) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6046) ~ (all_52_14 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6046) implies:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6047) ~ (all_52_14 = e3)
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (168), (6045) imply:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6048) op(e3, e0) = e3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6049) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (5930), (5936),
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6049), (function-axioms) are inconsistent by
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #177.
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6050) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6050) gives:
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.03 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6051) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6051) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6052) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6053) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6054) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6055) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5994), (6005), (6052), (6055),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #176.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6056) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6056) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6057) all_57_7 = e0 & op(e1, e2) = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6057) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6058) all_57_7 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6059) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6059) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6060) all_57_1 = e2 & op(e3, e2) = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6060) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6061) all_57_1 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6062) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6062) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6063) all_57_6 = e3 & op(e1, e3) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6063) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6064) all_57_6 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (117),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (135), (136), (140), (143), (144), (148),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (163), (164), (165),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (169), (170), (191), (192), (195), (196),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (214), (216),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (220), (222), (223), (229), (230), (234),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (249), (258), (259), (261), (5891), (5896),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5897), (5902), (5903), (5906), (5907), (5911),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5914), (5926), (5931), (5932), (5939), (5952),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5953), (5970), (5972), (5976), (5979), (5985),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5993), (6007), (6027), (6033), (6037), (6039),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6052), (6053), (6054), (6058), (6064),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #164.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6065) all_57_7 = e3 & op(e1, e2) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6065) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6066) all_57_7 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (45), (51), (207), (228),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (229), (5902), (5906), (5907), (5909), (5911),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6061), (6066), (function-axioms) are inconsistent
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #161.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6067) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (5976), (6047), (6067),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6068) all_57_3 = e2 & op(e2, e2) = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6068) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6069) op(e2, e2) = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (164), (224), (5955), (5993), (6014),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6069), (function-axioms) are inconsistent by
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #695.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6070) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6070) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6071) all_57_7 = e2 & op(e1, e2) = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6071) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6072) all_57_7 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6058), (6072) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #578.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6073) all_57_13 = e2 & op(e0, e2) = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6073) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6074) all_57_13 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6027) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6075) all_54_6 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (6075) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6076) all_52_9 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6076) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6077) all_52_9 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (6077) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6078) ~ (all_52_13 = e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6078) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6079) ~ (all_52_13 = e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5897), (6077) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6080) ~ (e3 = e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6081) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6081) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6082) all_57_6 = e3 & op(e1, e3) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6082) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6083) all_57_6 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (128),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (135), (136), (140), (143), (144), (148), (149),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (158), (159), (162), (163), (164), (167), (169),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (191), (192), (195), (196), (207), (209),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (211), (212), (214), (216), (217), (220),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (222), (223), (234), (248), (249), (258), (259),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5891), (5896), (5906), (5907), (5911), (5914),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5926), (5931), (5932), (5939), (5952), (5953),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5970), (5976), (5979), (5985), (5994), (6033),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6042), (6052), (6053), (6054), (6074), (6079),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6083), (function-axioms) are inconsistent by
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #167.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6084) all_57_7 = e3 & op(e1, e2) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6058), (6084) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #713.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6085) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (5976), (6047), (6085),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6086) all_54_6 = e1 | all_54_6 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (5972), (6007), (6086) are inconsistent by
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #166.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6087) all_57_13 = e0 & op(e0, e2) = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6087) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6088) op(e0, e2) = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5953), (6088), (function-axioms) are
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6089) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5936), (6048), (6089), (function-axioms) are
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6090) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5935), (6009), (6041), (6090) are
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6091) all_54_1 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6091) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6092) all_52_4 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6005), (6092) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6093) $false
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6093) is inconsistent.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6094) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6094) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6095) all_57_6 = e3 & op(e1, e3) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6095) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6096) all_57_6 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6097) all_54_1 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6097) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6098) all_52_4 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5894), (6098) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6099) $false
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6099) is inconsistent.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6100) ~ (all_54_1 = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6101) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6101) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6102) all_54_1 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6102) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6103) all_52_4 = e2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5933), (6103) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6104) $false
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6104) is inconsistent.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6105) ~ (all_54_1 = e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6106) all_54_1 = e1 | all_54_1 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6107) all_54_6 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (5897), (6107) are inconsistent by
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #763.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6108) ~ (all_54_6 = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6109) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6110) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (5894), (5936), (6110),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6111) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6111) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6112) all_57_4 = e3 & op(e3, e1) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6112) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6113) op(e3, e1) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (5979), (6113), (function-axioms) are
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6114) all_57_9 = e3 & op(e3, e0) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6114) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6115) all_57_9 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6116) op(e3, e0) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6106) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6117) all_54_1 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6117) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6118) all_52_4 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6118) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6119) ~ (all_52_6 = e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6119) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6120) ~ (all_52_6 = e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (6118) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6121) ~ (all_52_7 = e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6121) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6122) ~ (all_52_7 = e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6123) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (5930), (5936),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6123), (function-axioms) are inconsistent by
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #177.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6124) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6124) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6125) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6125) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6126) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6127) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6128) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6129) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (5994), (6005), (6126), (6129),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #176.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6130) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6130) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6131) all_57_7 = e0 & op(e1, e2) = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6131) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6132) all_57_7 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (117),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (128), (135), (136), (140), (143), (144), (148),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (149), (158), (159), (162), (163), (164), (165),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (167), (169), (170), (191), (192), (195), (196),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (212), (214), (216),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (217), (220), (222), (223), (229), (230), (234),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (248), (249), (258), (259), (261), (5891), (5896),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5897), (5902), (5903), (5906), (5907), (5911),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5914), (5926), (5931), (5932), (5939), (5952),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5953), (5970), (5972), (5976), (5979), (5985),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5993), (6007), (6096), (6109), (6115), (6120),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6122), (6126), (6127), (6128), (6132),
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #164.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6133) all_57_13 = e0 & op(e0, e2) = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6133) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6134) op(e0, e2) = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5953), (6134), (function-axioms) are
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6135) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5936), (6116), (6135), (function-axioms) are
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6136) all_54_1 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6136) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6137) all_52_4 = e0
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6005), (6137) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6138) $false
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6138) is inconsistent.
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6139) all_57_12 = e3 & op(e0, e3) = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6139) implies:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6140) all_57_12 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (203) gives:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6141) all_54_1 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6141) imply:
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6142) all_52_4 = e3
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.04 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5894), (6142) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6143) $false
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6143) is inconsistent.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6144) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6144) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6145) all_54_1 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6145) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6146) all_52_4 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5933), (6146) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6147) $false
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6147) is inconsistent.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6148) ~ (all_54_1 = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6149) all_54_1 = e1 | all_54_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6149) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6150) all_54_1 = e1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6150) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6151) all_52_4 = e1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (6151) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6152) ~ (all_52_12 = e1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6152) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6153) ~ (all_52_12 = e1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6154) all_54_3 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (6154) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6155) all_52_12 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6155) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6156) all_52_12 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (6156) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6157) ~ (all_52_14 = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6157) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6158) ~ (all_52_14 = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6159) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6159) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6160) all_57_1 = e0 & op(e3, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (6005), (6160), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1102.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6161) all_57_3 = e0 & op(e2, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6161) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6162) op(e2, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (5906), (5907),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5909), (5911), (6162), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6163) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6163) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6164) all_57_7 = e0 & op(e1, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6164) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6165) all_57_7 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6166) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6166) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6167) all_57_6 = e3 & op(e1, e3) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (232), (234), (5936),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6140), (6167), (function-axioms) are inconsistent
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #155.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6168) all_57_7 = e3 & op(e1, e2) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6165), (6168) are inconsistent by sub-proof
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #713.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6169) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (160), (5976), (6158), (6169),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #159.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6170) all_57_13 = e0 & op(e0, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6170) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6171) op(e0, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (5953), (6171), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6172) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (5935), (6009), (6153), (6172) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6173) all_54_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (272), (6173) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6174) all_52_4 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6005), (6174) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6175) $false
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6175) is inconsistent.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6176) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6176) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6177) all_57_8 = e2 & op(e1, e1) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6177) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6178) op(e1, e1) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (5976), (6178), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6179) all_57_14 = e2 & op(e0, e1) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5985), (6179) are inconsistent by sub-proof
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | #704.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6180) ~ (all_54_14 = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6181) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (247), (6180) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6182) ~ (all_52_11 = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6181) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6183) all_54_14 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (247), (6183) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6184) all_52_11 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (6184) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6185) ~ (all_52_9 = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6182), (6184) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6186) ~ (e3 = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6187) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6187) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6188) all_57_4 = e3 & op(e3, e1) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6188) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6189) op(e3, e1) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6190) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (5903), (5930), (6190),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | #154.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6191) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6191) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6192) all_57_5 = e2 & op(e2, e1) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6192) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6193) op(e2, e1) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6185), (6193), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6194) all_57_10 = e2 & op(e2, e0) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6194) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6195) op(e2, e0) = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (45), (51), (167), (170), (206),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (5894), (5903), (5906), (5907), (5909),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (5911), (5930), (5936), (6189), (6195),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | #150.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6196) all_57_5 = e3 & op(e2, e1) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5897), (6196), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6197) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6197) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6198) all_57_8 = e3 & op(e1, e1) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6198) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6199) op(e1, e1) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5976), (6199), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1096.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6200) all_57_14 = e3 & op(e0, e1) = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6182), (6200), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6201) all_54_14 = e1 | all_54_14 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (247), (5954), (5973), (6201) are inconsistent by
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #761.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | (6202) all_54_10 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (5960), (6202) are inconsistent by
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | (6203) all_48_2 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (6203) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | (6204) all_4_2 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | REDUCE: (360), (6204) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | (6205) ~ (all_52_6 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | REDUCE: (363), (6204) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | (6206) ~ (all_52_9 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | (6207) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | BETA: splitting (6207) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | (6208) all_57_2 = e0 & op(e2, e3) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | ALPHA: (6208) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | (6209) op(e2, e3) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | (6210) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6210) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6211) all_57_1 = e0 & op(e3, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6211) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6212) op(e3, e2) = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e0,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (6209) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6213) all_52_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e0,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (6212) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6214) all_52_4 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (6213) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6215) ~ (all_52_2 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | SIMP: (6215) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6216) ~ (all_52_2 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (148), (6213) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6217) ~ (all_52_3 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (136), (6214) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6218) ~ (all_52_6 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (135), (6214) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | (6219) ~ (all_52_7 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5914) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6220) ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_26_1 & $i(all_26_0) &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6220) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6221) ~ (all_26_0 = e1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6222) op(e2, e3) = all_26_1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | (6223) op(all_26_1, e2) = all_26_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5926) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6224) ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_36_1 & $i(all_36_0) &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6224) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6225) op(e3, e2) = all_36_1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6226) op(all_36_1, e3) = all_36_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6227) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_44_1 & $i(all_44_0) &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6227) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6228) ~ (all_44_0 = e1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6229) op(e3, e2) = all_44_1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6230) op(all_44_1, e3) = all_44_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_26_1,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (6209), (6222) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6231) all_26_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_44_1,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (6212), (6229) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6232) all_44_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_1, e2, e3, simplifying with (6225), (6229)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6233) all_44_1 = all_36_1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6232), (6233) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6234) all_36_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6230), (6232) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6235) op(e0, e3) = all_44_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6226), (6234) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6236) op(e0, e3) = all_36_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6223), (6231) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6237) op(e0, e2) = all_26_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_26_0, e2, e0, simplifying with (158), (6237)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6238) all_52_7 = all_26_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_36_0, e3, e0, simplifying with (159), (6236)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6239) all_52_3 = all_36_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, e3, e0, simplifying with (159), (6235)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6240) all_52_3 = all_44_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6239), (6240) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6241) all_44_0 = all_36_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (6238) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6242) all_54_13 = all_26_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6239) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6243) all_54_12 = all_36_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (6239) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6244) ~ (all_52_2 = all_36_0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (6238), (6239) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6245) ~ (all_36_0 = all_26_0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5932), (6239) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6246) ~ (all_36_0 = e2)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5952), (6239) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6247) ~ (all_36_0 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (6238) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6248) ~ (all_52_6 = all_26_0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5953), (6238) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6249) ~ (all_26_0 = e0)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6228), (6241) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6250) ~ (all_36_0 = e1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6251) all_54_12 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6243), (6251) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6252) all_36_0 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6252) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6253) all_36_0 = e3
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6244), (6253) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6254) ~ (all_52_2 = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6245), (6253) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6255) ~ (all_26_0 = e3)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (191), (195), (196), (258), (259), (5895),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (5931), (6205), (6216), (6221), (6242), (6248),
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6249), (6254), (6255) are inconsistent by
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | (6256) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6256) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6257) all_54_12 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6243), (6257) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6258) all_36_0 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6258) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6259) all_36_0 = e2
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6246), (6259) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6260) $false
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6260) is inconsistent.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6261) all_54_12 = e1 | all_54_12 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6261) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6262) all_54_12 = e1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6243), (6262) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6263) all_36_0 = e1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6263) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6264) all_36_0 = e1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6250), (6264) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6265) $false
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6265) is inconsistent.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6266) all_54_12 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6243), (6266) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6267) all_36_0 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6267) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6268) all_36_0 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6247), (6268) imply:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6269) $false
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6269) is inconsistent.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6270) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6212), (6225), (6270), (function-axioms) are
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #147.
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6271) ~ (all_36_1 = e1) & op(e3, e2) = all_36_1 &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_36_1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6271) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | (6272) op(e3, e2) = all_36_1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (5939) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6273) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_44_1 & $i(all_44_0) &
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6273) implies:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6274) ~ (all_44_0 = e1)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6275) op(e3, e2) = all_44_1
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6276) op(all_44_1, e3) = all_44_0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_26_1,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e2, simplifying with (6209), (6222) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6277) all_26_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0, all_44_1,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (6212), (6275) gives:
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | (6278) all_44_1 = e0
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_36_1,
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_1, e2, e3, simplifying with (6272), (6275)
% 139.51/20.05 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6279) all_44_1 = all_36_1
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6278), (6279) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6280) all_36_1 = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6276), (6278) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6281) op(e0, e3) = all_44_0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6223), (6277) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6282) op(e0, e2) = all_26_0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7,
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_26_0, e2, e0, simplifying with (158), (6282)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6283) all_52_7 = all_26_0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3,
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | all_44_0, e3, e0, simplifying with (159), (6281)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6284) all_52_3 = all_44_0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (248), (6283) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6285) all_54_13 = all_26_0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (249), (6284) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6286) all_54_12 = all_44_0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (144), (6284) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6287) ~ (all_52_2 = all_44_0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (140), (6283), (6284) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6288) ~ (all_44_0 = all_26_0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5932), (6284) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6289) ~ (all_44_0 = e2)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5952), (6284) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6290) ~ (all_44_0 = e0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (6283) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6291) ~ (all_52_6 = all_26_0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5953), (6283) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6292) ~ (all_26_0 = e0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (192) gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6293) all_54_12 = e3
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6286), (6293) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6294) all_44_0 = e3
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6294) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6295) all_44_0 = e3
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6287), (6295) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6296) ~ (all_52_2 = e3)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6288), (6295) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6297) ~ (all_26_0 = e3)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (143), (191), (195), (196), (258), (259), (5895),
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (5931), (6205), (6216), (6221), (6285), (6291),
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6292), (6296), (6297) are inconsistent by
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #148.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6298) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6298) gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6299) all_54_12 = e2
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6286), (6299) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6300) all_44_0 = e2
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6300) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6301) all_44_0 = e2
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6289), (6301) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6302) $false
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6302) is inconsistent.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6303) all_54_12 = e1 | all_54_12 = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6303) gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6304) all_54_12 = e1
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6286), (6304) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6305) all_44_0 = e1
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6305) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6306) all_44_0 = e1
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6274), (6306) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6307) $false
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6307) is inconsistent.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6308) all_54_12 = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6286), (6308) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6309) all_44_0 = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6309) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6310) all_44_0 = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6290), (6310) imply:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6311) $false
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (6311) is inconsistent.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6312) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 &
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_44_1)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6212), (6272), (6312), (function-axioms) are
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #147.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | (6313) ~ (all_26_1 = e0) & op(e2, e3) = all_26_1 &
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6209), (6313), (function-axioms) are inconsistent
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #146.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | (6314) all_57_3 = e0 & op(e2, e2) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6314) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | (6315) op(e2, e2) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (5906), (5907),
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | (5909), (5911), (6315), (function-axioms) are
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | (6316) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (5953), (6205), (6316),
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | | #464.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | (6317) all_57_3 = e0 & op(e2, e2) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (6317) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | (6318) op(e2, e2) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (5906), (5907),
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | (5909), (5911), (6318), (function-axioms) are
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | (6319) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 139.51/20.06 | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (6319) gives:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | (6320) all_57_5 = e0 & op(e2, e1) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (6320) implies:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | (6321) op(e2, e1) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (6206), (6321), (function-axioms) are
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | (6322) all_57_10 = e0 & op(e2, e0) = e0
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (5955), (6322), (function-axioms) are
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | End of split
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | Case 2:
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | (6323) all_42_2 = e3
% 139.51/20.06 | | | | | | | | | | | | | | (6324) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0
% 139.51/20.06 | | | | | | | | | | | | | | & op(e0, e3) = all_42_1 & $i(all_42_0) &
% 139.51/20.06 | | | | | | | | | | | | | | $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0, e3)
% 139.51/20.06 | | | | | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | COMBINE_EQS: (303), (6323) imply:
% 139.51/20.06 | | | | | | | | | | | | | | (6325) all_10_2 = e3
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | SIMP: (6325) implies:
% 139.51/20.06 | | | | | | | | | | | | | | (6326) all_10_2 = e3
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | COMBINE_EQS: (297), (6326) imply:
% 139.51/20.06 | | | | | | | | | | | | | | (6327) all_46_2 = e3
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | REDUCE: (368), (6326) imply:
% 139.51/20.06 | | | | | | | | | | | | | | (6328) ~ (all_52_11 = e3)
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | REDUCE: (371), (6326) imply:
% 139.51/20.06 | | | | | | | | | | | | | | (6329) ~ (all_52_14 = e3)
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | REDUCE: (45), (6326) imply:
% 139.51/20.06 | | | | | | | | | | | | | | (6330) op(e0, e0) = e3
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.51/20.06 | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | Case 1:
% 139.51/20.06 | | | | | | | | | | | | | | |
% 139.51/20.06 | | | | | | | | | | | | | | | (6331) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.74/20.06 | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | BETA: splitting (6331) gives:
% 139.74/20.06 | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | (6332) all_57_4 = e3 & op(e3, e1) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | ALPHA: (6332) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | (6333) all_57_4 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | (6334) op(e3, e1) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | (6335) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | BETA: splitting (6335) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6336) all_57_0 = e3 & op(e3, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | ALPHA: (6336) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6337) op(e3, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5936), (6337), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6338) all_57_2 = e3 & op(e2, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | ALPHA: (6338) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6339) all_57_2 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | (6340) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (6340) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6341) all_57_6 = e3 & op(e1, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (45), (51), (100),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (120), (134), (141), (158), (160), (163), (164),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (167), (168), (169), (170), (194), (206), (207),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (210), (214), (216), (217), (219), (220), (226),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (230), (233), (235), (335), (362), (367), (372),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (5896), (5903), (5906), (5907), (5909), (5911),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (5930), (5934), (5936), (6324), (6327), (6330),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6333), (6334), (6341), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #134.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6342) all_57_7 = e3 & op(e1, e2) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (6342) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6343) all_57_7 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | (6344) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6344) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6345) all_57_1 = e2 & op(e3, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6345) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6346) all_57_1 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (45), (51), (207), (228),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (229), (5902), (5906), (5907), (5909), (5911),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6343), (6346), (function-axioms) are inconsistent
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #161.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6347) all_57_3 = e2 & op(e2, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6347) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6348) op(e2, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5903), (6348), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | (6349) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6349) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6350) all_57_7 = e2 & op(e1, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (235), (239),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (5936), (6333), (6343), (6350), (function-axioms)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #133.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6351) all_57_13 = e2 & op(e0, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6351) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6352) all_57_13 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | (6353) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6353) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6354) all_57_6 = e2 & op(e1, e3) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6354) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6355) all_57_6 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (5936), (6339), (6355), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6356) all_57_7 = e2 & op(e1, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (235), (239),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (5936), (6333), (6343), (6356), (function-axioms)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #133.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | (6357) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6357) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6358) all_57_8 = e2 & op(e1, e1) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6358) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6359) op(e1, e1) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6359), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6360) all_57_11 = e2 & op(e1, e0) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6360) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6361) all_57_11 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6362) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6362) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6363) all_57_1 = e0 & op(e3, e2) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6363) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6364) all_57_1 = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6365) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (5936), (6364), (6365),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | #144.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6366) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6366) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6367) all_57_4 = e1 & op(e3, e1) = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6333), (6367) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #143.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6368) all_57_9 = e1 & op(e3, e0) = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6368) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6369) all_57_9 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6370) all_57_15 = e0 & op(e0, e0) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6370) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6371) op(e0, e0) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6330), (6371), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6372) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6372) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6373) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6373) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6374) all_57_9 = e0 & op(e3, e0) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6369), (6374) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #813.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6375) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6375) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6376) all_57_10 = e0 & op(e2, e0) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6376) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6377) all_57_10 = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6378) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (5903), (5930), (6378),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #154.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6379) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6379) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6380) all_57_5 = e2 & op(e2, e1) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6380) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6381) all_57_5 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6382) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6382) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6383) all_57_1 = e1 & op(e3, e2) = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6364), (6383) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #145.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6384) all_57_3 = e1 & op(e2, e2) = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6384) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6385) all_57_3 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (5902), (6385) imply:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6386) e3 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (227), (5902), (6339), (6377),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6381), (6386) are inconsistent by sub-proof #130.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6387) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6387) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6388) all_57_7 = e1 & op(e1, e2) = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6388) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6389) all_57_7 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6343), (6389) imply:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6390) e3 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6390) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6391) e3 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (9), (227), (5902), (6339), (6377),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6381), (6391) are inconsistent by sub-proof #130.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6392) all_57_13 = e1 & op(e0, e2) = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6392) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6393) all_57_13 = e1
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6352), (6393) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1057.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6394) all_57_10 = e2 & op(e2, e0) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6394) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6395) all_57_10 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6377), (6395) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #609.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6396) all_57_11 = e0 & op(e1, e0) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6361), (6396) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #992.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6397) all_57_3 = e0 & op(e2, e2) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6397) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6398) op(e2, e2) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (5906), (5907),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (5909), (5911), (6398), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #235.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | (6399) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6399) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6400) all_57_7 = e0 & op(e1, e2) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6343), (6400) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #1061.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | (6401) all_57_13 = e0 & op(e0, e2) = e0
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6352), (6401) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | | #1060.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | (6402) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (160), (5905), (6329), (6402),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | #129.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | (6403) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.74/20.06 | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | BETA: splitting (6403) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6404) all_57_6 = e3 & op(e1, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (45), (51), (100),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (120), (134), (141), (158), (160), (163), (164),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (167), (168), (169), (170), (194), (206), (207),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (210), (214), (216), (217), (219), (220), (226),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (230), (233), (235), (335), (362), (367), (372),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (5896), (5903), (5906), (5907), (5909), (5911),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (5930), (5934), (5936), (6324), (6327), (6330),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6333), (6334), (6404), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #134.
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6405) all_57_12 = e3 & op(e0, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | ALPHA: (6405) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | (6406) all_57_12 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | (6407) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | BETA: splitting (6407) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6408) all_57_6 = e3 & op(e1, e3) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (232), (234), (5936),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6406), (6408), (function-axioms) are inconsistent
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | by sub-proof #155.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6409) all_57_7 = e3 & op(e1, e2) = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | ALPHA: (6409) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | (6410) all_57_7 = e3
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | (6411) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6411) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6412) all_57_1 = e2 & op(e3, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6412) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | (6413) all_57_1 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | (6414) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6414) gives:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6415) all_57_6 = e2 & op(e1, e3) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6415) implies:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6416) all_57_6 = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (5936), (6406), (6416), (function-axioms) are
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #128.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (6417) all_57_7 = e2 & op(e1, e2) = e2
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (235), (239),
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | (5936), (6333), (6410), (6417), (function-axioms)
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #133.
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.06 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | (6418) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6418) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | (6419) all_57_8 = e2 & op(e1, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6419) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | (6420) op(e1, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6420), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | (6421) all_57_11 = e2 & op(e1, e0) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6421) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | (6422) all_57_11 = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | (6423) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (5936), (6413), (6423), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #127.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | (6424) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6424) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (6425) all_57_4 = e0 & op(e3, e1) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6333), (6425) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | #337.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (6426) all_57_9 = e0 & op(e3, e0) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6426) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | (6427) all_57_9 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6428) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6428) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6429) all_57_9 = e1 & op(e3, e0) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6429) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6430) all_57_9 = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6427), (6430) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1079.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6431) all_57_10 = e1 & op(e2, e0) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6431) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6432) op(e2, e0) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6433) all_57_15 = e0 & op(e0, e0) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6433) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6434) op(e0, e0) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6330), (6434), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6435) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6435) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6436) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6437) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6437) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6438) all_57_1 = e1 & op(e3, e2) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6413), (6438) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1092.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6439) all_57_3 = e1 & op(e2, e2) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (6439) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #163.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6440) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6440) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6441) all_57_7 = e1 & op(e1, e2) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6410), (6441) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1058.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6442) all_57_13 = e1 & op(e0, e2) = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6442) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6443) all_57_13 = e1
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6444) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6444) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6445) all_57_12 = e2 & op(e0, e3) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6445) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6446) op(e0, e3) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (100), (159), (164), (6324), (6327), (6432),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6446), (function-axioms) are inconsistent by
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #269.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6447) all_57_13 = e2 & op(e0, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6443), (6447) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #552.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6448) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6448) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6449) all_57_14 = e2 & op(e0, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6449) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6450) all_57_14 = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6436) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6451) all_57_12 = e0 & op(e0, e3) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6451) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6452) all_57_12 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6406), (6452) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #828.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6453) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6453) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6454) all_57_13 = e0 & op(e0, e2) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6454) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6455) all_57_13 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (210), (6330), (6406), (6450),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6455), (function-axioms) are inconsistent by
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #709.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6456) all_57_14 = e0 & op(e0, e1) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6456) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6457) all_57_14 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (211), (6330), (6406), (6443),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6457), (function-axioms) are inconsistent by
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #658.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6458) all_57_15 = e2 & op(e0, e0) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6458) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6459) op(e0, e0) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (6422),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6427), (6459), (function-axioms) are inconsistent
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #851.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6460) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (6330), (6422), (6460),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | | #693.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | (6461) all_57_3 = e2 & op(e2, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6461) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | (6462) op(e2, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5903), (6462), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | (6463) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6463) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | (6464) all_57_7 = e2 & op(e1, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (235), (239),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | (5936), (6333), (6410), (6464), (function-axioms)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #133.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | (6465) all_57_13 = e2 & op(e0, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6465) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | (6466) all_57_13 = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | (6467) all_57_15 = e0 & op(e0, e0) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6467) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | (6468) op(e0, e0) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6330), (6468), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #751.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | (6469) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6469) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | (6470) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6470) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | (6471) all_57_12 = e0 & op(e0, e3) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6406), (6471) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | #156.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | (6472) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6472) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | (6473) all_57_13 = e0 & op(e0, e2) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6466), (6473) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | #1060.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | (6474) all_57_14 = e0 & op(e0, e1) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6474) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | (6475) all_57_14 = e0
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (210), (211), (6330),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | (6406), (6475), (function-axioms) are inconsistent
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #657.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6476) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (160), (5905), (6329), (6476),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | #129.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | (6477) all_57_5 = e3 & op(e2, e1) = e3
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5897), (6477), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | (6478) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.74/20.07 | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | REF_CLOSE: (36), (157), (5905), (6328), (6478),
% 139.74/20.07 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | #126.
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | (6479) all_24_2 = e2
% 139.74/20.07 | | | | | | | | | | (6480) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0
% 139.74/20.07 | | | | | | | | | | & op(e0, e2) = all_24_1 & $i(all_24_0) &
% 139.74/20.07 | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2)
% 139.74/20.07 | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | COMBINE_EQS: (319), (6479) imply:
% 139.74/20.07 | | | | | | | | | | (6481) all_10_2 = e2
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | COMBINE_EQS: (307), (6481) imply:
% 139.74/20.07 | | | | | | | | | | (6482) all_40_2 = e2
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | REDUCE: (361), (6481) imply:
% 139.74/20.07 | | | | | | | | | | (6483) ~ (all_52_7 = e2)
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | REDUCE: (45), (6481) imply:
% 139.74/20.07 | | | | | | | | | | (6484) op(e0, e0) = e2
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | BETA: splitting (85) gives:
% 139.74/20.07 | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | (6485) ~ (all_36_2 = e2)
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | REDUCE: (305), (6485) imply:
% 139.74/20.07 | | | | | | | | | | | (6486) ~ (all_14_2 = e2)
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | BETA: splitting (204) gives:
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | (6487) all_54_0 = e3
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | COMBINE_EQS: (279), (6487) imply:
% 139.74/20.07 | | | | | | | | | | | | (6488) all_14_2 = e3
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | SIMP: (6488) implies:
% 139.74/20.07 | | | | | | | | | | | | (6489) all_14_2 = e3
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | REDUCE: (51), (6489) imply:
% 139.74/20.07 | | | | | | | | | | | | (6490) op(e3, e3) = e3
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | (6491) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.74/20.07 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.74/20.07 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.74/20.07 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.74/20.07 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.74/20.07 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.74/20.07 | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.74/20.07 | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.74/20.07 | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.74/20.07 | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.74/20.07 | | | | | | | | | | | | | $i(all_56_6))
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | BETA: splitting (6491) gives:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | (6492) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.74/20.07 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.74/20.07 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.74/20.07 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.74/20.07 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.74/20.07 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | REF_CLOSE: (9), (6490), (6492), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | (6493) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.74/20.07 | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.74/20.07 | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.74/20.07 | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.74/20.07 | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (6493), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | (6494) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.74/20.07 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.74/20.07 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.74/20.07 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.74/20.07 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.74/20.07 | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.74/20.07 | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.74/20.07 | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.74/20.07 | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.74/20.07 | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.74/20.07 | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.74/20.07 | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.74/20.07 | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.74/20.07 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.74/20.07 | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.74/20.07 | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.07 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.07 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.07 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.07 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | BETA: splitting (6494) gives:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | (6495) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.74/20.07 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.74/20.07 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.74/20.07 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.74/20.07 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (372), (6484), (6495),
% 139.74/20.07 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | #529.
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | (6496) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.74/20.07 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.74/20.07 | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.74/20.07 | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.74/20.07 | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.74/20.07 | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.74/20.07 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.74/20.07 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.74/20.07 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.74/20.07 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.07 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.07 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.07 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.07 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | BETA: splitting (6496) gives:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | (6497) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.74/20.07 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.74/20.07 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | ALPHA: (6497) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | (6498) op(e1, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6498), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | (6499) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.74/20.07 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.74/20.07 | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.74/20.07 | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.74/20.07 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.74/20.07 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.74/20.07 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.07 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.07 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.74/20.07 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.07 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.07 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.74/20.07 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | BETA: splitting (6499) gives:
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | (6500) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.74/20.07 | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | ALPHA: (6500) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | (6501) op(e2, e2) = e0
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5903), (6501), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | (6502) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.74/20.07 | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.74/20.07 | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.74/20.07 | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.74/20.07 | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.07 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.74/20.07 | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.74/20.07 | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | ALPHA: (6502) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | (6503) op(e0, e0) = all_56_15
% 139.74/20.07 | | | | | | | | | | | | | | | | (6504) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.74/20.07 | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.07 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.74/20.07 | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.74/20.07 | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.74/20.07 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (51), (5903), (5907), (6484), (6503),
% 139.74/20.07 | | | | | | | | | | | | | | | | (6504), (function-axioms) are inconsistent by
% 139.74/20.07 | | | | | | | | | | | | | | | | sub-proof #123.
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | (6505) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | REF_CLOSE: (279), (5907), (5909), (6486), (6505) are
% 139.74/20.07 | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | (6506) all_36_2 = e2
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | COMBINE_EQS: (305), (6506) imply:
% 139.74/20.07 | | | | | | | | | | | (6507) all_14_2 = e2
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | SIMP: (6507) implies:
% 139.74/20.07 | | | | | | | | | | | (6508) all_14_2 = e2
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | REDUCE: (341), (6508) imply:
% 139.74/20.07 | | | | | | | | | | | (6509) ~ (all_52_3 = e2)
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | REDUCE: (51), (6508) imply:
% 139.74/20.07 | | | | | | | | | | | (6510) op(e3, e3) = e2
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | BETA: splitting (222) gives:
% 139.74/20.07 | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | (6511) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.74/20.07 | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | BETA: splitting (6511) gives:
% 139.74/20.07 | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | (6512) all_57_4 = e2 & op(e3, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | ALPHA: (6512) implies:
% 139.74/20.07 | | | | | | | | | | | | | (6513) all_57_4 = e2
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (233), (235), (239),
% 139.74/20.07 | | | | | | | | | | | | | (6510), (6513), (function-axioms) are inconsistent
% 139.74/20.07 | | | | | | | | | | | | | by sub-proof #407.
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | (6514) all_57_5 = e2 & op(e2, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | ALPHA: (6514) implies:
% 139.74/20.07 | | | | | | | | | | | | | (6515) all_57_5 = e2
% 139.74/20.07 | | | | | | | | | | | | | (6516) op(e2, e1) = e2
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.74/20.07 | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | (6517) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.74/20.07 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | BETA: splitting (6517) gives:
% 139.74/20.07 | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | (6518) all_57_1 = e2 & op(e3, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | ALPHA: (6518) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | (6519) all_57_1 = e2
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 139.74/20.07 | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | (6520) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | BETA: splitting (6520) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | (6521) all_57_6 = e2 & op(e1, e3) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | ALPHA: (6521) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | (6522) all_57_6 = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | (6523) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | BETA: splitting (6523) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6524) all_57_0 = e3 & op(e3, e3) = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | ALPHA: (6524) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6525) op(e3, e3) = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6510), (6525), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6526) all_57_2 = e3 & op(e2, e3) = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | ALPHA: (6526) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6527) all_57_2 = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6510), (6522), (6527), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #131.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | (6528) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.74/20.07 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | BETA: splitting (6528) gives:
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6529) all_57_6 = e3 & op(e1, e3) = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | ALPHA: (6529) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6530) all_57_6 = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6522), (6530) are inconsistent by sub-proof
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | #1004.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6531) all_57_12 = e3 & op(e0, e3) = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | ALPHA: (6531) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6532) all_57_12 = e3
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | (6510), (6522), (6532), (function-axioms) are
% 139.74/20.07 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #128.
% 139.74/20.07 | | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | End of split
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | (6533) all_57_7 = e2 & op(e1, e2) = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.07 | | | | | | | | | | | | | | | | | ALPHA: (6533) implies:
% 139.74/20.07 | | | | | | | | | | | | | | | | | (6534) all_57_7 = e2
% 139.74/20.07 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (228), (229), (5902),
% 139.74/20.08 | | | | | | | | | | | | | | | | | (5903), (6519), (6534), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #122.
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | (6535) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 139.74/20.08 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | BETA: splitting (6535) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6536) all_57_8 = e2 & op(e1, e1) = e2
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | ALPHA: (6536) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6537) op(e1, e1) = e2
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6537), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6538) all_57_11 = e2 & op(e1, e0) = e2
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | ALPHA: (6538) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6539) all_57_11 = e2
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6540) op(e1, e0) = e2
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | (6541) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | BETA: splitting (6541) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | (6542) all_57_9 = e3 & op(e3, e0) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | ALPHA: (6542) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | (6543) all_57_9 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | (6544) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6544) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6545) all_57_6 = e3 & op(e1, e3) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6545) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6546) all_57_6 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | (6547) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6510), (6519), (6547), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #127.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | (6548) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6548) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6549) all_57_4 = e0 & op(e3, e1) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6549) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6550) all_57_4 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | (6551) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6551) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6552) all_57_4 = e3 & op(e3, e1) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6552) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6553) all_57_4 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6550), (6553) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6554) e3 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (6484),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6539), (6543), (6554), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6555) all_57_5 = e3 & op(e2, e1) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (5897), (6555), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | (6556) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6556) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6557) all_57_8 = e3 & op(e1, e1) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6557) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6558) op(e1, e1) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (6558), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6559) all_57_14 = e3 & op(e0, e1) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6559) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6560) all_57_14 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (6561) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6561) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6562) all_57_4 = e1 & op(e3, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6550), (6562) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | #121.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6563) all_57_5 = e1 & op(e2, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6563) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6564) all_57_5 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6515), (6564) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1031.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (6565) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6565) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6566) all_57_8 = e1 & op(e1, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6566) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6567) all_57_8 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6568) op(e1, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6569) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6569) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6570) all_57_6 = e0 & op(e1, e3) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6570) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6571) all_57_6 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6546), (6571) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6572) e3 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (6484),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6539), (6543), (6572), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #253.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6573) all_57_7 = e0 & op(e1, e2) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6573) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6574) all_57_7 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6575) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6510), (6519), (6575), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6576) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6576) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6577) all_57_4 = e1 & op(e3, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6577) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6578) all_57_4 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6550), (6578) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6579) e1 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6567), (6579) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6580) all_57_8 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (217), (219), (6539),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6574), (6580) are inconsistent by sub-proof #436.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6581) all_57_9 = e1 & op(e3, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6581) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6582) all_57_9 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6543), (6582) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6583) e3 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6583) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6584) e3 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6560), (6584) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6585) all_57_14 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6568), (6585), (function-axioms) are inconsistent
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #785.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6586) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6539), (6568), (6586),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #680.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6587) all_57_14 = e1 & op(e0, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6587) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6588) all_57_14 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6560), (6588) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1045.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6589) all_57_9 = e0 & op(e3, e0) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6589) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6590) all_57_9 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (6484),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6539), (6590), (function-axioms) are inconsistent
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #851.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6591) all_57_7 = e3 & op(e1, e2) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6591) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6592) all_57_7 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | (6593) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6510), (6519), (6593), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #127.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | (6594) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6594) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6595) all_57_4 = e0 & op(e3, e1) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6595) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6596) all_57_4 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | (6597) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6597) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6598) all_57_1 = e1 & op(e3, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6519), (6598) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | #1092.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6599) all_57_3 = e1 & op(e2, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (6599) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | #163.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | (6600) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6600) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6601) all_57_7 = e1 & op(e1, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6592), (6601) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | #1058.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6602) all_57_13 = e1 & op(e0, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6602) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6603) all_57_13 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (6604) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6510), (6519), (6604), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #142.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (6605) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6605) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6606) all_57_4 = e1 & op(e3, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6606) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6607) all_57_4 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6596), (6607) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6608) e1 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6603), (6608) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6609) all_57_13 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (229), (5902), (6519), (6592),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6609) are inconsistent by sub-proof #162.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6610) all_57_9 = e1 & op(e3, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6543), (6610) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | | #599.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6611) all_57_9 = e0 & op(e3, e0) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6611) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6612) all_57_9 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (213), (215), (6484),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6539), (6612), (function-axioms) are inconsistent
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #851.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | (6613) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (36), (5905), (6539), (6613),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | #861.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | (6614) all_57_10 = e3 & op(e2, e0) = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | ALPHA: (6614) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | (6615) all_57_10 = e3
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | (6616) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6616) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6617) all_57_9 = e1 & op(e3, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6617) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6618) all_57_9 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | (6619) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6619) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6620) all_57_2 = e1 & op(e2, e3) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6620) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6621) all_57_2 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | (6622) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6622) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6623) all_57_2 = e0 & op(e2, e3) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6623) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6624) all_57_2 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6621), (6624) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6625) e1 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6625) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6626) e1 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6618), (6626) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6627) all_57_9 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (6615), (6616), (6627) are inconsistent
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #854.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | (6628) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6484), (6539), (6628), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #853.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6629) all_57_3 = e0 & op(e2, e2) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6629) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6630) op(e2, e2) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (213), (215),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (225), (227), (6484), (6515), (6539), (6630),
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | #849.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | (6631) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6631) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6632) all_57_5 = e0 & op(e2, e1) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6632) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6633) all_57_5 = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6515), (6633) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | #1042.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | (6634) all_57_10 = e0 & op(e2, e0) = e0
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6615), (6634) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | | #692.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6635) all_57_3 = e1 & op(e2, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (6635) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | #163.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | (6636) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6636) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6637) all_57_5 = e1 & op(e2, e1) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6515), (6637) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | #938.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | (6638) all_57_10 = e1 & op(e2, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6615), (6638) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | | #929.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6639) all_57_10 = e1 & op(e2, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6615), (6639) are inconsistent by sub-proof
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | #929.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | (6640) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6640) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6641) all_57_11 = e1 & op(e1, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6641) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6642) op(e1, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6540), (6642), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6643) all_57_15 = e1 & op(e0, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6643) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | (6644) op(e0, e0) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6484), (6644), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | (6645) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.74/20.08 | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6484), (6539), (6645), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #852.
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | (6646) all_57_3 = e2 & op(e2, e2) = e2
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | ALPHA: (6646) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | (6647) op(e2, e2) = e2
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | REF_CLOSE: (9), (5903), (6647), (function-axioms) are
% 139.74/20.08 | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | End of split
% 139.74/20.08 | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | (6648) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.74/20.08 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.74/20.08 | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | BETA: splitting (6648) gives:
% 139.74/20.08 | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | (6649) all_57_7 = e2 & op(e1, e2) = e2
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | ALPHA: (6649) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | (6650) all_57_7 = e2
% 139.74/20.08 | | | | | | | | | | | | | | | (6651) op(e1, e2) = e2
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 139.74/20.08 | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (6651) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | (6652) all_52_6 = e2
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e2,
% 139.74/20.08 | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (6516) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | (6653) all_52_9 = e2
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | REDUCE: (146), (6653) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | (6654) ~ (all_52_1 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | REDUCE: (126), (6652) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | (6655) ~ (all_52_14 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | SIMP: (6655) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | (6656) ~ (all_52_14 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | REDUCE: (117), (6653) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | (6657) ~ (all_52_13 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | SIMP: (6657) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | (6658) ~ (all_52_13 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | REDUCE: (363), (6653) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | (6659) ~ (all_4_2 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | REDUCE: (5897), (6653) imply:
% 139.74/20.08 | | | | | | | | | | | | | | | (6660) ~ (e3 = e2)
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.74/20.08 | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | (6661) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.74/20.08 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.74/20.08 | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.74/20.08 | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.74/20.08 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.74/20.08 | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.74/20.08 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (6510), (6654),
% 139.74/20.08 | | | | | | | | | | | | | | | | (6661), (function-axioms) are inconsistent by
% 139.74/20.08 | | | | | | | | | | | | | | | | sub-proof #177.
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | Case 2:
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | (6662) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.74/20.08 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.74/20.08 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.74/20.08 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.74/20.08 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.74/20.08 | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.74/20.08 | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.74/20.08 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | BETA: splitting (6662) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6663) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.74/20.08 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.74/20.08 | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.74/20.08 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.74/20.08 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.74/20.08 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.74/20.08 | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.74/20.08 | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.74/20.08 | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.74/20.08 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.74/20.08 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.74/20.08 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | ALPHA: (6663) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6664) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.74/20.08 | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.74/20.08 | | | | | | | | | | | | | | | | | (6665) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.74/20.08 | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.74/20.08 | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | BETA: splitting (6664) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | (6666) all_56_11 = e1 & op(e2, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | ALPHA: (6666) implies:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | (6667) all_56_11 = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | | (6668) op(e2, e2) = e1
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.74/20.08 | | | | | | | | | | | | | | | | | |
% 139.74/20.08 | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.08 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (6669) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (6669) gives:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (6670) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6667), (6670) are inconsistent by sub-proof
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | #119.
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (6671) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (6671), (function-axioms) are
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (6672) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (6672) gives:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (6673) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6484), (6665), (6673), (function-axioms) are
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #118.
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (6674) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (6674) gives:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (6675) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | ALPHA: (6675) implies:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (6676) op(e1, e1) = e2
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6676), (function-axioms) are
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (6677) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6677) gives:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (6678) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6678) implies:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (6679) op(e2, e2) = e0
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6516), (6664), (6679), (function-axioms) are
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #950.
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (6680) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6680) implies:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (6681) op(e0, e0) = all_56_15
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (6682) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (6484), (6668), (6681), (6682),
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | | #526.
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.09 | | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | End of split
% 139.74/20.09 | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | (6683) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.74/20.09 | | | | | | | | | | | | | | | | | | $i(all_56_4)
% 139.74/20.09 | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | ALPHA: (6683) implies:
% 139.74/20.09 | | | | | | | | | | | | | | | | | | (6684) ~ (all_56_4 = e2)
% 139.74/20.09 | | | | | | | | | | | | | | | | | | (6685) op(e2, e1) = all_56_4
% 139.74/20.09 | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6516), (6684), (6685), (function-axioms) are
% 139.74/20.09 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 139.74/20.09 | | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | | End of split
% 139.74/20.09 | | | | | | | | | | | | | | | | |
% 139.74/20.09 | | | | | | | | | | | | | | | | Case 2:
% 139.74/20.09 | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6686) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.77/20.09 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.77/20.09 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.77/20.09 | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.77/20.09 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.77/20.09 | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.77/20.09 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.77/20.09 | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | ALPHA: (6686) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6687) op(e0, e0) = all_56_15
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6688) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6689) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6690) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6691) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.77/20.09 | | | | | | | | | | | | | | | | | (6692) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.77/20.09 | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.77/20.09 | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | BETA: splitting (6689) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | (6693) all_56_9 = e0 & op(e3, e3) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | ALPHA: (6693) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | (6694) op(e3, e3) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6510), (6694), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | (6695) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | ALPHA: (6695) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | (6696) ~ (all_56_2 = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | (6697) op(e3, e0) = all_56_2
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | BETA: splitting (6691) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | (6698) all_56_5 = e2 & op(e2, e0) = e2
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | ALPHA: (6698) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | (6699) op(e2, e0) = e2
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6658), (6699), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | (6700) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | ALPHA: (6700) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | (6701) ~ (all_56_11 = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | (6702) op(e2, e2) = all_56_11
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | BETA: splitting (6692) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6703) all_56_2 = e3 & op(e3, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | ALPHA: (6703) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6704) op(e3, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6696), (6697), (6704), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6705) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | ALPHA: (6705) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6706) ~ (all_56_9 = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6707) op(e3, e3) = all_56_9
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (6484), (6687)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6708) all_56_15 = e2
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (5903), (6702)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6709) all_56_11 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e3, simplifying with (168), (6697)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6710) all_56_2 = all_52_12
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (6510), (6707) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6711) all_56_9 = e2
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | REDUCE: (6696), (6710) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | (6712) ~ (all_52_12 = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | (6713) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (5894), (6510), (6713),
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | #180.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | (6714) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6714) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | (6715) all_57_4 = e3 & op(e3, e1) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6715) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | (6716) all_57_4 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | (6717) op(e3, e1) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | (6718) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6718) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6719) all_57_9 = e3 & op(e3, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6719) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6720) op(e3, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (6712), (6720), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1105.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6721) all_57_10 = e3 & op(e2, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6721) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6722) all_57_10 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6723) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6723) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6724) all_57_2 = e0 & op(e2, e3) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6724) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6725) all_57_2 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6726) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6726) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6727) all_57_2 = e1 & op(e2, e3) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6725), (6727) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #878.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6728) all_57_3 = e1 & op(e2, e2) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6728) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6729) all_57_3 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (6729) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #591.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6730) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6730) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6731) all_57_5 = e1 & op(e2, e1) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6731) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6732) all_57_5 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6515), (6732) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1031.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6733) all_57_10 = e1 & op(e2, e0) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6733) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6734) all_57_10 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6722), (6734) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6735) all_57_3 = e0 & op(e2, e2) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6735) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6736) op(e2, e2) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6701), (6702), (6736), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6737) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6737) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6738) all_57_5 = e0 & op(e2, e1) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6515), (6738) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | #627.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6739) all_57_10 = e0 & op(e2, e0) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6739) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6740) all_57_10 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6722), (6740) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | #935.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | (6741) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6741) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6742) all_57_11 = e3 & op(e1, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6742) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6743) op(e1, e0) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e1, simplifying with (160), (6743) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6744) all_52_14 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (6717) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6745) all_52_8 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (121), (6745) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6746) ~ (all_52_11 = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6746) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6747) ~ (all_52_11 = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (6744) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | (6748) ~ (all_4_2 = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6690) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6749) all_56_8 = e1 & op(e1, e0) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6749) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6750) op(e1, e0) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6743), (6750), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6751) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6751) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6752) ~ (all_56_13 = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | (6753) op(e1, e1) = all_56_13
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6688) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6754) all_56_13 = e0 & op(e1, e1) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6754) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6755) op(e1, e1) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6752), (6753), (6755), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6756) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6756) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6757) ~ (all_56_8 = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | (6758) op(e1, e0) = all_56_8
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6759) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6759) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6760) all_57_12 = e3 & op(e0, e3) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6760) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6761) all_57_12 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6762) op(e0, e3) = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (6762) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6763) all_52_3 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_8,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, simplifying with (6743), (6758) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6764) all_56_8 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_4_2,
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (36), (6753)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6765) all_56_13 = all_4_2
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6752), (6765) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6766) ~ (all_4_2 = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6767) all_54_10 = e3
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (5905), (6767) are inconsistent by
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1112.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6768) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6768) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6769) all_54_10 = e2
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (6769) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1111.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6770) ~ (all_54_10 = e2)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6771) all_54_10 = e1 | all_54_10 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6772) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (6515), (6716), (6772) are inconsistent
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #138.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6773) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6773) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6774) all_57_8 = e0 & op(e1, e1) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6774) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6775) op(e1, e1) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (335), (6766), (6771), (6775),
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #457.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6776) all_57_14 = e0 & op(e0, e1) = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6776) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6777) all_57_14 = e0
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6778) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6778) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6779) all_57_4 = e1 & op(e3, e1) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6779) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6780) all_57_4 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6716), (6780) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6781) e3 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (6781) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6782) e3 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6764), (6782) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6783) all_56_8 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (335), (372), (6688), (6766), (6768),
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6783), (function-axioms) are inconsistent by
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #136.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6784) all_57_5 = e1 & op(e2, e1) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6515), (6784) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #938.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6785) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6785) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6786) all_57_8 = e1 & op(e1, e1) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6786) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6787) op(e1, e1) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6788) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6788) gives:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6789) all_57_12 = e1 & op(e0, e3) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6789) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6790) all_57_12 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6761), (6790) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6791) e3 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (6764), (6791) imply:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6792) all_56_8 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6688), (6787), (6792), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #141.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6793) all_57_13 = e1 & op(e0, e2) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (6480), (6482), (6743), (6793),
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #116.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6794) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (220), (222), (223),
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6484), (6787), (6794), (function-axioms) are
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #784.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6795) all_57_14 = e1 & op(e0, e1) = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6795) implies:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6796) all_57_14 = e1
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6777), (6796) are inconsistent by sub-proof
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1071.
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.09 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6797) all_57_13 = e3 & op(e0, e2) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6797) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6798) op(e0, e2) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6799) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6799) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6800) all_57_1 = e1 & op(e3, e2) = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6800) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6801) all_57_1 = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6802) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5903), (6801), (6802),
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #115.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6803) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6803) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6804) all_57_7 = e0 & op(e1, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6650), (6804) are inconsistent by sub-proof
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1017.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6805) all_57_13 = e0 & op(e0, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6805) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6806) op(e0, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6798), (6806), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #243.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6807) all_57_3 = e1 & op(e2, e2) = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (6807) are inconsistent by sub-proof
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #163.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6808) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6808) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6809) all_57_7 = e1 & op(e1, e2) = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6809) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6810) all_57_7 = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6650), (6810) are inconsistent by sub-proof
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #872.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6811) all_57_13 = e1 & op(e0, e2) = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (91), (6480), (6482), (6743), (6811),
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #116.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6812) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6812) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6813) all_57_14 = e3 & op(e0, e1) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6747), (6813), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6814) all_57_15 = e3 & op(e0, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6814) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (6815) op(e0, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6484), (6815), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | (6816) all_57_15 = e3 & op(e0, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6816) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | (6817) op(e0, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6484), (6817), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | (6818) all_57_9 = e3 & op(e3, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6818) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | (6819) op(e3, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (6712), (6819), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1105.
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | (6820) all_57_13 = e2 & op(e0, e2) = e2
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | REF_CLOSE: (158), (6483), (6820), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | (6821) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.77/20.10 | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (209), (210),
% 139.77/20.10 | | | | | | | | | | | | (212), (372), (6484), (6821), (function-axioms)
% 139.77/20.10 | | | | | | | | | | | | are inconsistent by sub-proof #766.
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | (6822) all_22_2 = e1
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | COMBINE_EQS: (321), (6822) imply:
% 139.77/20.10 | | | | | | | | | (6823) all_14_2 = e1
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | SIMP: (6823) implies:
% 139.77/20.10 | | | | | | | | | (6824) all_14_2 = e1
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | REDUCE: (51), (6824) imply:
% 139.77/20.10 | | | | | | | | | (6825) op(e3, e3) = e1
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | BETA: splitting (207) gives:
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | (6826) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.10 | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.10 | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.10 | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.10 | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.10 | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.77/20.10 | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.77/20.10 | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.77/20.10 | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.77/20.10 | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.77/20.10 | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.77/20.10 | | | | | | | | | | $i(all_56_6))
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | BETA: splitting (6826) gives:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | (6827) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.10 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.10 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.10 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.10 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.10 | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | REF_CLOSE: (6), (6825), (6827), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | (6828) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.77/20.10 | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.77/20.10 | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.77/20.10 | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.77/20.10 | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.77/20.10 | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | REF_CLOSE: (36), (5905), (6828), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | (6829) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.10 | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.10 | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.10 | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.10 | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.10 | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.77/20.10 | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.77/20.10 | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.77/20.10 | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.77/20.10 | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.77/20.10 | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.77/20.10 | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.77/20.10 | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.77/20.10 | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.77/20.10 | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.77/20.10 | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.77/20.10 | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.10 | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | BETA: splitting (6829) gives:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | (6830) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.10 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.10 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.10 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.10 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.10 | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | REF_CLOSE: (4), (36), (372), (6825), (6830),
% 139.77/20.10 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.10 | | | | | | | | | | | #248.
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | (6831) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.10 | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.77/20.10 | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.77/20.10 | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.77/20.10 | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.77/20.10 | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.77/20.10 | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.10 | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.10 | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.10 | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.10 | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.10 | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.10 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | BETA: splitting (6831) gives:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | (6832) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.10 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.77/20.10 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | ALPHA: (6832) implies:
% 139.77/20.10 | | | | | | | | | | | | (6833) op(e1, e1) = e2
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | REF_CLOSE: (36), (372), (6833), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | (6834) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.10 | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.77/20.10 | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.77/20.10 | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.10 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.10 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.10 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.10 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | BETA: splitting (6834) gives:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | (6835) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.10 | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.77/20.10 | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | ALPHA: (6835) implies:
% 139.77/20.10 | | | | | | | | | | | | | (6836) op(e2, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | REF_CLOSE: (7), (5903), (6836), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | (6837) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.77/20.10 | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.10 | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.77/20.10 | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.77/20.10 | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.77/20.10 | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.77/20.10 | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.10 | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.77/20.10 | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.77/20.10 | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | ALPHA: (6837) implies:
% 139.77/20.10 | | | | | | | | | | | | | (6838) op(e0, e0) = all_56_15
% 139.77/20.10 | | | | | | | | | | | | | (6839) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.10 | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.77/20.10 | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.77/20.10 | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.77/20.10 | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.77/20.10 | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.10 | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (5903), (5906), (6825), (6838),
% 139.77/20.10 | | | | | | | | | | | | | (6839), (function-axioms) are inconsistent by
% 139.77/20.10 | | | | | | | | | | | | | sub-proof #113.
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | End of split
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | (6840) all_14_2 = e0
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | REDUCE: (337), (6840) imply:
% 139.77/20.10 | | | | | | | | (6841) ~ (all_52_1 = e0)
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | REDUCE: (341), (6840) imply:
% 139.77/20.10 | | | | | | | | (6842) ~ (all_52_3 = e0)
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | REDUCE: (343), (6840) imply:
% 139.77/20.10 | | | | | | | | (6843) ~ (all_52_4 = e0)
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | REDUCE: (345), (6840) imply:
% 139.77/20.10 | | | | | | | | (6844) ~ (all_52_8 = e0)
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | REDUCE: (51), (6840) imply:
% 139.77/20.10 | | | | | | | | (6845) op(e3, e3) = e0
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | BETA: splitting (67) gives:
% 139.77/20.10 | | | | | | | |
% 139.77/20.10 | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | (6846) ~ (all_24_2 = e2)
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | REDUCE: (319), (6846) imply:
% 139.77/20.10 | | | | | | | | | (6847) ~ (all_10_2 = e2)
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | BETA: splitting (70) gives:
% 139.77/20.10 | | | | | | | | |
% 139.77/20.10 | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | (6848) ~ (all_26_2 = e3)
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | REDUCE: (5892), (6848) imply:
% 139.77/20.10 | | | | | | | | | | (6849) $false
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | CLOSE: (6849) is inconsistent.
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | (6850) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0
% 139.77/20.10 | | | | | | | | | | & op(e2, e3) = all_26_1 & $i(all_26_0) &
% 139.77/20.10 | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3)
% 139.77/20.10 | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | BETA: splitting (94) gives:
% 139.77/20.10 | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | (6851) ~ (all_42_2 = e3)
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | REDUCE: (303), (6851) imply:
% 139.77/20.10 | | | | | | | | | | | (6852) ~ (all_10_2 = e3)
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | BETA: splitting (189) gives:
% 139.77/20.10 | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | (6853) all_54_15 = e3
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | REF_CLOSE: (246), (6852), (6853) are inconsistent by
% 139.77/20.10 | | | | | | | | | | | | sub-proof #755.
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | (6854) ~ (all_54_15 = e3)
% 139.77/20.10 | | | | | | | | | | | | (6855) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | BETA: splitting (6855) gives:
% 139.77/20.10 | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | (6856) all_54_15 = e2
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | REF_CLOSE: (246), (6847), (6856) are inconsistent by
% 139.77/20.10 | | | | | | | | | | | | | sub-proof #754.
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | (6857) ~ (all_54_15 = e2)
% 139.77/20.10 | | | | | | | | | | | | | (6858) all_54_15 = e1 | all_54_15 = e0
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.77/20.10 | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | (6859) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.10 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.10 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.10 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.10 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.10 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.77/20.10 | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.77/20.10 | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.77/20.10 | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.77/20.10 | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.77/20.10 | | | | | | | | | | | | | | $i(all_56_6))
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | BETA: splitting (6859) gives:
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | (6860) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.10 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.10 | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.10 | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.10 | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.10 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6845), (6860), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | (6861) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.77/20.10 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.77/20.10 | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.77/20.10 | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.77/20.10 | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (6861), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | (6862) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.10 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.10 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.10 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.10 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.77/20.10 | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.77/20.10 | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.77/20.10 | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.77/20.10 | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.77/20.10 | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.77/20.10 | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.77/20.10 | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.77/20.10 | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.77/20.10 | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.77/20.10 | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | BETA: splitting (6862) gives:
% 139.77/20.10 | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | (6863) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.10 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.10 | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.10 | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.10 | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | BETA: splitting (6863) gives:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | (6864) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.10 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.77/20.10 | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | ALPHA: (6864) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | (6865) op(e0, e0) = e3
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (246), (5906), (6847), (6852), (6855),
% 139.77/20.10 | | | | | | | | | | | | | | | | (6865), (function-axioms) are inconsistent by
% 139.77/20.10 | | | | | | | | | | | | | | | | sub-proof #202.
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | (6866) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.77/20.10 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.77/20.10 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | ALPHA: (6866) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | (6867) op(e1, e1) = e2
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6867), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | End of split
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | (6868) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.10 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.77/20.10 | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.77/20.10 | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.77/20.10 | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.77/20.10 | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.77/20.10 | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.10 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.10 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.10 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | BETA: splitting (6868) gives:
% 139.77/20.10 | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | (6869) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.10 | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.77/20.10 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | ALPHA: (6869) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | (6870) op(e1, e1) = e2
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6870), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | (6871) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.10 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.77/20.10 | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.77/20.10 | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.10 | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.10 | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.10 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.10 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.10 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.10 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | BETA: splitting (6871) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | (6872) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.77/20.10 | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | ALPHA: (6872) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | (6873) op(e0, e0) = e2
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (6847), (6873), (function-axioms) are
% 139.77/20.10 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1115.
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | (6874) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.77/20.10 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.77/20.10 | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.77/20.10 | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.77/20.10 | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.10 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.77/20.10 | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.77/20.10 | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | ALPHA: (6874) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | (6875) op(e0, e0) = all_56_15
% 139.77/20.10 | | | | | | | | | | | | | | | | | (6876) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.77/20.10 | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.10 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.77/20.10 | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.10 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.77/20.10 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | BETA: splitting (6858) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6877) all_54_15 = e1
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (5906), (6877) are inconsistent by
% 139.77/20.10 | | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6878) all_54_15 = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (6878) imply:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6879) all_10_2 = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | SIMP: (6879) implies:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6880) all_10_2 = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | REDUCE: (370), (6880) imply:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6881) ~ (all_52_13 = e0)
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | REDUCE: (6852), (6880) imply:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6882) ~ (e3 = e0)
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | REDUCE: (45), (6880) imply:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | (6883) op(e0, e0) = e0
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 139.77/20.10 | | | | | | | | | | | | | | | | | |
% 139.77/20.10 | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.10 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | (6884) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (5903), (6841), (6884),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | #112.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | (6885) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (6885) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6886) all_57_5 = e0 & op(e2, e1) = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | ALPHA: (6886) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6887) op(e2, e1) = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (6875), (6883)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6888) all_56_15 = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (6887) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6889) all_52_9 = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | REDUCE: (363), (6889) imply:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6890) ~ (all_4_2 = e0)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | SIMP: (6890) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6891) ~ (all_4_2 = e0)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | (6892) all_54_10 = e3
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (5905), (6892) are inconsistent by
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | sub-proof #1112.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | (6893) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6893) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | (6894) all_54_10 = e2
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (6894) are inconsistent by sub-proof
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | #1111.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | (6895) all_54_10 = e1 | all_54_10 = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6876) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | (6896) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6896) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | (6897) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (6888), (6897) are inconsistent by sub-proof
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | #747.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | (6898) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (6898) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | (6899) op(e2, e2) = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5903), (6899), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | (6900) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (335), (6891), (6895), (6900),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | | #456.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | (6901) all_57_10 = e0 & op(e2, e0) = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6881), (6901), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | (6902) all_42_2 = e3
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | COMBINE_EQS: (303), (6902) imply:
% 139.77/20.11 | | | | | | | | | | | (6903) all_10_2 = e3
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | SIMP: (6903) implies:
% 139.77/20.11 | | | | | | | | | | | (6904) all_10_2 = e3
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | REDUCE: (368), (6904) imply:
% 139.77/20.11 | | | | | | | | | | | (6905) ~ (all_52_11 = e3)
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | REDUCE: (45), (6904) imply:
% 139.77/20.11 | | | | | | | | | | | (6906) op(e0, e0) = e3
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | BETA: splitting (223) gives:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | (6907) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.77/20.11 | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | BETA: splitting (6907) gives:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | (6908) all_57_4 = e3 & op(e3, e1) = e3
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | ALPHA: (6908) implies:
% 139.77/20.11 | | | | | | | | | | | | | (6909) all_57_4 = e3
% 139.77/20.11 | | | | | | | | | | | | | (6910) op(e3, e1) = e3
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 139.77/20.11 | | | | | | | | | | | | | e1, e3, simplifying with (169), (6910) gives:
% 139.77/20.11 | | | | | | | | | | | | | (6911) all_52_8 = e3
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | REDUCE: (120), (6911) imply:
% 139.77/20.11 | | | | | | | | | | | | | (6912) ~ (all_52_12 = e3)
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | SIMP: (6912) implies:
% 139.77/20.11 | | | | | | | | | | | | | (6913) ~ (all_52_12 = e3)
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | (6914) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.77/20.11 | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.77/20.11 | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.77/20.11 | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | BETA: splitting (6914) gives:
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | (6915) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.77/20.11 | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.77/20.11 | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.77/20.11 | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.77/20.11 | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | ALPHA: (6915) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | (6916) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_15))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | REF_CLOSE: (159), (6842), (6906), (6916), (function-axioms)
% 139.77/20.11 | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | (6917) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.77/20.11 | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.77/20.11 | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.77/20.11 | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.77/20.11 | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.77/20.11 | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.77/20.11 | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | ALPHA: (6917) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | (6918) op(e2, e2) = all_56_11
% 139.77/20.11 | | | | | | | | | | | | | | | (6919) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_12))
% 139.77/20.11 | | | | | | | | | | | | | | | (6920) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 139.77/20.11 | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 139.77/20.11 | | | | | | | | | | | | | | | (6921) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_15))
% 139.77/20.11 | | | | | | | | | | | | | | | (6922) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 139.77/20.11 | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 139.77/20.11 | | | | | | | | | | | | | | | (6923) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.77/20.11 | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_13))
% 139.77/20.11 | | | | | | | | | | | | | | | (6924) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.77/20.11 | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | BETA: splitting (6919) gives:
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | (6925) all_56_15 = e2 & op(e0, e0) = e2
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | ALPHA: (6925) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | (6926) op(e0, e0) = e2
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6906), (6926), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | (6927) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.77/20.11 | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | ALPHA: (6927) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | (6928) ~ (all_56_12 = e0)
% 139.77/20.11 | | | | | | | | | | | | | | | | (6929) op(e0, e2) = all_56_12
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | BETA: splitting (6921) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | (6930) all_56_12 = e0 & op(e0, e2) = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | ALPHA: (6930) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | (6931) op(e0, e2) = e0
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (6928), (6929), (6931), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | (6932) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | ALPHA: (6932) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | (6933) ~ (all_56_15 = e2)
% 139.77/20.11 | | | | | | | | | | | | | | | | | (6934) op(e0, e0) = all_56_15
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | BETA: splitting (6920) gives:
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6935) all_56_13 = e2 & op(e1, e1) = e2
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | ALPHA: (6935) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6936) op(e1, e1) = e2
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (6936), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6937) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.77/20.11 | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | ALPHA: (6937) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6938) ~ (all_56_7 = e1)
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6939) op(e1, e2) = all_56_7
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (158), (159), (167),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (169), (170), (209), (220), (221), (222), (223),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (224), (225), (227), (228), (5891), (5894),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (5902), (5903), (6841), (6842), (6843), (6844),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6845), (6850), (6906), (6909), (6918), (6921),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6922), (6923), (6924), (6928), (6929), (6933),
% 139.77/20.11 | | | | | | | | | | | | | | | | | | (6934), (6938), (6939), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #109.
% 139.77/20.11 | | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | (6940) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.77/20.11 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.77/20.11 | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.77/20.11 | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.77/20.11 | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.77/20.11 | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.77/20.11 | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.77/20.11 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | BETA: splitting (6940) gives:
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | (6941) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.77/20.11 | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.77/20.11 | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.77/20.11 | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.77/20.11 | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.77/20.11 | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.77/20.11 | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.77/20.11 | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.77/20.11 | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6845), (6910), (6941), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | | | inconsistent by sub-proof #733.
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | (6942) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.77/20.11 | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.77/20.11 | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.77/20.11 | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.77/20.11 | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.77/20.11 | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.77/20.11 | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.77/20.11 | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.77/20.11 | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.77/20.11 | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.77/20.11 | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | ALPHA: (6942) implies:
% 139.77/20.11 | | | | | | | | | | | | | | | (6943) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.77/20.11 | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (9), (36), (168), (207), (372),
% 139.77/20.11 | | | | | | | | | | | | | | | (6845), (6906), (6913), (6943), (function-axioms)
% 139.77/20.11 | | | | | | | | | | | | | | | are inconsistent by sub-proof #530.
% 139.77/20.11 | | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | (6944) all_57_5 = e3 & op(e2, e1) = e3
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | | REF_CLOSE: (165), (5897), (6944), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 139.77/20.11 | | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | (6945) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.77/20.11 | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | REF_CLOSE: (36), (157), (5905), (6905), (6945),
% 139.77/20.11 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.11 | | | | | | | | | | | | #126.
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | (6946) all_24_2 = e2
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | COMBINE_EQS: (319), (6946) imply:
% 139.77/20.11 | | | | | | | | | (6947) all_10_2 = e2
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | SIMP: (6947) implies:
% 139.77/20.11 | | | | | | | | | (6948) all_10_2 = e2
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | REDUCE: (45), (6948) imply:
% 139.77/20.11 | | | | | | | | | (6949) op(e0, e0) = e2
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | BETA: splitting (207) gives:
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | (6950) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.11 | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.11 | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.11 | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.11 | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.11 | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.77/20.11 | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.77/20.11 | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.77/20.11 | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.77/20.11 | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.77/20.11 | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.77/20.11 | | | | | | | | | | $i(all_56_6))
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | BETA: splitting (6950) gives:
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | (6951) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.11 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.11 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.11 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.11 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.11 | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | REF_CLOSE: (5), (6845), (6951), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | inconsistent by sub-proof #753.
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | (6952) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.77/20.11 | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.77/20.11 | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.77/20.11 | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.77/20.11 | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.77/20.11 | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | REF_CLOSE: (36), (5905), (6952), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | (6953) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.11 | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.11 | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.11 | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.11 | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.11 | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.77/20.11 | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.77/20.11 | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.77/20.11 | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.77/20.11 | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.77/20.11 | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.77/20.11 | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.77/20.11 | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.77/20.11 | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.77/20.11 | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.77/20.11 | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.77/20.11 | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.77/20.11 | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.11 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.11 | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.11 | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.11 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.11 | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.11 | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | BETA: splitting (6953) gives:
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | (6954) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.11 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.11 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.11 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.11 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.11 | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | BETA: splitting (6954) gives:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | (6955) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.11 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.77/20.11 | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | ALPHA: (6955) implies:
% 139.77/20.11 | | | | | | | | | | | | (6956) op(e0, e0) = e3
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | REF_CLOSE: (9), (6949), (6956), (function-axioms) are
% 139.77/20.11 | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | (6957) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.77/20.11 | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.77/20.11 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | ALPHA: (6957) implies:
% 139.77/20.11 | | | | | | | | | | | | (6958) op(e2, e2) = e1
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (207), (372), (6845),
% 139.77/20.11 | | | | | | | | | | | | (6949), (6958), (function-axioms) are inconsistent
% 139.77/20.11 | | | | | | | | | | | | by sub-proof #525.
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | (6959) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.11 | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.77/20.11 | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.77/20.11 | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.77/20.11 | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.77/20.11 | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.77/20.11 | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.11 | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.11 | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.11 | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.11 | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.11 | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.11 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.11 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.11 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.11 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.11 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.11 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | BETA: splitting (6959) gives:
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | (6960) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.11 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.77/20.11 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | ALPHA: (6960) implies:
% 139.77/20.11 | | | | | | | | | | | | (6961) op(e2, e2) = e1
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (36), (207), (372), (6845),
% 139.77/20.11 | | | | | | | | | | | | (6949), (6961), (function-axioms) are inconsistent
% 139.77/20.11 | | | | | | | | | | | | by sub-proof #525.
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | Case 2:
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | (6962) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.11 | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.77/20.11 | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.77/20.11 | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.11 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.11 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.11 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.11 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.11 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.11 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.11 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.11 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.11 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.11 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.11 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | | REF_CLOSE: (6), (7), (9), (5903), (6949), (6962),
% 139.77/20.11 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.11 | | | | | | | | | | | | #107.
% 139.77/20.11 | | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | | |
% 139.77/20.11 | | | | | | | | | End of split
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | End of split
% 139.77/20.11 | | | | | | | |
% 139.77/20.11 | | | | | | | End of split
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | Case 2:
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | (6963) all_10_2 = e1
% 139.77/20.11 | | | | | | | (6964) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 139.77/20.11 | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) |
% 139.77/20.11 | | | | | | | ( ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 139.77/20.11 | | | | | | | $i(all_10_1))
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | COMBINE_EQS: (309), (6963) imply:
% 139.77/20.11 | | | | | | | (6965) all_30_2 = e1
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | REDUCE: (350), (6963) imply:
% 139.77/20.11 | | | | | | | (6966) ~ (all_52_3 = e1)
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | REDUCE: (361), (6963) imply:
% 139.77/20.11 | | | | | | | (6967) ~ (all_52_7 = e1)
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | REDUCE: (368), (6963) imply:
% 139.77/20.11 | | | | | | | (6968) ~ (all_52_11 = e1)
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | REDUCE: (369), (6963) imply:
% 139.77/20.11 | | | | | | | (6969) ~ (all_52_12 = e1)
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | REDUCE: (370), (6963) imply:
% 139.77/20.11 | | | | | | | (6970) ~ (all_52_13 = e1)
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | REDUCE: (371), (6963) imply:
% 139.77/20.11 | | | | | | | (6971) ~ (all_52_14 = e1)
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | BETA: splitting (210) gives:
% 139.77/20.11 | | | | | | |
% 139.77/20.11 | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | |
% 139.77/20.11 | | | | | | | | (6972) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 &
% 139.77/20.11 | | | | | | | | op(e0, e2) = e1)
% 139.77/20.11 | | | | | | | |
% 139.77/20.11 | | | | | | | | BETA: splitting (6972) gives:
% 139.77/20.11 | | | | | | | |
% 139.77/20.11 | | | | | | | | Case 1:
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | (6973) all_57_12 = e1 & op(e0, e3) = e1
% 139.77/20.11 | | | | | | | | |
% 139.77/20.11 | | | | | | | | | REF_CLOSE: (159), (6966), (6973), (function-axioms) are
% 139.77/20.11 | | | | | | | | | inconsistent by sub-proof #350.
% 139.77/20.11 | | | | | | | | |
% 139.77/20.12 | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | (6974) all_57_13 = e1 & op(e0, e2) = e1
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | REF_CLOSE: (158), (6967), (6974), (function-axioms) are
% 139.77/20.12 | | | | | | | | | inconsistent by sub-proof #366.
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | End of split
% 139.77/20.12 | | | | | | | |
% 139.77/20.12 | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | |
% 139.77/20.12 | | | | | | | | (6975) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 &
% 139.77/20.12 | | | | | | | | op(e0, e0) = e1)
% 139.77/20.12 | | | | | | | |
% 139.77/20.12 | | | | | | | | BETA: splitting (6975) gives:
% 139.77/20.12 | | | | | | | |
% 139.77/20.12 | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | (6976) all_57_14 = e1 & op(e0, e1) = e1
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | REF_CLOSE: (157), (6968), (6976), (function-axioms) are
% 139.77/20.12 | | | | | | | | | inconsistent by sub-proof #347.
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | (6977) all_57_15 = e1 & op(e0, e0) = e1
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | ALPHA: (6977) implies:
% 139.77/20.12 | | | | | | | | | (6978) all_57_15 = e1
% 139.77/20.12 | | | | | | | | | (6979) op(e0, e0) = e1
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | BETA: splitting (52) gives:
% 139.77/20.12 | | | | | | | | |
% 139.77/20.12 | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | (6980) ~ (all_14_2 = e0)
% 139.77/20.12 | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | BETA: splitting (64) gives:
% 139.77/20.12 | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | (6981) ~ (all_22_2 = e1)
% 139.77/20.12 | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | REDUCE: (321), (6981) imply:
% 139.77/20.12 | | | | | | | | | | | (6982) ~ (all_14_2 = e1)
% 139.77/20.12 | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | BETA: splitting (70) gives:
% 139.77/20.12 | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | (6983) ~ (all_26_2 = e3)
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | REDUCE: (5892), (6983) imply:
% 139.77/20.12 | | | | | | | | | | | | (6984) $false
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | CLOSE: (6984) is inconsistent.
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | (6985) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0
% 139.77/20.12 | | | | | | | | | | | | & op(e2, e3) = all_26_1 & $i(all_26_0) &
% 139.77/20.12 | | | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3)
% 139.77/20.12 | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | BETA: splitting (76) gives:
% 139.77/20.12 | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | (6986) ~ (all_30_2 = e1)
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | REDUCE: (6965), (6986) imply:
% 139.77/20.12 | | | | | | | | | | | | | (6987) $false
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | CLOSE: (6987) is inconsistent.
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | (6988) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0
% 139.77/20.12 | | | | | | | | | | | | | & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 139.77/20.12 | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1)
% 139.77/20.12 | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 139.77/20.12 | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | (6989) ~ (all_36_2 = e2)
% 139.77/20.12 | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | REDUCE: (305), (6989) imply:
% 139.77/20.12 | | | | | | | | | | | | | | (6990) ~ (all_14_2 = e2)
% 139.77/20.12 | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.77/20.12 | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | (6991) all_54_0 = e3
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | COMBINE_EQS: (279), (6991) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | (6992) all_14_2 = e3
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | SIMP: (6992) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | (6993) all_14_2 = e3
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | REDUCE: (345), (6993) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | (6994) ~ (all_52_8 = e3)
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | REDUCE: (347), (6993) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | (6995) ~ (all_52_12 = e3)
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | REDUCE: (51), (6993) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | (6996) op(e3, e3) = e3
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.77/20.12 | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | (6997) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (5897), (6994), (6997),
% 139.77/20.12 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | #319.
% 139.77/20.12 | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | (6998) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.77/20.12 | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | BETA: splitting (6998) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | (6999) all_57_8 = e3 & op(e1, e1) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | ALPHA: (6999) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | (7000) op(e1, e1) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (7000), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | (7001) all_57_14 = e3 & op(e0, e1) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | ALPHA: (7001) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | (7002) all_57_14 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | (7003) op(e0, e1) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | (7004) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | BETA: splitting (7004) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7005) all_57_6 = e3 & op(e1, e3) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | ALPHA: (7005) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7006) all_57_6 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | (7007) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7007) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7008) all_57_0 = e1 & op(e3, e3) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7008) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7009) op(e3, e3) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6996), (7009), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7010) all_57_2 = e1 & op(e2, e3) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7010) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7011) all_57_2 = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (7012) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7012) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7013) all_57_0 = e3 & op(e3, e3) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7013) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7014) all_57_0 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7015) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7015) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7016) all_57_0 = e2 & op(e3, e3) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7016) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7017) op(e3, e3) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6996), (7017), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7018) all_57_2 = e2 & op(e2, e3) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7018) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7019) all_57_2 = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7011), (7019) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | #943.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7020) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7020) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7021) all_57_6 = e2 & op(e1, e3) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7006), (7021) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | #998.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7022) all_57_12 = e2 & op(e0, e3) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7022) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7023) all_57_12 = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (168), (169), (170), (232), (239),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (5894), (6994), (6995), (7006), (7011), (7014),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7023), (function-axioms) are inconsistent by
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #448.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7024) all_57_1 = e3 & op(e3, e2) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7024) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7025) op(e3, e2) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5894), (7025), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (7026) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (6994), (6995), (7026),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | #1104.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | (7027) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7027) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7028) all_57_6 = e1 & op(e1, e3) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7006), (7028) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | #865.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7029) all_57_12 = e1 & op(e0, e3) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6966), (7029), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7030) all_57_7 = e3 & op(e1, e2) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | ALPHA: (7030) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7031) all_57_7 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | (7032) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7032) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7033) all_57_0 = e3 & op(e3, e3) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7033) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7034) all_57_0 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (7035) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7035) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7036) all_57_1 = e1 & op(e3, e2) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7036) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7037) all_57_1 = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7038) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7038) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7039) all_57_1 = e2 & op(e3, e2) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7037), (7039) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | #1074.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7040) all_57_3 = e2 & op(e2, e2) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7040) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7041) op(e2, e2) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5903), (7041), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7042) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7042) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7043) all_57_7 = e2 & op(e1, e2) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7031), (7043) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | #1084.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7044) all_57_13 = e2 & op(e0, e2) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7044) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7045) all_57_13 = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (7046) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (5903), (7037), (7046),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #115.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (7047) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7047) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7048) all_57_7 = e0 & op(e1, e2) = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7048) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7049) all_57_7 = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7031), (7049) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7050) e3 = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7034), (7050) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7051) all_57_0 = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (5894), (6994),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (6995), (7051), (function-axioms) are inconsistent
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1103.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7052) all_57_13 = e0 & op(e0, e2) = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7045), (7052) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | #1060.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7053) all_57_3 = e1 & op(e2, e2) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (7053) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | #163.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (7054) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7054) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7055) all_57_7 = e1 & op(e1, e2) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7031), (7055) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | #1058.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7056) all_57_13 = e1 & op(e0, e2) = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (6967), (7056), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7057) all_57_1 = e3 & op(e3, e2) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7057) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7058) op(e3, e2) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5894), (7058), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | (7059) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (6994), (6995), (7059),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | #1104.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | (7060) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | BETA: splitting (7060) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7061) all_57_8 = e3 & op(e1, e1) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | ALPHA: (7061) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7062) op(e1, e1) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (7062), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1127.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7063) all_57_11 = e3 & op(e1, e0) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | ALPHA: (7063) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7064) all_57_11 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | (7065) op(e1, e0) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | (7066) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7066) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7067) all_57_0 = e3 & op(e3, e3) = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7067) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | (7068) all_57_0 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (7069) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7069) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7070) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (6996), (7070), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7071) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (7071), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (7072) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7072) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7073) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (372), (6979), (7073),
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | #462.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (7074) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7074) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7075) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7075) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7076) op(e1, e1) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7076), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (7077) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7077) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7078) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7078) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7079) op(e0, e0) = e2
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6979), (7079), (function-axioms) are
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7080) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7080) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7081) op(e0, e0) = all_56_15
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7082) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (6979), (7081)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7083) all_56_15 = e1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, e0, simplifying with (157), (7003) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7084) all_52_11 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e0, e1, simplifying with (160), (7065) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7085) all_52_14 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (367), (7085) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | (7086) ~ (all_4_2 = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6988) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (7087) ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_30_1 & $i(all_30_0) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7087) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (7088) ~ (all_30_0 = e3)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (7089) op(e0, e1) = all_30_1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (7090) op(all_30_1, e0) = all_30_0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6964) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7091) ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) &
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7091) implies:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7092) ~ (all_10_0 = e2)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7093) op(e0, e1) = all_10_1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7094) op(all_10_1, e0) = all_10_0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (7003), (7089) gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7095) all_30_1 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_30_1, e1, e0, simplifying with (7089), (7093)
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7096) all_30_1 = all_10_1
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7095), (7096) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7097) all_10_1 = e3
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7090), (7095) imply:
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7098) op(e3, e0) = all_30_0
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7094), (7097) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7099) op(e3, e0) = all_10_0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_0, e0, e3, simplifying with (168), (7099)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7100) all_52_12 = all_10_0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_30_0, e0, e3, simplifying with (168), (7098)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7101) all_52_12 = all_30_0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7100), (7101) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7102) all_30_0 = all_10_0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7102) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7103) all_30_0 = all_10_0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7100) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7104) all_54_3 = all_10_0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (7100) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7105) ~ (all_52_4 = all_10_0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (7100) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7106) ~ (all_52_8 = all_10_0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (7100) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7107) ~ (all_52_13 = all_10_0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7107) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7108) ~ (all_52_13 = all_10_0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6969), (7100) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7109) ~ (all_10_0 = e1)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7088), (7103) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7110) ~ (all_10_0 = e3)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7111) all_54_3 = e3
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7104), (7111) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7112) all_10_0 = e3
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7112) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7113) all_10_0 = e3
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7110), (7113) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7114) $false
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7114) is inconsistent.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7115) ~ (all_54_3 = e3)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7116) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7117) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7117) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7118) all_57_9 = e2 & op(e3, e0) = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7118) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7119) all_57_9 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7116) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7120) all_54_3 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7092), (7104), (7120) are inconsistent by
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7121) all_54_3 = e1 | all_54_3 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7122) all_57_15 = e0 & op(e0, e0) = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7122) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7123) all_57_15 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6978), (7123) are inconsistent by sub-proof
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #291.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7124) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7124) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7125) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7121) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7126) all_54_3 = e1
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7104), (7109), (7126) are inconsistent by
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #105.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7127) all_54_3 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7104), (7127) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7128) all_10_0 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7128) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7129) all_10_0 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7105), (7129) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7130) ~ (all_52_4 = e0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7106), (7129) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7131) ~ (all_52_8 = e0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7108), (7129) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7132) ~ (all_52_13 = e0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7110), (7129) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7133) ~ (e3 = e0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7109), (7129) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7134) ~ (e1 = e0)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7135) all_54_7 = e3
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5898), (7135) are inconsistent by
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1007.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7136) ~ (all_54_7 = e3)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7137) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7137) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7138) all_54_7 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (7138) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7139) all_52_13 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7139) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7140) all_52_13 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7140) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7141) ~ (all_52_1 = e2)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (7140) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7142) ~ (all_52_9 = e2)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5898), (7140) imply:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7143) ~ (e3 = e2)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7144) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (51), (103), (106),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (134), (160), (165), (167), (168), (169),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (194), (206), (222), (233), (235), (239),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (299), (335), (362), (372), (5894), (5903),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5905), (6971), (6980), (6994), (6995), (6996),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7002), (7003), (7065), (7068), (7082), (7083),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7130), (7131), (7141), (7142), (7144),
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #102.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7145) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7145) gives:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7146) all_57_8 = e2 & op(e1, e1) = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7146) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7147) op(e1, e1) = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7147), (function-axioms) are
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7148) all_57_14 = e2 & op(e0, e1) = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7148) implies:
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7149) all_57_14 = e2
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.77/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7002), (7149) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7150) e3 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7150) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7151) e3 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7064), (7151) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7152) all_57_11 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (9), (215), (6979), (7119), (7125),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7152), (function-axioms) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #367.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7153) all_54_7 = e1 | all_54_7 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (6970), (7132), (7153) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #101.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7154) all_57_10 = e2 & op(e2, e0) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7154) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7155) all_57_10 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7116) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7156) all_54_3 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7092), (7104), (7156) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7157) all_54_3 = e1 | all_54_3 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7157) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7158) all_54_3 = e1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7104), (7109), (7158) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #105.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7159) all_54_3 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7104), (7159) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7160) all_10_0 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7160) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7161) all_10_0 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7105), (7161) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7162) ~ (all_52_4 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7106), (7161) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7163) ~ (all_52_8 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7108), (7161) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7164) ~ (all_52_13 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7110), (7161) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7165) ~ (e3 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7109), (7161) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7166) ~ (e1 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7167) all_54_7 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5898), (7167) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1007.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7168) ~ (all_54_7 = e3)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7169) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7169) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7170) all_54_7 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (7170) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7171) all_52_13 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7171) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7172) all_52_13 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7172) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7173) ~ (all_52_1 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (7172) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7174) ~ (all_52_9 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5898), (7172) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7175) ~ (e3 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7176) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (51), (103), (106),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (134), (160), (165), (167), (168), (169),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (194), (206), (222), (233), (235), (239),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (299), (335), (362), (372), (5894), (5903),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5905), (6971), (6980), (6994), (6995), (6996),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7002), (7003), (7065), (7068), (7082), (7083),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7162), (7163), (7173), (7174), (7176),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #102.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7177) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7177) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7178) all_57_8 = e2 & op(e1, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7178) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7179) op(e1, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7179), (function-axioms) are
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7180) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7180) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7181) all_57_14 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7002), (7181) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7182) e3 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7182) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7183) e3 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7064), (7183) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7184) all_57_11 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (215), (6979), (6995), (7155),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7184), (function-axioms) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #188.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7185) all_54_7 = e1 | all_54_7 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (6970), (7164), (7185) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #101.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7186) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7186) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7187) all_57_11 = e2 & op(e1, e0) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7187) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7188) all_57_11 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7064), (7188) are inconsistent by sub-proof
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1055.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7189) all_57_15 = e2 & op(e0, e0) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7189) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7190) op(e0, e0) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6979), (7190), (function-axioms) are
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7191) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7191) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7192) ~ (all_10_1 = e3)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7193) op(e0, e1) = all_10_1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7003), (7089), (7192), (7193), (function-axioms)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #372.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (7194) ~ (all_30_1 = e2) & op(e0, e1) = all_30_1 &
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7194) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (7195) ~ (all_30_1 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | (7196) op(e0, e1) = all_30_1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (6964) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7197) ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) &
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7197) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7198) ~ (all_10_0 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7199) op(e0, e1) = all_10_1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7200) op(all_10_1, e0) = all_10_0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_30_1,
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (7003), (7196) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7201) all_30_1 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_1,
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_30_1, e1, e0, simplifying with (7196), (7199)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7202) all_30_1 = all_10_1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7201), (7202) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7203) all_10_1 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7200), (7203) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7204) op(e3, e0) = all_10_0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_10_0, e0, e3, simplifying with (168), (7204)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7205) all_52_12 = all_10_0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (7205) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7206) all_54_3 = all_10_0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (7205) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7207) ~ (all_52_4 = all_10_0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (7205) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7208) ~ (all_52_8 = all_10_0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (7205) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7209) ~ (all_52_13 = all_10_0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7209) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7210) ~ (all_52_13 = all_10_0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6995), (7205) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7211) ~ (all_10_0 = e3)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (6969), (7205) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7212) ~ (all_10_0 = e1)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7213) all_54_3 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7206), (7213) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7214) all_10_0 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7211), (7214) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7215) $false
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (7215) is inconsistent.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7216) ~ (all_54_3 = e3)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7217) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7217) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7218) all_54_3 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7198), (7206), (7218) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #106.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7219) all_54_3 = e1 | all_54_3 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7219) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7220) all_54_3 = e1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7206), (7212), (7220) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #105.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7221) all_54_3 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7206), (7221) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7222) all_10_0 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7222) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7223) all_10_0 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7207), (7223) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7224) ~ (all_52_4 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7208), (7223) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7225) ~ (all_52_8 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7210), (7223) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7226) ~ (all_52_13 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7211), (7223) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7227) ~ (e3 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7212), (7223) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7228) ~ (e1 = e0)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (197) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7229) all_54_7 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (5898), (7229) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1007.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7230) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7230) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7231) all_54_7 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (260), (7231) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7232) all_52_13 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7232) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7233) all_52_13 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (7233) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7234) ~ (all_52_1 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (7233) imply:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7235) ~ (all_52_9 = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7236) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7236) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7237) all_57_4 = e2 & op(e3, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7237) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7238) all_57_4 = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7239) op(e3, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (51), (103), (106),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (123), (134), (160), (165), (167), (168), (169),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (194), (206), (222), (233), (235), (239),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295), (299), (335), (362), (372), (5894), (5903),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5905), (6971), (6980), (6994), (6995), (6996),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7002), (7003), (7065), (7068), (7082), (7083),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7224), (7225), (7234), (7238), (7239),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #103.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7240) all_57_5 = e2 & op(e2, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7240) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7241) op(e2, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7235), (7241), (function-axioms) are
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7242) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7242) gives:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7243) all_57_8 = e2 & op(e1, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7243) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7244) op(e1, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7244), (function-axioms) are
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7245) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7245) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7246) op(e0, e1) = e2
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7195), (7196), (7199), (7246), (function-axioms)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #381.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7247) all_54_7 = e1 | all_54_7 = e0
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (260), (6970), (7226), (7247) are inconsistent by
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #101.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7248) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7248) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7249) ~ (all_10_1 = e3)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7250) op(e0, e1) = all_10_1
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7003), (7196), (7249), (7250), (function-axioms)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #372.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | (7251) all_57_1 = e3 & op(e3, e2) = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7251) implies:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | (7252) op(e3, e2) = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (5894), (7252), (function-axioms) are
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | (7253) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (6994), (6995), (7253),
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | | #1104.
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | (7254) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.83/20.13 | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | | REF_CLOSE: (279), (6980), (6982), (6990), (7254) are
% 139.83/20.13 | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.83/20.13 | | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | | End of split
% 139.83/20.13 | | | | | | | | | | | | | |
% 139.83/20.13 | | | | | | | | | | | | | Case 2:
% 139.83/20.13 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | (7255) all_36_2 = e2
% 139.83/20.14 | | | | | | | | | | | | | | (7256) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 139.83/20.14 | | | | | | | | | | | | | | & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 139.83/20.14 | | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2)
% 139.83/20.14 | | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | COMBINE_EQS: (305), (7255) imply:
% 139.83/20.14 | | | | | | | | | | | | | | (7257) all_14_2 = e2
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | SIMP: (7257) implies:
% 139.83/20.14 | | | | | | | | | | | | | | (7258) all_14_2 = e2
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | COMBINE_EQS: (281), (7258) imply:
% 139.83/20.14 | | | | | | | | | | | | | | (7259) all_44_2 = e2
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | REDUCE: (337), (7258) imply:
% 139.83/20.14 | | | | | | | | | | | | | | (7260) ~ (all_52_1 = e2)
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | REDUCE: (339), (7258) imply:
% 139.83/20.14 | | | | | | | | | | | | | | (7261) ~ (all_52_2 = e2)
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | REDUCE: (341), (7258) imply:
% 139.83/20.14 | | | | | | | | | | | | | | (7262) ~ (all_52_3 = e2)
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | REDUCE: (51), (7258) imply:
% 139.83/20.14 | | | | | | | | | | | | | | (7263) op(e3, e3) = e2
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | BETA: splitting (97) gives:
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | (7264) ~ (all_44_2 = e2)
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | REDUCE: (7259), (7264) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | (7265) $false
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | CLOSE: (7265) is inconsistent.
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | (7266) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0
% 139.83/20.14 | | | | | | | | | | | | | | | & op(e3, e2) = all_44_1 & $i(all_44_0) &
% 139.83/20.14 | | | | | | | | | | | | | | | $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3, e2)
% 139.83/20.14 | | | | | | | | | | | | | | | = all_44_1 & $i(all_44_1))
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | (7267) ~ (all_48_2 = e0)
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | REDUCE: (299), (7267) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | (7268) ~ (all_4_2 = e0)
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7269) all_54_10 = e3
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (5905), (7269) are inconsistent by
% 139.83/20.14 | | | | | | | | | | | | | | | | | sub-proof #1112.
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7270) ~ (all_54_10 = e3)
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7271) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | BETA: splitting (7271) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7272) all_54_10 = e2
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (7272) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | | | | #1111.
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7273) ~ (all_54_10 = e2)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7274) all_54_10 = e1 | all_54_10 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | BETA: splitting (7274) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7275) all_54_10 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (7275) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7276) all_4_2 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | SIMP: (7276) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7277) all_4_2 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7277) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7278) ~ (all_52_2 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (360), (7277) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7279) ~ (all_52_6 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (5905), (7277) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7280) ~ (e3 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (372), (7277) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7281) ~ (e2 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (229) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | (7282) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7282) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | (7283) all_57_1 = e1 & op(e3, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7283) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | (7284) op(e3, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7285) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7285) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7286) all_57_0 = e1 & op(e3, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7286) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7287) op(e3, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7263), (7287), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7288) all_57_2 = e1 & op(e2, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (135), (136), (140), (143), (144), (148),
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (149), (162), (163), (167), (170), (191), (192),
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (195), (196), (248), (249), (258), (259), (5891),
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (5896), (6985), (7256), (7261), (7262), (7266),
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7284), (7288), (function-axioms) are inconsistent
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #169.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7289) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7289) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7290) all_57_6 = e1 & op(e1, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7290) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7291) op(e1, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7278), (7291), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | (7292) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (6966), (7292), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #350.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | (7293) all_57_3 = e1 & op(e2, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (7293) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | #163.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | (7294) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (162), (6967), (7279), (7294),
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | #165.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7295) all_54_10 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (7268), (7295) are inconsistent by
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | sub-proof #899.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | (7296) all_48_2 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | COMBINE_EQS: (299), (7296) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | (7297) all_4_2 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | REDUCE: (365), (7297) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | (7298) ~ (all_52_11 = e0)
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | REDUCE: (36), (7297) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | (7299) op(e1, e1) = e0
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7300) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.14 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (7260), (7263),
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7300), (function-axioms) are inconsistent by
% 139.83/20.14 | | | | | | | | | | | | | | | | | sub-proof #177.
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7301) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | BETA: splitting (7301) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7302) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | ALPHA: (7302) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7303) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7304) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (6979), (7298), (7303), (7304),
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | | | | #99.
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7305) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | ALPHA: (7305) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7306) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 139.83/20.14 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6971), (7299), (7306), (function-axioms)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #98.
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | (7307) all_22_2 = e1
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | COMBINE_EQS: (321), (7307) imply:
% 139.83/20.14 | | | | | | | | | | | (7308) all_14_2 = e1
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | SIMP: (7308) implies:
% 139.83/20.14 | | | | | | | | | | | (7309) all_14_2 = e1
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | REDUCE: (337), (7309) imply:
% 139.83/20.14 | | | | | | | | | | | (7310) ~ (all_52_1 = e1)
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | REDUCE: (343), (7309) imply:
% 139.83/20.14 | | | | | | | | | | | (7311) ~ (all_52_4 = e1)
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | REDUCE: (51), (7309) imply:
% 139.83/20.14 | | | | | | | | | | | (7312) op(e3, e3) = e1
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | BETA: splitting (229) gives:
% 139.83/20.14 | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | (7313) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 139.83/20.14 | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | BETA: splitting (7313) gives:
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | (7314) all_57_1 = e1 & op(e3, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | REF_CLOSE: (170), (7311), (7314), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | inconsistent by sub-proof #844.
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | (7315) all_57_3 = e1 & op(e2, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (7315) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | #163.
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | (7316) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 139.83/20.14 | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | BETA: splitting (7316) gives:
% 139.83/20.14 | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | (7317) all_57_7 = e1 & op(e1, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | ALPHA: (7317) implies:
% 139.83/20.14 | | | | | | | | | | | | | (7318) op(e1, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.14 | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | (7319) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.14 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.14 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.14 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.14 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.14 | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.14 | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.14 | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.14 | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.14 | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | BETA: splitting (7319) gives:
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | (7320) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.14 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.14 | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.14 | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.14 | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7312), (7320), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | (7321) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.14 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.14 | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.14 | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.14 | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (36), (5905), (7321), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | inconsistent by sub-proof #1126.
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | (7322) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.14 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.14 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.14 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.14 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.14 | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.14 | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.14 | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.14 | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.14 | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.14 | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.14 | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.14 | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.14 | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.14 | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.14 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.14 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.14 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.14 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | BETA: splitting (7322) gives:
% 139.83/20.14 | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | (7323) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.14 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.14 | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.14 | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.14 | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | REF_CLOSE: (8), (36), (372), (6979), (7323),
% 139.83/20.14 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | #462.
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | (7324) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.14 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.14 | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.14 | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.14 | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.14 | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.14 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.14 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.14 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.14 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.14 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.14 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.14 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.14 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.14 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | BETA: splitting (7324) gives:
% 139.83/20.14 | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | (7325) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.14 | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.83/20.14 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | ALPHA: (7325) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | (7326) op(e1, e1) = e2
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7326), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | (7327) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.14 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.83/20.14 | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.83/20.14 | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.14 | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.14 | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.14 | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.14 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.14 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.14 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.14 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.14 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.14 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | BETA: splitting (7327) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7328) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | ALPHA: (7328) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7329) op(e0, e0) = e2
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6979), (7329), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7330) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.14 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.83/20.14 | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.83/20.14 | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.83/20.14 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.14 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.83/20.14 | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.83/20.14 | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | ALPHA: (7330) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | (7331) op(e0, e0) = all_56_15
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7332) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | BETA: splitting (7332) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7333) all_57_2 = e1 & op(e2, e3) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7310), (7333), (function-axioms) are
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #846.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7334) all_57_3 = e1 & op(e2, e2) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (5902), (7334) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | #163.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | (7335) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 139.83/20.14 | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | BETA: splitting (7335) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7336) all_57_5 = e1 & op(e2, e1) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | ALPHA: (7336) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7337) op(e2, e1) = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (6979), (7331)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7338) all_56_15 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (7318) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7339) all_52_6 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e1,
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (7337) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7340) all_52_9 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (126), (7339) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7341) ~ (all_52_14 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (363), (7340) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7342) ~ (all_4_2 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | SIMP: (7342) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7343) ~ (all_4_2 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | REDUCE: (5897), (7340) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | (7344) ~ (e3 = e1)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | (7345) all_54_10 = e3
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (5905), (7345) are inconsistent by
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | sub-proof #1112.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | (7346) ~ (all_54_10 = e3)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | (7347) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7347) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | (7348) all_54_10 = e2
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (372), (7348) are inconsistent by sub-proof
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | #1111.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | (7349) ~ (all_54_10 = e2)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | (7350) all_54_10 = e1 | all_54_10 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7350) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7351) all_54_10 = e1
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (335), (7343), (7351) are inconsistent by
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | sub-proof #378.
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7352) all_54_10 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (335), (7352) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7353) all_4_2 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | SIMP: (7353) implies:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7354) all_4_2 = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (349), (7354) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7355) ~ (all_52_2 = e0)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (365), (7354) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7356) ~ (all_52_11 = e0)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5905), (7354) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7357) ~ (e3 = e0)
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (36), (7354) imply:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | (7358) op(e1, e1) = e0
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.14 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (7359) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7359) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7360) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7360) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7361) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7362) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7363) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7363) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | (7364) all_56_3 = e2 & op(e2, e3) = e2
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7364) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | (7365) op(e2, e3) = e2
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7361) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (7366) all_56_15 = e3 & op(e0, e0) = e3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7366) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (7367) op(e0, e0) = e3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (6979), (7367), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (7368) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7368) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (7369) ~ (all_56_10 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (7370) op(e0, e3) = all_56_10
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (148), (149), (159), (163), (167),
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (192), (196), (249), (259), (6966), (7355),
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (7358), (7362), (7365), (7369), (7370),
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | | #97.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | (7371) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5903), (7371), (function-axioms) are inconsistent
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #179.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7372) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7372) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7373) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7318), (7373), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #421.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (7374) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7374) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7375) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7375) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7376) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7338), (7356), (7376), (function-axioms)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #432.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7377) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7377) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | (7378) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (6971), (7358), (7378), (function-axioms)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #98.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7379) all_57_10 = e1 & op(e2, e0) = e1
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (6970), (7379), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | (7380) all_57_13 = e1 & op(e0, e2) = e1
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | REF_CLOSE: (158), (6967), (7380), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | (7381) all_14_2 = e0
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | REDUCE: (337), (7381) imply:
% 139.83/20.15 | | | | | | | | | | (7382) ~ (all_52_1 = e0)
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | REDUCE: (343), (7381) imply:
% 139.83/20.15 | | | | | | | | | | (7383) ~ (all_52_4 = e0)
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | REDUCE: (51), (7381) imply:
% 139.83/20.15 | | | | | | | | | | (7384) op(e3, e3) = e0
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.15 | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | (7385) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.15 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.15 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.15 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.15 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.15 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.15 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.15 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.15 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.15 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.15 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.15 | | | | | | | | | | | $i(all_56_6))
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | BETA: splitting (7385) gives:
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | (7386) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.15 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.15 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.15 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.15 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.15 | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | REF_CLOSE: (5), (7384), (7386), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | inconsistent by sub-proof #753.
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | (7387) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.15 | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.15 | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.15 | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.15 | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | BETA: splitting (7387) gives:
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | (7388) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.15 | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1 &
% 139.83/20.15 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1)
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | ALPHA: (7388) implies:
% 139.83/20.15 | | | | | | | | | | | | | (7389) op(e1, e1) = e3
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (207), (372),
% 139.83/20.15 | | | | | | | | | | | | | (6979), (7384), (7389), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | (7390) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 =
% 139.83/20.15 | | | | | | | | | | | | | e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 139.83/20.15 | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_6)
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | ALPHA: (7390) implies:
% 139.83/20.15 | | | | | | | | | | | | | (7391) op(e1, e1) = e3
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (207), (372),
% 139.83/20.15 | | | | | | | | | | | | | (6979), (7384), (7391), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | (7392) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.15 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.15 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.15 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.15 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.15 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.15 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.15 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.15 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.15 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.15 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.15 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.15 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.15 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.15 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.15 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.15 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.15 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.15 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.15 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.15 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | BETA: splitting (7392) gives:
% 139.83/20.15 | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | (7393) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.15 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.15 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.15 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.15 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | REF_CLOSE: (8), (36), (372), (6979), (7393),
% 139.83/20.15 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.15 | | | | | | | | | | | | #462.
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | (7394) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.15 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.15 | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.15 | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.15 | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.15 | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.15 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.15 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.15 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.15 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.15 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.15 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.15 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.15 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | BETA: splitting (7394) gives:
% 139.83/20.15 | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | (7395) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.15 | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.83/20.15 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | ALPHA: (7395) implies:
% 139.83/20.15 | | | | | | | | | | | | | (7396) op(e1, e1) = e2
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7396), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | (7397) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.15 | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.83/20.15 | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.83/20.15 | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.15 | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.15 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.15 | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.15 | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.15 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.15 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.15 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.15 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | BETA: splitting (7397) gives:
% 139.83/20.15 | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | (7398) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.15 | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.83/20.15 | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | ALPHA: (7398) implies:
% 139.83/20.15 | | | | | | | | | | | | | | (7399) op(e0, e0) = e2
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | REF_CLOSE: (6), (6979), (7399), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | (7400) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.15 | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.15 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.83/20.15 | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.83/20.15 | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.83/20.15 | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.15 | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.83/20.15 | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.15 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.83/20.15 | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.83/20.15 | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | ALPHA: (7400) implies:
% 139.83/20.15 | | | | | | | | | | | | | | (7401) op(e0, e0) = all_56_15
% 139.83/20.15 | | | | | | | | | | | | | | (7402) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.15 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.83/20.15 | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.83/20.15 | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.83/20.15 | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.15 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.83/20.15 | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.83/20.15 | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.15 | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.83/20.15 | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.83/20.15 | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (6979), (7401)
% 139.83/20.15 | | | | | | | | | | | | | | gives:
% 139.83/20.15 | | | | | | | | | | | | | | (7403) all_56_15 = e1
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | BETA: splitting (103) gives:
% 139.83/20.15 | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | (7404) ~ (all_48_2 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REDUCE: (299), (7404) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7405) ~ (all_4_2 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (36), (194), (335), (372), (5905),
% 139.83/20.15 | | | | | | | | | | | | | | | (7402), (7403), (7405), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | inconsistent by sub-proof #333.
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | (7406) all_48_2 = e0
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | COMBINE_EQS: (299), (7406) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7407) all_4_2 = e0
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REDUCE: (349), (7407) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7408) ~ (all_52_2 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REDUCE: (360), (7407) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7409) ~ (all_52_6 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REDUCE: (363), (7407) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7410) ~ (all_52_9 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REDUCE: (5905), (7407) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7411) ~ (e3 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | REDUCE: (36), (7407) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | (7412) op(e1, e1) = e0
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.83/20.15 | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | (7413) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | BETA: splitting (7413) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7414) all_57_1 = e0 & op(e3, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7383), (7414), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1102.
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7415) all_57_3 = e0 & op(e2, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | ALPHA: (7415) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7416) op(e2, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5903), (7416), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | End of split
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | (7417) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.83/20.15 | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | BETA: splitting (7417) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7418) all_57_7 = e0 & op(e1, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | ALPHA: (7418) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7419) op(e1, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7409), (7419), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7420) all_57_13 = e0 & op(e0, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | ALPHA: (7420) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | (7421) op(e0, e2) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | BETA: splitting (224) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | (7422) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (167), (5903), (7382), (7422),
% 139.83/20.15 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.15 | | | | | | | | | | | | | | | | | | #112.
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | (7423) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | BETA: splitting (7423) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7424) all_57_5 = e0 & op(e2, e1) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | ALPHA: (7424) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7425) op(e2, e1) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7410), (7425), (function-axioms) are
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7426) all_57_10 = e0 & op(e2, e0) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | ALPHA: (7426) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7427) op(e2, e0) = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_7, e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | e2, e0, simplifying with (158), (7421) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7428) all_52_7 = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | e0, e0, e2, simplifying with (164), (7427) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7429) all_52_13 = e0
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | REDUCE: (140), (7428) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7430) ~ (all_52_3 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | REDUCE: (125), (7428) imply:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7431) ~ (all_52_11 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | SIMP: (7431) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | (7432) ~ (all_52_11 = e0)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (7433) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7433) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (7434) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7434) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (7435) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (7436) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (7437) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | (7438) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7435) gives:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | (7439) all_56_15 = e3 & op(e0, e0) = e3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7439) implies:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | (7440) op(e0, e0) = e3
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (7430), (7437), (7440), (function-axioms)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | (7441) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.15 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7441) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7442) ~ (all_56_10 = e0)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7443) op(e0, e3) = all_56_10
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7438) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | (7444) all_56_3 = e2 & op(e2, e3) = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7444) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | (7445) op(e2, e3) = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (144), (148), (149), (159), (163), (167),
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | (192), (196), (249), (259), (6966), (7408),
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | (7412), (7436), (7442), (7443), (7445),
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | #97.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | (7446) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5903), (7446), (function-axioms) are inconsistent
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #179.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7447) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7447) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7448) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7448) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7449) all_56_15 = e2 & op(e0, e0) = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7449) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7450) op(e0, e0) = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (6979), (7450), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7451) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7451) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7452) ~ (all_56_12 = e0)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7453) op(e0, e2) = all_56_12
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7421), (7452), (7453), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (7454) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7454) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7455) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7455) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7456) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7403), (7432), (7456), (function-axioms)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #432.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7457) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (160), (5903), (6971), (7402), (7403),
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7457), (function-axioms) are inconsistent by
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | sub-proof #104.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | |
% 139.83/20.16 | | | | | | | | End of split
% 139.83/20.16 | | | | | | | |
% 139.83/20.16 | | | | | | | End of split
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | End of split
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | Case 2:
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | (7458) all_8_2 = e3
% 139.83/20.16 | | | | | | (7459) ( ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 & op(e1,
% 139.83/20.16 | | | | | | e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)) | ( ~
% 139.83/20.16 | | | | | | (all_8_1 = e2) & op(e1, e3) = all_8_1 & $i(all_8_1))
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | COMBINE_EQS: (330), (7458) imply:
% 139.83/20.16 | | | | | | (7460) all_4_2 = e3
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | SIMP: (7460) implies:
% 139.83/20.16 | | | | | | (7461) all_4_2 = e3
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | COMBINE_EQS: (317), (7461) imply:
% 139.83/20.16 | | | | | | (7462) all_12_2 = e3
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | REDUCE: (349), (7461) imply:
% 139.83/20.16 | | | | | | (7463) ~ (all_52_2 = e3)
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | REDUCE: (362), (7461) imply:
% 139.83/20.16 | | | | | | (7464) ~ (all_52_8 = e3)
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | REDUCE: (365), (7461) imply:
% 139.83/20.16 | | | | | | (7465) ~ (all_52_11 = e3)
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | REDUCE: (367), (7461) imply:
% 139.83/20.16 | | | | | | (7466) ~ (all_52_14 = e3)
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | REDUCE: (36), (7461) imply:
% 139.83/20.16 | | | | | | (7467) op(e1, e1) = e3
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | BETA: splitting (49) gives:
% 139.83/20.16 | | | | | |
% 139.83/20.16 | | | | | | Case 1:
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | | (7468) ~ (all_12_2 = e3)
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | | REDUCE: (7462), (7468) imply:
% 139.83/20.16 | | | | | | | (7469) $false
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | | CLOSE: (7469) is inconsistent.
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | Case 2:
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | | (7470) ( ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 &
% 139.83/20.16 | | | | | | | op(e1, e3) = all_12_1 & $i(all_12_0) & $i(all_12_1)) |
% 139.83/20.16 | | | | | | | ( ~ (all_12_1 = e0) & op(e1, e3) = all_12_1 &
% 139.83/20.16 | | | | | | | $i(all_12_1))
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | | BETA: splitting (46) gives:
% 139.83/20.16 | | | | | | |
% 139.83/20.16 | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | |
% 139.83/20.16 | | | | | | | | (7471) ~ (all_10_2 = e1)
% 139.83/20.16 | | | | | | | |
% 139.83/20.16 | | | | | | | | BETA: splitting (52) gives:
% 139.83/20.16 | | | | | | | |
% 139.83/20.16 | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | |
% 139.83/20.16 | | | | | | | | | (7472) ~ (all_14_2 = e0)
% 139.83/20.16 | | | | | | | | |
% 139.83/20.16 | | | | | | | | | BETA: splitting (64) gives:
% 139.83/20.16 | | | | | | | | |
% 139.83/20.16 | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | (7473) ~ (all_22_2 = e1)
% 139.83/20.16 | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | REDUCE: (321), (7473) imply:
% 139.83/20.16 | | | | | | | | | | (7474) ~ (all_14_2 = e1)
% 139.83/20.16 | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | BETA: splitting (67) gives:
% 139.83/20.16 | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | (7475) ~ (all_24_2 = e2)
% 139.83/20.16 | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | REDUCE: (319), (7475) imply:
% 139.83/20.16 | | | | | | | | | | | (7476) ~ (all_10_2 = e2)
% 139.83/20.16 | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | BETA: splitting (85) gives:
% 139.83/20.16 | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | (7477) ~ (all_36_2 = e2)
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | REDUCE: (305), (7477) imply:
% 139.83/20.16 | | | | | | | | | | | | (7478) ~ (all_14_2 = e2)
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | (7479) all_54_0 = e3
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | COMBINE_EQS: (279), (7479) imply:
% 139.83/20.16 | | | | | | | | | | | | | (7480) all_14_2 = e3
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | SIMP: (7480) implies:
% 139.83/20.16 | | | | | | | | | | | | | (7481) all_14_2 = e3
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | REDUCE: (51), (7481) imply:
% 139.83/20.16 | | | | | | | | | | | | | (7482) op(e3, e3) = e3
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | (7483) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.16 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.16 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.16 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.16 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.16 | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.16 | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.16 | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.16 | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.16 | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | BETA: splitting (7483) gives:
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | (7484) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.16 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.16 | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.16 | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.16 | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | REF_CLOSE: (9), (7482), (7484), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | (7485) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.16 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.16 | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.16 | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.16 | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | BETA: splitting (7485) gives:
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | (7486) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.16 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1 &
% 139.83/20.16 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_1)
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | ALPHA: (7486) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7487) op(e3, e3) = e1
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7482), (7487), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | (7488) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 =
% 139.83/20.16 | | | | | | | | | | | | | | | | e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 139.83/20.16 | | | | | | | | | | | | | | | | op(e1, e1) = e3 & $i(all_56_6)
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | ALPHA: (7488) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7489) op(e3, e3) = e1
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7482), (7489), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | (7490) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.16 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.16 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.16 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.16 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.16 | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.16 | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.16 | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.16 | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.16 | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.16 | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.16 | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.16 | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.16 | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.16 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.16 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.16 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.16 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | REF_CLOSE: (36), (45), (51), (372), (7471), (7472), (7476),
% 139.83/20.16 | | | | | | | | | | | | | | (7490), (function-axioms) are inconsistent by
% 139.83/20.16 | | | | | | | | | | | | | | sub-proof #181.
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | (7491) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | REF_CLOSE: (279), (7472), (7474), (7478), (7491) are
% 139.83/20.16 | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | (7492) all_36_2 = e2
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | COMBINE_EQS: (305), (7492) imply:
% 139.83/20.16 | | | | | | | | | | | | (7493) all_14_2 = e2
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | SIMP: (7493) implies:
% 139.83/20.16 | | | | | | | | | | | | (7494) all_14_2 = e2
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | REDUCE: (337), (7494) imply:
% 139.83/20.16 | | | | | | | | | | | | (7495) ~ (all_52_1 = e2)
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | REDUCE: (347), (7494) imply:
% 139.83/20.16 | | | | | | | | | | | | (7496) ~ (all_52_12 = e2)
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | REDUCE: (51), (7494) imply:
% 139.83/20.16 | | | | | | | | | | | | (7497) op(e3, e3) = e2
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | BETA: splitting (238) gives:
% 139.83/20.16 | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | (7498) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.83/20.16 | | | | | | | | | | | | | & op(e2, e3) = e3)
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | REF_CLOSE: (9), (167), (5893), (7497), (7498),
% 139.83/20.16 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.16 | | | | | | | | | | | | | #96.
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | (7499) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.83/20.16 | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | BETA: splitting (7499) gives:
% 139.83/20.16 | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | (7500) all_57_6 = e3 & op(e1, e3) = e3
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | REF_CLOSE: (163), (7463), (7500), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | inconsistent by sub-proof #95.
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | (7501) all_57_12 = e3 & op(e0, e3) = e3
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | ALPHA: (7501) implies:
% 139.83/20.16 | | | | | | | | | | | | | | (7502) all_57_12 = e3
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.83/20.16 | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | (7503) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (5894), (7497), (7503),
% 139.83/20.16 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.16 | | | | | | | | | | | | | | | #180.
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | (7504) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | BETA: splitting (7504) gives:
% 139.83/20.16 | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | (7505) all_57_4 = e3 & op(e3, e1) = e3
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | ALPHA: (7505) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7506) op(e3, e1) = e3
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7464), (7506), (function-axioms) are
% 139.83/20.16 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | (7507) all_57_9 = e3 & op(e3, e0) = e3
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | ALPHA: (7507) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7508) all_57_9 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | | (7509) op(e3, e0) = e3
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.83/20.16 | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (7509) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7510) all_52_12 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | REDUCE: (369), (7510) imply:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7511) ~ (all_10_2 = e3)
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | SIMP: (7511) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | (7512) ~ (all_10_2 = e3)
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | (7513) all_54_15 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7512), (7513) are inconsistent by
% 139.83/20.16 | | | | | | | | | | | | | | | | | sub-proof #755.
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | (7514) ~ (all_54_15 = e3)
% 139.83/20.16 | | | | | | | | | | | | | | | | | (7515) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (7516) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.16 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (7495), (7497),
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (7516), (function-axioms) are inconsistent by
% 139.83/20.16 | | | | | | | | | | | | | | | | | | sub-proof #177.
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (7517) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | BETA: splitting (7517) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7518) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | ALPHA: (7518) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7519) op(e1, e1) = all_56_13
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7520) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7521) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7522) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7523) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7524) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | (7525) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | BETA: splitting (7522) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (7526) all_56_11 = e1 & op(e2, e2) = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | ALPHA: (7526) implies:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (7527) all_56_11 = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | (7528) op(e2, e2) = e1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7529) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7529) gives:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7530) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7527), (7530) are inconsistent by sub-proof
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | #119.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | (7531) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7464), (7525), (7531), (function-axioms)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #94.
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (7532) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.16 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7532) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (7533) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7533) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7534) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7534) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7535) op(e0, e0) = e3
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (246), (7471), (7476), (7512), (7515),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7535), (function-axioms) are inconsistent by
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #202.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7536) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7536) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7537) ~ (all_56_4 = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7524), (7527), (7537) are inconsistent by
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (7538) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7538) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7539) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7539) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7540) op(e1, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7540), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7541) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7541) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7542) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7542) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7543) op(e0, e0) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (169), (207),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (212), (222), (233), (235), (239),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (372), (5903), (7464), (7497), (7522), (7524),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7525), (7543), (function-axioms) are inconsistent
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #92.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7544) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7544) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7545) op(e0, e0) = all_56_15
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7546) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (246), (7467), (7471), (7476),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7512), (7515), (7528), (7545), (7546),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | #200.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | (7547) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | $i(all_56_4)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | ALPHA: (7547) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | (7548) ~ (all_56_4 = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | (7549) op(e2, e1) = all_56_4
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7520) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | (7550) all_56_15 = e1 & op(e0, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7550) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | (7551) op(e0, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7471), (7551), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | (7552) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7552) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | (7553) ~ (all_56_14 = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | (7554) op(e0, e1) = all_56_14
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7515) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (7555) all_54_15 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7476), (7555) are inconsistent by
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (7556) ~ (all_54_15 = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | (7557) all_54_15 = e1 | all_54_15 = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7557) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7558) all_54_15 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7471), (7558) are inconsistent by
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7559) all_54_15 = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (7559) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7560) all_10_2 = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7560) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7561) all_10_2 = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (7561) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7562) ~ (all_52_7 = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7512), (7561) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7563) ~ (e3 = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7476), (7561) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7564) ~ (e2 = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (7561) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | (7565) op(e0, e0) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7523) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7566) all_56_9 = e1 & op(e3, e3) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7566) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7567) all_56_9 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7464), (7525), (7567), (function-axioms)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #898.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7568) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7568) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7569) ~ (all_56_1 = e3)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | (7570) op(e3, e1) = all_56_1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7524) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | (7571) all_56_4 = e2 & op(e2, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7571) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | (7572) op(e2, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7548), (7549), (7572), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | (7573) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7573) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | (7574) ~ (all_56_11 = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | (7575) op(e2, e2) = all_56_11
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7525) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (7576) all_56_1 = e3 & op(e3, e1) = e3
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7576) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (7577) op(e3, e1) = e3
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7569), (7570), (7577), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #734.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (7578) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7578) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (7579) ~ (all_56_9 = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | (7580) op(e3, e3) = all_56_9
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7521) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7581) all_56_14 = e0 & op(e0, e1) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7581) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7582) op(e0, e1) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7553), (7554), (7582), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7583) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7583) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7584) ~ (all_56_15 = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7585) op(e0, e0) = all_56_15
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (7565), (7585)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7586) all_56_15 = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14, e1, e0, simplifying with (157), (7554)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7587) all_56_14 = all_52_11
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (7467), (7519)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7588) all_56_13 = e3
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e1, e2, simplifying with (165), (7549)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7589) all_56_4 = all_52_9
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (5903), (7575)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7590) all_56_11 = e3
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, e1, e3, simplifying with (169), (7570)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7591) all_56_1 = all_52_8
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (7497), (7580) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7592) all_56_9 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7548), (7589) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7593) ~ (all_52_9 = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7553), (7587) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7594) ~ (all_52_11 = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7584), (7586) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7595) ~ (e1 = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7596) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (233), (235),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (239), (7497), (7593), (7596), (function-axioms)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #406.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7597) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7597) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7598) all_57_8 = e2 & op(e1, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7598) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7599) op(e1, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7599), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7600) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7600) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7601) all_57_14 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7602) op(e0, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7603) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7603) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7604) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7604) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7605) all_57_12 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7502), (7605) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7606) e3 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7606) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7607) e3 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7590), (7607) imply:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7608) all_56_11 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7524), (7593), (7608), (function-axioms)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #91.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7609) all_57_13 = e1 & op(e0, e2) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7609) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7610) all_57_13 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7611) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (5903), (7495), (7611),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #154.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7612) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7612) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7613) all_57_5 = e2 & op(e2, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7613) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7614) op(e2, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7593), (7614), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7615) all_57_10 = e2 & op(e2, e0) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7615) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7616) all_57_10 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7617) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7617) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7618) all_57_1 = e2 & op(e3, e2) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7618) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7619) all_57_1 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7620) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7464), (7508), (7524), (7525),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7590), (7592), (7593), (7616), (7620),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7621) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7621) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7622) all_57_11 = e1 & op(e1, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7622) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7623) op(e1, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (218) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7624) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7624) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7625) all_57_6 = e2 & op(e1, e3) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7625) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7626) all_57_6 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7497), (7502), (7626), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #128.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7627) all_57_7 = e2 & op(e1, e2) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7627) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7628) all_57_7 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (228), (229), (5902),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (5903), (7619), (7628), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #122.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7629) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7629) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7630) all_57_8 = e2 & op(e1, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7630) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7631) op(e1, e1) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7631), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7632) all_57_11 = e2 & op(e1, e0) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7632) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7633) op(e1, e0) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7623), (7633), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #139.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7634) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7634) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7635) all_57_15 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7636) op(e0, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (211),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (7562), (7610), (7635), (7636),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7637) all_57_3 = e2 & op(e2, e2) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7637) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7638) op(e2, e2) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (5903), (7638), (function-axioms) are
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7639) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7639) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7640) all_57_7 = e2 & op(e1, e2) = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7640) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7641) all_57_7 = e2
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7642) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7464), (7508), (7524), (7525),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7590), (7592), (7593), (7616), (7642),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #89.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7643) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7643) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7644) all_57_11 = e1 & op(e1, e0) = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7644) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7645) all_57_11 = e1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7646) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7646) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7647) all_57_6 = e0 & op(e1, e3) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7647) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7648) op(e1, e3) = e0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7470) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7649) ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_12_1 & $i(all_12_0) &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7649) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7650) ~ (all_12_0 = e2)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7651) op(e1, e3) = all_12_1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7652) op(all_12_1, e1) = all_12_0
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7459) gives:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7653) ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7653) implies:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7654) op(e1, e3) = all_8_1
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7602), (7648), (7650), (7651), (7652), (7654),
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #88.
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7655) ~ (all_8_1 = e2) & op(e1, e3) = all_8_1 &
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.17 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7655) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7656) op(e1, e3) = all_8_1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7602), (7648), (7650), (7651), (7652), (7656),
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #88.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7657) ~ (all_12_1 = e0) & op(e1, e3) = all_12_1 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7657) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7658) ~ (all_12_1 = e0)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7659) op(e1, e3) = all_12_1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7459) gives:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7660) ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7660) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7661) op(e1, e3) = all_8_1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7648), (7658), (7659), (7661), (function-axioms)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #87.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7662) ~ (all_8_1 = e2) & op(e1, e3) = all_8_1 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7662) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7663) op(e1, e3) = all_8_1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7648), (7658), (7659), (7663), (function-axioms)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #87.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7664) all_57_7 = e0 & op(e1, e2) = e0
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7664) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7665) all_57_7 = e0
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7641), (7665) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #578.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7666) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (7467), (7645), (7666),
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #246.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7667) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7667) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7668) all_57_15 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7669) op(e0, e0) = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (211),
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (212), (7562), (7610), (7668), (7669),
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #355.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7670) all_57_13 = e2 & op(e0, e2) = e2
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7670) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7671) all_57_13 = e2
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7610), (7671) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7672) e2 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7592), (7672) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7673) all_56_9 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7464), (7525), (7673), (function-axioms)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #898.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7674) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7674) gives:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7675) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7675) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7676) all_57_14 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7601), (7676) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7677) e2 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (7677) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7678) e2 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7592), (7678) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7679) all_56_9 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7464), (7525), (7679), (function-axioms)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #898.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7680) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7680) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7681) op(e0, e0) = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (7520), (7521), (7585), (7594), (7681),
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #100.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | (7682) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.18 | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7497), (7509), (7682), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 139.83/20.18 | | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7683) all_24_2 = e2
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | COMBINE_EQS: (319), (7683) imply:
% 139.83/20.18 | | | | | | | | | | | (7684) all_10_2 = e2
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | REDUCE: (45), (7684) imply:
% 139.83/20.18 | | | | | | | | | | | (7685) op(e0, e0) = e2
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | BETA: splitting (215) gives:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7686) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.83/20.18 | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | BETA: splitting (7686) gives:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | (7687) all_57_9 = e3 & op(e3, e0) = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | ALPHA: (7687) implies:
% 139.83/20.18 | | | | | | | | | | | | | (7688) op(e3, e0) = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.83/20.18 | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (7688) gives:
% 139.83/20.18 | | | | | | | | | | | | | (7689) all_52_12 = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | REDUCE: (347), (7689) imply:
% 139.83/20.18 | | | | | | | | | | | | | (7690) ~ (all_14_2 = e3)
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | SIMP: (7690) implies:
% 139.83/20.18 | | | | | | | | | | | | | (7691) ~ (all_14_2 = e3)
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | (7692) all_54_0 = e3
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | COMBINE_EQS: (279), (7692) imply:
% 139.83/20.18 | | | | | | | | | | | | | | (7693) all_14_2 = e3
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | REDUCE: (7691), (7693) imply:
% 139.83/20.18 | | | | | | | | | | | | | | (7694) $false
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | CLOSE: (7694) is inconsistent.
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | (7695) ~ (all_54_0 = e3)
% 139.83/20.18 | | | | | | | | | | | | | | (7696) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | BETA: splitting (7696) gives:
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | (7697) all_54_0 = e2
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7697) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | (7698) all_14_2 = e2
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | REDUCE: (337), (7698) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | (7699) ~ (all_52_1 = e2)
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | REDUCE: (7691), (7698) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | (7700) ~ (e3 = e2)
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | REDUCE: (51), (7698) imply:
% 139.83/20.18 | | | | | | | | | | | | | | | (7701) op(e3, e3) = e2
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | (7702) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.18 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.18 | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.18 | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (7699), (7701),
% 139.83/20.18 | | | | | | | | | | | | | | | | (7702), (function-axioms) are inconsistent by
% 139.83/20.18 | | | | | | | | | | | | | | | | sub-proof #177.
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | (7703) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.18 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.18 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.18 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.18 | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | BETA: splitting (7703) gives:
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | (7704) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.18 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.18 | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.18 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | ALPHA: (7704) implies:
% 139.83/20.18 | | | | | | | | | | | | | | | | | (7705) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.18 | | | | | | | | | | | | | | | | | (7706) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.18 | | | | | | | | | | | | | | | | | (7707) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (169), (207),
% 139.83/20.18 | | | | | | | | | | | | | | | | | (209), (210), (212), (222), (233), (235), (239),
% 139.83/20.18 | | | | | | | | | | | | | | | | | (372), (5903), (7464), (7685), (7701), (7705),
% 139.83/20.18 | | | | | | | | | | | | | | | | | (7706), (7707), (function-axioms) are inconsistent
% 139.83/20.18 | | | | | | | | | | | | | | | | | by sub-proof #92.
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | (7708) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.18 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.18 | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.18 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.18 | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.18 | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.18 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7688), (7701), (7708), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 139.83/20.18 | | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | (7709) all_54_0 = e1 | all_54_0 = e0
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | | REF_CLOSE: (279), (7472), (7474), (7709) are inconsistent by
% 139.83/20.18 | | | | | | | | | | | | | | | sub-proof #884.
% 139.83/20.18 | | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | (7710) all_57_10 = e3 & op(e2, e0) = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | ALPHA: (7710) implies:
% 139.83/20.18 | | | | | | | | | | | | | (7711) op(e2, e0) = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.83/20.18 | | | | | | | | | | | | | e3, e0, e2, simplifying with (164), (7711) gives:
% 139.83/20.18 | | | | | | | | | | | | | (7712) all_52_13 = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | REDUCE: (5898), (7712) imply:
% 139.83/20.18 | | | | | | | | | | | | | (7713) $false
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | CLOSE: (7713) is inconsistent.
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7714) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.83/20.18 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | REF_CLOSE: (9), (160), (7466), (7685), (7714),
% 139.83/20.18 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | #86.
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | (7715) all_22_2 = e1
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | COMBINE_EQS: (321), (7715) imply:
% 139.83/20.18 | | | | | | | | | | (7716) all_14_2 = e1
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | REDUCE: (339), (7716) imply:
% 139.83/20.18 | | | | | | | | | | (7717) ~ (all_52_2 = e1)
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | REDUCE: (343), (7716) imply:
% 139.83/20.18 | | | | | | | | | | (7718) ~ (all_52_4 = e1)
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | REDUCE: (345), (7716) imply:
% 139.83/20.18 | | | | | | | | | | (7719) ~ (all_52_8 = e1)
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | REDUCE: (347), (7716) imply:
% 139.83/20.18 | | | | | | | | | | (7720) ~ (all_52_12 = e1)
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | REDUCE: (51), (7716) imply:
% 139.83/20.18 | | | | | | | | | | (7721) op(e3, e3) = e1
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | BETA: splitting (238) gives:
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7722) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.83/20.18 | | | | | | | | | | | & op(e2, e3) = e3)
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | BETA: splitting (7722) gives:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7723) all_57_0 = e3 & op(e3, e3) = e3
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | ALPHA: (7723) implies:
% 139.83/20.18 | | | | | | | | | | | | (7724) op(e3, e3) = e3
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | REF_CLOSE: (8), (7721), (7724), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7725) all_57_2 = e3 & op(e2, e3) = e3
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | REF_CLOSE: (167), (5893), (7725), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | inconsistent by sub-proof #183.
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7726) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.83/20.18 | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | BETA: splitting (7726) gives:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7727) all_57_6 = e3 & op(e1, e3) = e3
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | REF_CLOSE: (163), (7463), (7727), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | inconsistent by sub-proof #95.
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7728) all_57_12 = e3 & op(e0, e3) = e3
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | ALPHA: (7728) implies:
% 139.83/20.18 | | | | | | | | | | | | (7729) all_57_12 = e3
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (45), (70), (112),
% 139.83/20.18 | | | | | | | | | | | | (120), (125), (133), (157), (158), (160), (162),
% 139.83/20.18 | | | | | | | | | | | | (163), (165), (168), (169), (170), (206), (209),
% 139.83/20.18 | | | | | | | | | | | | (210), (211), (212), (214), (217), (221), (224),
% 139.83/20.18 | | | | | | | | | | | | (229), (239), (372), (5891), (5892), (5894),
% 139.83/20.18 | | | | | | | | | | | | (5897), (5902), (5903), (7464), (7467), (7717),
% 139.83/20.18 | | | | | | | | | | | | (7718), (7719), (7720), (7721), (7729),
% 139.83/20.18 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | #84.
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | (7730) all_14_2 = e0
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | REDUCE: (337), (7730) imply:
% 139.83/20.18 | | | | | | | | | (7731) ~ (all_52_1 = e0)
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | REDUCE: (339), (7730) imply:
% 139.83/20.18 | | | | | | | | | (7732) ~ (all_52_2 = e0)
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | REDUCE: (341), (7730) imply:
% 139.83/20.18 | | | | | | | | | (7733) ~ (all_52_3 = e0)
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | REDUCE: (347), (7730) imply:
% 139.83/20.18 | | | | | | | | | (7734) ~ (all_52_12 = e0)
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | BETA: splitting (239) gives:
% 139.83/20.18 | | | | | | | | |
% 139.83/20.18 | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | (7735) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.83/20.18 | | | | | | | | | | & op(e3, e2) = e3)
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | BETA: splitting (7735) gives:
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7736) all_57_0 = e3 & op(e3, e3) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | ALPHA: (7736) implies:
% 139.83/20.18 | | | | | | | | | | | (7737) all_57_0 = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | BETA: splitting (232) gives:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7738) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 139.83/20.18 | | | | | | | | | | | | & op(e2, e3) = e0)
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | BETA: splitting (7738) gives:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | (7739) all_57_0 = e0 & op(e3, e3) = e0
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | ALPHA: (7739) implies:
% 139.83/20.18 | | | | | | | | | | | | | (7740) all_57_0 = e0
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | COMBINE_EQS: (7737), (7740) imply:
% 139.83/20.18 | | | | | | | | | | | | | (7741) e3 = e0
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | REDUCE: (7), (7741) imply:
% 139.83/20.18 | | | | | | | | | | | | | (7742) $false
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | CLOSE: (7742) is inconsistent.
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | (7743) all_57_2 = e0 & op(e2, e3) = e0
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | REF_CLOSE: (167), (7731), (7743), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | | inconsistent by sub-proof #1028.
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7744) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 139.83/20.18 | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | REF_CLOSE: (159), (163), (7732), (7733), (7744),
% 139.83/20.18 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.18 | | | | | | | | | | | | #196.
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7745) all_57_1 = e3 & op(e3, e2) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | ALPHA: (7745) implies:
% 139.83/20.18 | | | | | | | | | | | (7746) op(e3, e2) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | REF_CLOSE: (170), (5894), (7746), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | inconsistent by sub-proof #1107.
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | End of split
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | (7747) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.83/20.18 | | | | | | | | | | & op(e3, e0) = e3)
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | BETA: splitting (7747) gives:
% 139.83/20.18 | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7748) all_57_4 = e3 & op(e3, e1) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | ALPHA: (7748) implies:
% 139.83/20.18 | | | | | | | | | | | (7749) op(e3, e1) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | REF_CLOSE: (169), (7464), (7749), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | inconsistent by sub-proof #1106.
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | (7750) all_57_9 = e3 & op(e3, e0) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | ALPHA: (7750) implies:
% 139.83/20.18 | | | | | | | | | | | (7751) op(e3, e0) = e3
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | BETA: splitting (232) gives:
% 139.83/20.18 | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | (7752) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 139.83/20.18 | | | | | | | | | | | | & op(e2, e3) = e0)
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | BETA: splitting (7752) gives:
% 139.83/20.18 | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | (7753) all_57_0 = e0 & op(e3, e3) = e0
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | ALPHA: (7753) implies:
% 139.83/20.18 | | | | | | | | | | | | | (7754) op(e3, e3) = e0
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.83/20.18 | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (7751) gives:
% 139.83/20.18 | | | | | | | | | | | | | (7755) all_52_12 = e3
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | REDUCE: (369), (7755) imply:
% 139.83/20.18 | | | | | | | | | | | | | (7756) ~ (all_10_2 = e3)
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | SIMP: (7756) implies:
% 139.83/20.18 | | | | | | | | | | | | | (7757) ~ (all_10_2 = e3)
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.18 | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | Case 1:
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | (7758) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.18 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.18 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.18 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.18 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.18 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.18 | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.18 | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.18 | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.18 | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.18 | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.18 | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7754), (7758), (function-axioms) are
% 139.83/20.18 | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.18 | | | | | | | | | | | | | Case 2:
% 139.83/20.18 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | (7759) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.19 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.19 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.19 | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.19 | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.19 | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.19 | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.19 | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.19 | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.19 | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.19 | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.19 | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | BETA: splitting (7759) gives:
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | (7760) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.19 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.19 | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | BETA: splitting (7760) gives:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | (7761) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.19 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.83/20.19 | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | ALPHA: (7761) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7762) op(e0, e0) = e3
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7757), (7762), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #83.
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | (7763) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.83/20.19 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.83/20.19 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | ALPHA: (7763) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7764) op(e1, e1) = e2
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7764), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | (7765) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.19 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.19 | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.19 | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.19 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.19 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.19 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.19 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | BETA: splitting (7765) gives:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | (7766) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.19 | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.83/20.19 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | ALPHA: (7766) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7767) op(e1, e1) = e2
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7767), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | (7768) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.19 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.83/20.19 | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.83/20.19 | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.19 | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.19 | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.19 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.19 | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | BETA: splitting (7768) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7769) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | ALPHA: (7769) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7770) op(e2, e2) = e0
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5903), (7770), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7771) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.83/20.19 | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | ALPHA: (7771) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7772) op(e0, e0) = all_56_15
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7773) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.83/20.19 | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.83/20.19 | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | BETA: splitting (7773) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7774) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 139.83/20.19 | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | BETA: splitting (7774) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7775) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | ALPHA: (7775) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7776) all_56_15 = e3
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | REDUCE: (7772), (7776) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7777) op(e0, e0) = e3
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7757), (7777), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #83.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7778) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | ALPHA: (7778) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7779) op(e2, e2) = e0
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (5903), (7779), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7780) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 139.83/20.19 | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (7467), (7780), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #279.
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | (7781) all_57_2 = e0 & op(e2, e3) = e0
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | REF_CLOSE: (167), (7731), (7781), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | inconsistent by sub-proof #1028.
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | (7782) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 139.83/20.19 | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | REF_CLOSE: (159), (163), (7732), (7733), (7782),
% 139.83/20.19 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.19 | | | | | | | | | | | | #196.
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | |
% 139.83/20.19 | | | | | | | | End of split
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | | (7783) all_10_2 = e1
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | | REDUCE: (368), (7783) imply:
% 139.83/20.19 | | | | | | | | (7784) ~ (all_52_11 = e1)
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | | REDUCE: (369), (7783) imply:
% 139.83/20.19 | | | | | | | | (7785) ~ (all_52_12 = e1)
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | | REDUCE: (45), (7783) imply:
% 139.83/20.19 | | | | | | | | (7786) op(e0, e0) = e1
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | | BETA: splitting (212) gives:
% 139.83/20.19 | | | | | | | |
% 139.83/20.19 | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | |
% 139.83/20.19 | | | | | | | | | (7787) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3
% 139.83/20.19 | | | | | | | | | & op(e0, e2) = e3)
% 139.83/20.19 | | | | | | | | |
% 139.83/20.19 | | | | | | | | | BETA: splitting (7787) gives:
% 139.83/20.19 | | | | | | | | |
% 139.83/20.19 | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | (7788) all_57_12 = e3 & op(e0, e3) = e3
% 139.83/20.19 | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | ALPHA: (7788) implies:
% 139.83/20.19 | | | | | | | | | | (7789) all_57_12 = e3
% 139.83/20.19 | | | | | | | | | | (7790) op(e0, e3) = e3
% 139.83/20.19 | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | BETA: splitting (215) gives:
% 139.83/20.19 | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | (7791) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.83/20.19 | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.83/20.19 | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | BETA: splitting (7791) gives:
% 139.83/20.19 | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | (7792) all_57_9 = e3 & op(e3, e0) = e3
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | ALPHA: (7792) implies:
% 139.83/20.19 | | | | | | | | | | | | (7793) op(e3, e0) = e3
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e3,
% 139.83/20.19 | | | | | | | | | | | | e3, e0, simplifying with (159), (7790) gives:
% 139.83/20.19 | | | | | | | | | | | | (7794) all_52_3 = e3
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.83/20.19 | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (7793) gives:
% 139.83/20.19 | | | | | | | | | | | | (7795) all_52_12 = e3
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | REDUCE: (139), (7794) imply:
% 139.83/20.19 | | | | | | | | | | | | (7796) ~ (all_52_11 = e3)
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | REDUCE: (347), (7795) imply:
% 139.83/20.19 | | | | | | | | | | | | (7797) ~ (all_14_2 = e3)
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | SIMP: (7797) implies:
% 139.83/20.19 | | | | | | | | | | | | (7798) ~ (all_14_2 = e3)
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | BETA: splitting (52) gives:
% 139.83/20.19 | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | (7799) ~ (all_14_2 = e0)
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | BETA: splitting (64) gives:
% 139.83/20.19 | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | (7800) ~ (all_22_2 = e1)
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | REDUCE: (321), (7800) imply:
% 139.83/20.19 | | | | | | | | | | | | | | (7801) ~ (all_14_2 = e1)
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.83/20.19 | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | (7802) all_54_0 = e3
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7802) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | (7803) all_14_2 = e3
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | SIMP: (7803) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | (7804) all_14_2 = e3
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | REDUCE: (7798), (7804) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | (7805) $false
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | CLOSE: (7805) is inconsistent.
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | (7806) ~ (all_54_0 = e3)
% 139.83/20.19 | | | | | | | | | | | | | | | (7807) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | BETA: splitting (7807) gives:
% 139.83/20.19 | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | (7808) all_54_0 = e2
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (7808) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7809) all_14_2 = e2
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | SIMP: (7809) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7810) all_14_2 = e2
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | REDUCE: (337), (7810) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7811) ~ (all_52_1 = e2)
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | REDUCE: (7798), (7810) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7812) ~ (e3 = e2)
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | REDUCE: (51), (7810) imply:
% 139.83/20.19 | | | | | | | | | | | | | | | | (7813) op(e3, e3) = e2
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7814) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.19 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (5894), (5903), (7811), (7813),
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7814), (function-axioms) are inconsistent by
% 139.83/20.19 | | | | | | | | | | | | | | | | | sub-proof #177.
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (7815) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | BETA: splitting (7815) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7816) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.19 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.19 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | ALPHA: (7816) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7817) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7818) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7819) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7820) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7821) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | (7822) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.19 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | BETA: splitting (7819) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7823) all_56_11 = e1 & op(e2, e2) = e1
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | ALPHA: (7823) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | (7824) all_56_11 = e1
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (7825) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (169), (7464), (7822), (7824), (7825),
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | #93.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (7826) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7826) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | (7827) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7827) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7828) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7828) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7829) op(e0, e0) = e3
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7786), (7829), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7830) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7830) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7831) ~ (all_56_4 = e2)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7821), (7824), (7831) are inconsistent by
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | (7832) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7832) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7833) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7833) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7834) op(e1, e1) = e2
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7834), (function-axioms) are
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (7835) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7835) gives:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (7836) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7836) implies:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (7837) op(e0, e0) = e2
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (36), (169), (207),
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (212), (222), (233), (235), (239),
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (372), (5903), (7464), (7813), (7819), (7821),
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (7822), (7837), (function-axioms) are inconsistent
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #92.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (7838) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (8), (7467), (7786), (7838),
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | | #278.
% 139.83/20.19 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | (7839) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | $i(all_56_4)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | ALPHA: (7839) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | (7840) ~ (all_56_4 = e2)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | (7841) op(e2, e1) = all_56_4
% 139.83/20.20 | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | BETA: splitting (7818) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | (7842) all_56_14 = e0 & op(e0, e1) = e0
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | ALPHA: (7842) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | (7843) op(e0, e1) = e0
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7821) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | (7844) all_56_4 = e2 & op(e2, e1) = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7844) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | (7845) op(e2, e1) = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7840), (7841), (7845), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #951.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | (7846) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | ALPHA: (7846) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | (7847) ~ (all_56_11 = e1)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | (7848) op(e2, e2) = all_56_11
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7820) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | (7849) all_56_9 = e1 & op(e3, e3) = e1
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7849) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | (7850) all_56_9 = e1
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7464), (7822), (7850), (function-axioms)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #898.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | (7851) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7851) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | (7852) ~ (all_56_1 = e3)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | (7853) op(e3, e1) = all_56_1
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7817) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | (7854) all_56_15 = e1 & op(e0, e0) = e1
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7854) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | (7855) all_56_15 = e1
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7822) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7856) all_56_1 = e3 & op(e3, e1) = e3
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7856) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7857) op(e3, e1) = e3
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7852), (7853), (7857), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #734.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7858) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7858) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7859) ~ (all_56_9 = e1)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7860) op(e3, e3) = all_56_9
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (7843) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7861) all_52_11 = e0
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e1, e2, simplifying with (165), (7841)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7862) all_56_4 = all_52_9
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (5903), (7848)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7863) all_56_11 = e3
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (7813), (7860) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7864) all_56_9 = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7840), (7862) imply:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7865) ~ (all_52_9 = e2)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7465), (7861) imply:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7866) ~ (e3 = e0)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7784), (7861) imply:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | (7867) ~ (e1 = e0)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (222) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | (7868) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (165), (233), (235),
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | (239), (7813), (7865), (7868), (function-axioms)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #406.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | (7869) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7869) gives:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (7870) all_57_8 = e2 & op(e1, e1) = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7870) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (7871) op(e1, e1) = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (372), (7871), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1124.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (7872) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7872) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | (7873) op(e0, e1) = e2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7818), (7855), (7873), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #389.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | (7874) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (7874) implies:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | (7875) ~ (all_56_14 = e0)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | (7876) op(e0, e1) = all_56_14
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7843), (7875), (7876), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | (7877) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7786), (7877), (function-axioms) are inconsistent
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | | by sub-proof #82.
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | (7878) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.20 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.20 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.20 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.20 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.20 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.20 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.20 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.20 | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7793), (7813), (7878), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #158.
% 139.83/20.20 | | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | (7879) all_54_0 = e1 | all_54_0 = e0
% 139.83/20.20 | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | | REF_CLOSE: (279), (7799), (7801), (7879) are inconsistent by
% 139.83/20.20 | | | | | | | | | | | | | | | | sub-proof #884.
% 139.83/20.20 | | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | (7880) all_22_2 = e1
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | COMBINE_EQS: (321), (7880) imply:
% 139.83/20.20 | | | | | | | | | | | | | | (7881) all_14_2 = e1
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | SIMP: (7881) implies:
% 139.83/20.20 | | | | | | | | | | | | | | (7882) all_14_2 = e1
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | REDUCE: (339), (7882) imply:
% 139.83/20.20 | | | | | | | | | | | | | | (7883) ~ (all_52_2 = e1)
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | REDUCE: (343), (7882) imply:
% 139.83/20.20 | | | | | | | | | | | | | | (7884) ~ (all_52_4 = e1)
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | REDUCE: (345), (7882) imply:
% 139.83/20.20 | | | | | | | | | | | | | | (7885) ~ (all_52_8 = e1)
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | REDUCE: (7798), (7882) imply:
% 139.83/20.20 | | | | | | | | | | | | | | (7886) ~ (e3 = e1)
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | REDUCE: (51), (7882) imply:
% 139.83/20.20 | | | | | | | | | | | | | | (7887) op(e3, e3) = e1
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (8), (36), (45), (70), (112),
% 139.83/20.20 | | | | | | | | | | | | | | (120), (125), (133), (157), (158), (160), (162),
% 139.83/20.20 | | | | | | | | | | | | | | (163), (165), (168), (169), (170), (206), (209),
% 139.83/20.20 | | | | | | | | | | | | | | (210), (211), (212), (214), (217), (221), (224),
% 139.83/20.20 | | | | | | | | | | | | | | (229), (239), (372), (5891), (5892), (5894),
% 139.83/20.20 | | | | | | | | | | | | | | (5897), (5902), (5903), (7464), (7467), (7785),
% 139.83/20.20 | | | | | | | | | | | | | | (7789), (7883), (7884), (7885), (7887),
% 139.83/20.20 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.20 | | | | | | | | | | | | | | #84.
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | (7888) all_14_2 = e0
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | REDUCE: (7798), (7888) imply:
% 139.83/20.20 | | | | | | | | | | | | | (7889) ~ (e3 = e0)
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | REDUCE: (51), (7888) imply:
% 139.83/20.20 | | | | | | | | | | | | | (7890) op(e3, e3) = e0
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (36), (207), (372),
% 139.83/20.20 | | | | | | | | | | | | | (7467), (7786), (7890), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | inconsistent by sub-proof #210.
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7891) all_57_10 = e3 & op(e2, e0) = e3
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | REF_CLOSE: (164), (5898), (7891), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | inconsistent by sub-proof #81.
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | (7892) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.83/20.20 | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | BETA: splitting (7892) gives:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7893) all_57_11 = e3 & op(e1, e0) = e3
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | REF_CLOSE: (160), (7466), (7893), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | inconsistent by sub-proof #160.
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7894) all_57_15 = e3 & op(e0, e0) = e3
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | ALPHA: (7894) implies:
% 139.83/20.20 | | | | | | | | | | | | (7895) op(e0, e0) = e3
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | REF_CLOSE: (8), (7786), (7895), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | inconsistent by sub-proof #732.
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | (7896) all_57_13 = e3 & op(e0, e2) = e3
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | REF_CLOSE: (158), (5896), (7896), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | inconsistent by sub-proof #80.
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | (7897) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3
% 139.83/20.20 | | | | | | | | | & op(e0, e0) = e3)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | BETA: splitting (7897) gives:
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | (7898) all_57_14 = e3 & op(e0, e1) = e3
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | REF_CLOSE: (157), (7465), (7898), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | inconsistent by sub-proof #184.
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | (7899) all_57_15 = e3 & op(e0, e0) = e3
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | ALPHA: (7899) implies:
% 139.83/20.20 | | | | | | | | | | (7900) op(e0, e0) = e3
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | REF_CLOSE: (8), (7786), (7900), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | inconsistent by sub-proof #732.
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | End of split
% 139.83/20.20 | | | | | | | |
% 139.83/20.20 | | | | | | | End of split
% 139.83/20.20 | | | | | | |
% 139.83/20.20 | | | | | | End of split
% 139.83/20.20 | | | | | |
% 139.83/20.20 | | | | | End of split
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | End of split
% 139.83/20.20 | | | |
% 139.83/20.20 | | | Case 2:
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | (7901) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 139.83/20.20 | | | | e0) = e3)
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | BETA: splitting (7901) gives:
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | Case 1:
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | (7902) all_57_5 = e3 & op(e2, e1) = e3
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | REF_CLOSE: (165), (5897), (7902), (function-axioms) are inconsistent
% 139.83/20.20 | | | | | by sub-proof #320.
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | Case 2:
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | (7903) all_57_10 = e3 & op(e2, e0) = e3
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | REF_CLOSE: (164), (5898), (7903), (function-axioms) are inconsistent
% 139.83/20.20 | | | | | by sub-proof #81.
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | End of split
% 139.83/20.20 | | | |
% 139.83/20.20 | | | End of split
% 139.83/20.20 | | |
% 139.83/20.20 | | End of split
% 139.83/20.20 | |
% 139.83/20.20 | Case 2:
% 139.83/20.20 | |
% 139.83/20.20 | | (7904) all_4_2 = e2
% 139.83/20.20 | | (7905) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) =
% 139.83/20.20 | | all_4_1 & $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) &
% 139.83/20.20 | | op(e1, e2) = all_4_1 & $i(all_4_1))
% 139.83/20.20 | |
% 139.83/20.20 | | COMBINE_EQS: (301), (7904) imply:
% 139.83/20.20 | | (7906) all_32_2 = e2
% 139.83/20.20 | |
% 139.83/20.20 | | REDUCE: (349), (7904) imply:
% 139.83/20.20 | | (7907) ~ (all_52_2 = e2)
% 139.83/20.20 | |
% 139.83/20.20 | | REDUCE: (360), (7904) imply:
% 139.83/20.20 | | (7908) ~ (all_52_6 = e2)
% 139.83/20.20 | |
% 139.83/20.20 | | REDUCE: (362), (7904) imply:
% 139.83/20.20 | | (7909) ~ (all_52_8 = e2)
% 139.83/20.20 | |
% 139.83/20.20 | | REDUCE: (363), (7904) imply:
% 139.83/20.20 | | (7910) ~ (all_52_9 = e2)
% 139.83/20.20 | |
% 139.83/20.20 | | REDUCE: (365), (7904) imply:
% 139.83/20.20 | | (7911) ~ (all_52_11 = e2)
% 139.83/20.20 | |
% 139.83/20.20 | | REDUCE: (367), (7904) imply:
% 139.83/20.20 | | (7912) ~ (all_52_14 = e2)
% 139.83/20.20 | |
% 139.83/20.20 | | BETA: splitting (218) gives:
% 139.83/20.20 | |
% 139.83/20.20 | | Case 1:
% 139.83/20.20 | | |
% 139.83/20.20 | | | (7913) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 139.83/20.20 | | | = e2)
% 139.83/20.20 | | |
% 139.83/20.20 | | | BETA: splitting (7913) gives:
% 139.83/20.20 | | |
% 139.83/20.20 | | | Case 1:
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | (7914) all_57_6 = e2 & op(e1, e3) = e2
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | REF_CLOSE: (163), (7907), (7914), (function-axioms) are inconsistent by
% 139.83/20.20 | | | | sub-proof #79.
% 139.83/20.20 | | | |
% 139.83/20.20 | | | Case 2:
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | (7915) all_57_7 = e2 & op(e1, e2) = e2
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | REF_CLOSE: (162), (7908), (7915), (function-axioms) are inconsistent by
% 139.83/20.20 | | | | sub-proof #78.
% 139.83/20.20 | | | |
% 139.83/20.20 | | | End of split
% 139.83/20.20 | | |
% 139.83/20.20 | | Case 2:
% 139.83/20.20 | | |
% 139.83/20.20 | | | (7916) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 139.83/20.20 | | | = e2)
% 139.83/20.20 | | |
% 139.83/20.20 | | | BETA: splitting (7916) gives:
% 139.83/20.20 | | |
% 139.83/20.20 | | | Case 1:
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | (7917) all_57_8 = e2 & op(e1, e1) = e2
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | ALPHA: (7917) implies:
% 139.83/20.20 | | | | (7918) all_57_8 = e2
% 139.83/20.20 | | | | (7919) op(e1, e1) = e2
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | BETA: splitting (40) gives:
% 139.83/20.20 | | | |
% 139.83/20.20 | | | | Case 1:
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | (7920) ~ (all_6_2 = e3)
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | BETA: splitting (46) gives:
% 139.83/20.20 | | | | |
% 139.83/20.20 | | | | | Case 1:
% 139.83/20.20 | | | | | |
% 139.83/20.20 | | | | | | (7921) ~ (all_10_2 = e1)
% 139.83/20.20 | | | | | |
% 139.83/20.20 | | | | | | BETA: splitting (52) gives:
% 139.83/20.20 | | | | | |
% 139.83/20.20 | | | | | | Case 1:
% 139.83/20.20 | | | | | | |
% 139.83/20.20 | | | | | | | (7922) ~ (all_14_2 = e0)
% 139.83/20.20 | | | | | | |
% 139.83/20.20 | | | | | | | BETA: splitting (55) gives:
% 139.83/20.20 | | | | | | |
% 139.83/20.20 | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | |
% 139.83/20.20 | | | | | | | | (7923) ~ (all_16_2 = e0)
% 139.83/20.20 | | | | | | | |
% 139.83/20.20 | | | | | | | | REDUCE: (328), (7923) imply:
% 139.83/20.20 | | | | | | | | (7924) ~ (all_6_2 = e0)
% 139.83/20.20 | | | | | | | |
% 139.83/20.20 | | | | | | | | BETA: splitting (61) gives:
% 139.83/20.20 | | | | | | | |
% 139.83/20.20 | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | (7925) ~ (all_20_2 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (283), (7925) imply:
% 139.83/20.20 | | | | | | | | | (7926) ~ (all_6_2 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | BETA: splitting (199) gives:
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | (7927) all_54_5 = e3
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | COMBINE_EQS: (268), (7927) imply:
% 139.83/20.20 | | | | | | | | | | (7928) all_6_2 = e3
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | REDUCE: (7920), (7928) imply:
% 139.83/20.20 | | | | | | | | | | (7929) $false
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | CLOSE: (7929) is inconsistent.
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | (7930) ~ (all_54_5 = e3)
% 139.83/20.20 | | | | | | | | | | (7931) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | BETA: splitting (7931) gives:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | (7932) all_54_5 = e2
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | COMBINE_EQS: (268), (7932) imply:
% 139.83/20.20 | | | | | | | | | | | (7933) all_6_2 = e2
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | REDUCE: (7920), (7933) imply:
% 139.83/20.20 | | | | | | | | | | | (7934) ~ (e3 = e2)
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | REDUCE: (39), (7933) imply:
% 139.83/20.20 | | | | | | | | | | | (7935) op(e2, e2) = e2
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7936) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.20 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.20 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.20 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.20 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.20 | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.20 | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.20 | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.20 | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.20 | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.20 | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.20 | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | BETA: splitting (7936) gives:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | (7937) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.20 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.20 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.20 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.20 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.20 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | REF_CLOSE: (9), (7935), (7937), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | inconsistent by sub-proof #317.
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | (7938) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.20 | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.20 | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.20 | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.20 | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.20 | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (7938), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7939) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.20 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.20 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.20 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.20 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.20 | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.20 | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.20 | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.20 | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.20 | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.20 | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.20 | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.20 | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.20 | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.20 | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.20 | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.20 | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.20 | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.20 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.20 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.20 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.20 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.20 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.20 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | REF_CLOSE: (5), (6), (39), (45), (51), (7921), (7922),
% 139.83/20.20 | | | | | | | | | | | | (7924), (7935), (7939), (function-axioms) are
% 139.83/20.20 | | | | | | | | | | | | inconsistent by sub-proof #315.
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | (7940) all_54_5 = e1 | all_54_5 = e0
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | REF_CLOSE: (268), (7924), (7926), (7940) are inconsistent by
% 139.83/20.20 | | | | | | | | | | | sub-proof #641.
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | End of split
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | (7941) all_20_2 = e1
% 139.83/20.20 | | | | | | | | | (7942) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 &
% 139.83/20.20 | | | | | | | | | op(e2, e1) = all_20_1 & $i(all_20_0) &
% 139.83/20.20 | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1) =
% 139.83/20.20 | | | | | | | | | all_20_1 & $i(all_20_1))
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | COMBINE_EQS: (283), (7941) imply:
% 139.83/20.20 | | | | | | | | | (7943) all_6_2 = e1
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | SIMP: (7943) implies:
% 139.83/20.20 | | | | | | | | | (7944) all_6_2 = e1
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | COMBINE_EQS: (332), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7945) all_38_2 = e1
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (348), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7946) ~ (all_52_1 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (351), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7947) ~ (all_52_4 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (353), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7948) ~ (all_52_6 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (355), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7949) ~ (all_52_7 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (357), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7950) ~ (all_52_9 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (359), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7951) ~ (all_52_13 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (7920), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7952) ~ (e3 = e1)
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | REDUCE: (39), (7944) imply:
% 139.83/20.20 | | | | | | | | | (7953) op(e2, e2) = e1
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | BETA: splitting (64) gives:
% 139.83/20.20 | | | | | | | | |
% 139.83/20.20 | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | (7954) ~ (all_22_2 = e1)
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | REDUCE: (321), (7954) imply:
% 139.83/20.20 | | | | | | | | | | (7955) ~ (all_14_2 = e1)
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | BETA: splitting (67) gives:
% 139.83/20.20 | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | (7956) ~ (all_24_2 = e2)
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | REDUCE: (319), (7956) imply:
% 139.83/20.20 | | | | | | | | | | | (7957) ~ (all_10_2 = e2)
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | BETA: splitting (79) gives:
% 139.83/20.20 | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7958) ~ (all_32_2 = e2)
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | REDUCE: (7906), (7958) imply:
% 139.83/20.20 | | | | | | | | | | | | (7959) $false
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | CLOSE: (7959) is inconsistent.
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | Case 2:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | (7960) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0
% 139.83/20.20 | | | | | | | | | | | | & op(e1, e2) = all_32_1 & $i(all_32_0) &
% 139.83/20.20 | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2)
% 139.83/20.20 | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | BETA: splitting (85) gives:
% 139.83/20.20 | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | (7961) ~ (all_36_2 = e2)
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | REDUCE: (305), (7961) imply:
% 139.83/20.20 | | | | | | | | | | | | | (7962) ~ (all_14_2 = e2)
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.83/20.20 | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | Case 1:
% 139.83/20.20 | | | | | | | | | | | | | |
% 139.83/20.20 | | | | | | | | | | | | | | (7963) all_54_0 = e3
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | COMBINE_EQS: (279), (7963) imply:
% 139.83/20.21 | | | | | | | | | | | | | | (7964) all_14_2 = e3
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | SIMP: (7964) implies:
% 139.83/20.21 | | | | | | | | | | | | | | (7965) all_14_2 = e3
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | REDUCE: (337), (7965) imply:
% 139.83/20.21 | | | | | | | | | | | | | | (7966) ~ (all_52_1 = e3)
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | REDUCE: (339), (7965) imply:
% 139.83/20.21 | | | | | | | | | | | | | | (7967) ~ (all_52_2 = e3)
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | REDUCE: (343), (7965) imply:
% 139.83/20.21 | | | | | | | | | | | | | | (7968) ~ (all_52_4 = e3)
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | REDUCE: (345), (7965) imply:
% 139.83/20.21 | | | | | | | | | | | | | | (7969) ~ (all_52_8 = e3)
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | REDUCE: (347), (7965) imply:
% 139.83/20.21 | | | | | | | | | | | | | | (7970) ~ (all_52_12 = e3)
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 139.83/20.21 | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | (7971) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 139.83/20.21 | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | BETA: splitting (7971) gives:
% 139.83/20.21 | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | (7972) all_57_0 = e3 & op(e3, e3) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | ALPHA: (7972) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | (7973) all_57_0 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | (7974) op(e3, e3) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | (7975) ~ (all_38_2 = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | REDUCE: (7945), (7975) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | (7976) $false
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | CLOSE: (7976) is inconsistent.
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | (7977) ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0
% 139.83/20.21 | | | | | | | | | | | | | | | | | & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e2, e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | (7978) ~ (all_42_2 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | REDUCE: (303), (7978) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | (7979) ~ (all_10_2 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | (7980) all_54_15 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7979), (7980) are inconsistent by
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | sub-proof #755.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | (7981) ~ (all_54_15 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | (7982) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | BETA: splitting (7982) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | (7983) all_54_15 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7957), (7983) are inconsistent by
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | (7984) ~ (all_54_15 = e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | (7985) all_54_15 = e1 | all_54_15 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | BETA: splitting (7985) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7986) all_54_15 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7921), (7986) are inconsistent by
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7987) all_54_15 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (7987) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7988) all_10_2 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | SIMP: (7988) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7989) all_10_2 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (350), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7990) ~ (all_52_3 = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (361), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7991) ~ (all_52_7 = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (368), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7992) ~ (all_52_11 = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (7979), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7993) ~ (e3 = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (7957), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7994) ~ (e2 = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (7921), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7995) ~ (e1 = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | REDUCE: (45), (7989) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | (7996) op(e0, e0) = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | (7997) all_54_4 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7966), (7997) are inconsistent by
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | sub-proof #796.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | (7998) ~ (all_54_4 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | (7999) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (198) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | (8000) all_54_6 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (8000) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | (8001) all_52_9 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8001) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | (8002) all_52_9 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8002) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | (8003) ~ (all_52_11 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8003) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | (8004) ~ (all_52_11 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | (8005) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8005) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | (8006) all_57_4 = e3 & op(e3, e1) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8006) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | (8007) op(e3, e1) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (7969), (8007), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | (8008) all_57_5 = e3 & op(e2, e1) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8008) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | (8009) all_57_5 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | (8010) op(e2, e1) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | (8011) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8011) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8012) all_57_4 = e0 & op(e3, e1) = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8012) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8013) all_57_4 = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8014) op(e3, e1) = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8015) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8015) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8016) all_57_12 = e3 & op(e0, e3) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8016) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8017) all_57_12 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (168), (169),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (170), (232), (234), (236), (239), (7946), (7968),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7969), (7970), (7973), (7974), (8017),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #75.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8018) all_57_13 = e3 & op(e0, e2) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8018) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8019) all_57_13 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8020) op(e0, e2) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8021) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8021) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8022) all_57_4 = e1 & op(e3, e1) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8013), (8022) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #121.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8023) all_57_5 = e1 & op(e2, e1) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7950), (8023), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8024) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8024) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8025) all_57_8 = e1 & op(e1, e1) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8025) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8026) op(e1, e1) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7919), (8026), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8027) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8027) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8028) all_57_14 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8029) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8029) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8030) all_57_12 = e2 & op(e0, e3) = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8030) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8031) all_57_12 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8032) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (167), (7946), (7974), (8032),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #438.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8033) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8033) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8034) all_57_6 = e1 & op(e1, e3) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8034) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8035) op(e1, e3) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8036) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8036) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8037) all_57_0 = e1 & op(e3, e3) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8037) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8038) op(e3, e3) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7974), (8038), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #838.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8039) all_57_1 = e1 & op(e3, e2) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7947), (8039), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #844.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8040) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8040) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8041) all_57_4 = e1 & op(e3, e1) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8013), (8041) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #74.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8042) all_57_9 = e1 & op(e3, e0) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8042) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8043) all_57_9 = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8044) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8044) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8045) all_57_6 = e3 & op(e1, e3) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7967), (8045), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #95.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8046) all_57_7 = e3 & op(e1, e2) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8046) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8047) op(e1, e2) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7905), (7960), (8014), (8047), (function-axioms)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #72.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8048) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8048) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8049) all_57_8 = e3 & op(e1, e1) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8049) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8050) op(e1, e1) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8050), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8051) all_57_11 = e3 & op(e1, e0) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8051) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8052) all_57_11 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8053) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8053) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8054) all_57_9 = e2 & op(e3, e0) = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8054) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8055) all_57_9 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8043), (8055) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #815.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8056) all_57_10 = e2 & op(e2, e0) = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8056) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8057) op(e2, e0) = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8058) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8058) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8059) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8035), (8059), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #71.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8060) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8060) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8061) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8062) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8063) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8062) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8064) all_56_7 = e1 & op(e1, e2) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8064) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8065) op(e1, e2) = e1
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7948), (8065), (function-axioms) are
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8066) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8066) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8067) ~ (all_56_13 = e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8068) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (7919), (7968), (8063), (8068),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #70.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8069) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8069) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8070) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8070) gives:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8071) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8071) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8072) op(e0, e0) = e3
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (118),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (123), (125), (128), (135), (136), (162),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (169), (170), (190), (191), (202), (203),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (231), (247), (248),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (272), (7909), (7911), (7919), (7921),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7922), (7942), (7947), (7949), (7957), (7960),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7968), (7974), (7977), (8010), (8072),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #65.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8073) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8073) implies:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8074) all_56_13 = e2
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8067), (8074) imply:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8075) $false
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8075) is inconsistent.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8076) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (45), (51), (158), (7921), (7922), (7924),
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7991), (8061), (8067), (8076), (function-axioms)
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #64.
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.21 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8077) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8077) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8078) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8078) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8079) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8080) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8081) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8082) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (165), (7910), (7953), (7992), (8079),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8080), (8081), (8082), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8083) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (7921), (7922),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7955), (7957), (8057), (8083), (function-axioms)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #151.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8084) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8084) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8085) all_57_11 = e2 & op(e1, e0) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8052), (8085) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #963.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8086) all_57_15 = e2 & op(e0, e0) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8086) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8087) op(e0, e0) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (209), (210), (8019),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8020), (8031), (8087), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #62.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8088) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8088) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8089) all_57_12 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8031), (8089) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #970.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8090) all_57_13 = e2 & op(e0, e2) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8090) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8091) all_57_13 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8019), (8091) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1068.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8092) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8092) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8093) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8093) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8094) all_57_14 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8028), (8094) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1048.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8095) all_57_15 = e2 & op(e0, e0) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8095) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8096) op(e0, e0) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8096), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8097) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8097) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8098) all_57_14 = e3 & op(e0, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8004), (8098), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8099) all_57_15 = e3 & op(e0, e0) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8099) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8100) op(e0, e0) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (118),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (121), (123), (125), (128), (135), (136), (162),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (165), (169), (170), (190), (191), (202), (203),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (231), (247), (248),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (271), (272), (7909), (7911), (7919), (7921),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7922), (7942), (7947), (7949), (7957), (7960),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7968), (7974), (7977), (8010), (8100),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #65.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8101) all_57_5 = e0 & op(e2, e1) = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8101) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8102) all_57_5 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8009), (8102) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8103) e3 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8103) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8104) e3 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7973), (8104) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8105) all_57_0 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (168), (169), (170), (239), (7968), (7969),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (7970), (8105), (function-axioms) are inconsistent
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #1103.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (8106) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (7919), (7992), (8106),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | #60.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | (8107) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8107) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8108) all_57_8 = e3 & op(e1, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8108) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8109) op(e1, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8109), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8110) all_57_14 = e3 & op(e0, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8004), (8110), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | (8111) ~ (all_54_6 = e3)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | (8112) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (261), (8111) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | (8113) ~ (all_52_9 = e3)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | (8114) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (169), (7969), (8113), (8114),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | #319.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | (8115) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8115) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8116) all_57_8 = e3 & op(e1, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8116) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8117) op(e1, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8117), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8118) all_57_14 = e3 & op(e0, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8118) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8119) all_57_14 = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | (8120) op(e0, e1) = e3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8112) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (8121) all_54_6 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (7910), (8121) are inconsistent by
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #762.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (8122) ~ (all_54_6 = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | (8123) all_54_6 = e1 | all_54_6 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8123) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8124) all_54_6 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (261), (7950), (8124) are inconsistent by
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #741.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8125) all_54_6 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (261), (8125) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8126) all_52_9 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8126) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8127) all_52_9 = e0
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8127) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8128) ~ (all_52_1 = e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (123), (8127) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8129) ~ (all_52_8 = e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (118), (8127) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8130) ~ (all_52_11 = e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (117), (8127) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8131) ~ (all_52_13 = e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8131) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132) ~ (all_52_13 = e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8133) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8133) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8134) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8134) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8135) all_57_12 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8136) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8136) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8137) all_57_4 = e1 & op(e3, e1) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8137) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8138) all_57_4 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8139) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8139) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8140) all_57_12 = e2 & op(e0, e3) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8135), (8140) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #674.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8141) all_57_13 = e2 & op(e0, e2) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8141) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8142) all_57_13 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7999) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8143) all_54_4 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8143) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8144) all_52_1 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8144) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8145) all_52_1 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8145) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8146) ~ (all_52_13 = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8146) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8147) ~ (all_52_13 = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7966), (8145) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8148) ~ (e3 = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (167), (8145) imply:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8149) op(e2, e3) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8150) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8150) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8151) all_57_9 = e2 & op(e3, e0) = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8151) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8152) all_57_9 = e2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8153) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8153) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8154) all_57_9 = e1 & op(e3, e0) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8154) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8155) all_57_9 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8152), (8155) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #815.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8156) all_57_10 = e1 & op(e2, e0) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7951), (8156), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8157) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8157) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8158) all_57_11 = e1 & op(e1, e0) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8158) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8159) op(e1, e0) = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8160) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (51),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (157), (158), (159), (160), (162), (170),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (207), (209), (213), (214), (215), (228),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (260), (7905), (7919), (7921), (7922),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7924), (7948), (7951), (7955), (7957), (7960),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7968), (7974), (7990), (7991), (7992), (8120),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132), (8138), (8147), (8149), (8160),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #55.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8161) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8161) gives:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8162) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8162) implies:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8163) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8164) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8165) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8166) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (165), (7910), (7953), (7992), (8163),
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8164), (8165), (8166), (function-axioms) are
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63.
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8167) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.22 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8167) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8168) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (8159), (8168), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #54.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8169) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8169) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8170) op(e0, e0) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7921), (8170), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8171) all_57_10 = e2 & op(e2, e0) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8171) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8172) op(e2, e0) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8147), (8172), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8173) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8173) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8174) all_57_11 = e2 & op(e1, e0) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8174) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8175) all_57_11 = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8176) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (51),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (110), (157), (158), (159), (160), (162), (170),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (197), (207), (209), (213), (214), (215), (228),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (260), (7905), (7919), (7921), (7922),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7924), (7948), (7951), (7955), (7957), (7960),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (7968), (7974), (7990), (7991), (7992), (8120),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8132), (8138), (8147), (8149), (8176),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #55.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8177) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8177) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8178) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8178) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8179) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8180) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8181) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8182) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (165), (7910), (7953), (7992), (8179),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8180), (8181), (8182), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #63.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8183) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8183) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8184) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8185) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8185) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8186) all_57_6 = e1 & op(e1, e3) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8186) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8187) all_57_6 = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8188) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8188) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8189) all_57_6 = e0 & op(e1, e3) = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8187), (8189) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #427.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8190) all_57_7 = e0 & op(e1, e2) = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7905), (7960), (8120), (8190), (function-axioms)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #56.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8191) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8191) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8192) all_57_8 = e0 & op(e1, e1) = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8192) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8193) op(e1, e1) = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (8193), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8194) all_57_11 = e0 & op(e1, e0) = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8175), (8194) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #992.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8195) all_57_7 = e1 & op(e1, e2) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8195) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8196) op(e1, e2) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7948), (8196), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8197) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8197) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8198) all_57_8 = e1 & op(e1, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8198) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8199) op(e1, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (9), (169), (220), (222),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8119), (8129), (8138), (8199), (function-axioms)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #624.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8200) all_57_11 = e1 & op(e1, e0) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8200) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8201) op(e1, e0) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (8184), (8201), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #54.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8202) all_57_15 = e2 & op(e0, e0) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (159), (209),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (210), (212), (7990), (7991), (8142), (8202),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #168.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8203) all_54_4 = e1 | all_54_4 = e0
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (269), (7946), (8128), (8203) are inconsistent by
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #793.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8204) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8204) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8205) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8119), (8205) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #704.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8206) all_57_15 = e2 & op(e0, e0) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8206) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8207) op(e0, e0) = e2
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7996), (8207), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8208) all_57_5 = e1 & op(e2, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7950), (8208), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8209) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8209) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8210) all_57_8 = e1 & op(e1, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8210) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8211) op(e1, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7919), (8211), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8212) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8212) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8213) all_57_14 = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8119), (8213) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1045.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8214) all_57_13 = e1 & op(e0, e2) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7949), (8214), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8215) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8215) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8216) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8119), (8216) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #705.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8217) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8217) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8218) op(e0, e0) = e1
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7921), (8218), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8219) all_42_2 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (303), (8219) imply:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8220) all_10_2 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | REDUCE: (45), (8220) imply:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8221) op(e0, e0) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | (8222) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (8222) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8223) all_57_2 = e3 & op(e2, e3) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7966), (8223), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #183.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8224) all_57_3 = e3 & op(e2, e2) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (8224) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8225) op(e2, e2) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (45), (51), (207), (7919), (7921),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (7922), (7957), (7974), (8225), (function-axioms)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #68.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | (8226) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (8226) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8227) all_57_5 = e3 & op(e2, e1) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (8227) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8228) op(e2, e1) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (45), (51), (118),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (121), (123), (125), (128), (135), (136), (162),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (165), (169), (170), (190), (191), (202), (203),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (207), (209), (210), (211), (231), (247), (248),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (271), (272), (7909), (7911), (7919), (7921),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (7922), (7942), (7947), (7949), (7957), (7960),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (7968), (7974), (7977), (8221), (8228),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | #65.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8229) all_57_10 = e3 & op(e2, e0) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | ALPHA: (8229) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8230) all_57_10 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (213), (214),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | (8221), (8230), (function-axioms) are inconsistent
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | | by sub-proof #650.
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | (8231) all_57_2 = e3 & op(e2, e3) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | REF_CLOSE: (167), (7966), (8231), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | inconsistent by sub-proof #183.
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | (8232) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 139.83/20.23 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | BETA: splitting (8232) gives:
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | (8233) all_57_6 = e3 & op(e1, e3) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7967), (8233), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | inconsistent by sub-proof #95.
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | (8234) all_57_12 = e3 & op(e0, e3) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | ALPHA: (8234) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | (8235) all_57_12 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | (8236) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | BETA: splitting (8236) gives:
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8237) all_57_0 = e3 & op(e3, e3) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | ALPHA: (8237) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8238) all_57_0 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8239) op(e3, e3) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (167), (168), (169),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (170), (232), (234), (236), (239), (7946), (7968),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (7969), (7970), (8235), (8238), (8239),
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | | #75.
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8240) all_57_1 = e3 & op(e3, e2) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | ALPHA: (8240) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | | | | (8241) op(e3, e2) = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (7968), (8241), (function-axioms) are
% 139.83/20.23 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1107.
% 139.83/20.23 | | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | (8242) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.83/20.23 | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (7969), (7970), (8242),
% 139.83/20.23 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.23 | | | | | | | | | | | | | | | | | #1104.
% 139.83/20.23 | | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | (8243) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | REF_CLOSE: (279), (7922), (7955), (7962), (8243) are
% 139.83/20.23 | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | End of split
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | (8244) all_36_2 = e2
% 139.83/20.23 | | | | | | | | | | | | | (8245) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0
% 139.83/20.23 | | | | | | | | | | | | | & op(e3, e2) = all_36_1 & $i(all_36_0) &
% 139.83/20.23 | | | | | | | | | | | | | $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2)
% 139.83/20.23 | | | | | | | | | | | | | = all_36_1 & $i(all_36_1))
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | COMBINE_EQS: (305), (8244) imply:
% 139.83/20.23 | | | | | | | | | | | | | (8246) all_14_2 = e2
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | SIMP: (8246) implies:
% 139.83/20.23 | | | | | | | | | | | | | (8247) all_14_2 = e2
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | COMBINE_EQS: (281), (8247) imply:
% 139.83/20.23 | | | | | | | | | | | | | (8248) all_44_2 = e2
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | REDUCE: (337), (8247) imply:
% 139.83/20.23 | | | | | | | | | | | | | (8249) ~ (all_52_1 = e2)
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | REDUCE: (51), (8247) imply:
% 139.83/20.23 | | | | | | | | | | | | | (8250) op(e3, e3) = e2
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | BETA: splitting (211) gives:
% 139.83/20.23 | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | (8251) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 139.83/20.23 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | BETA: splitting (8251) gives:
% 139.83/20.23 | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | Case 1:
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | (8252) all_57_12 = e2 & op(e0, e3) = e2
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | ALPHA: (8252) implies:
% 139.83/20.23 | | | | | | | | | | | | | | | (8253) all_57_12 = e2
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.83/20.23 | | | | | | | | | | | | | | | (8250), (8253), (function-axioms) are inconsistent
% 139.83/20.23 | | | | | | | | | | | | | | | by sub-proof #50.
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | Case 2:
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.23 | | | | | | | | | | | | | | | (8254) all_57_13 = e2 & op(e0, e2) = e2
% 139.83/20.23 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (51),
% 139.83/20.24 | | | | | | | | | | | | | | | (97), (110), (112), (113), (117), (120), (133),
% 139.83/20.24 | | | | | | | | | | | | | | | (134), (135), (145), (158), (159), (160), (162),
% 139.83/20.24 | | | | | | | | | | | | | | | (163), (164), (165), (167), (168), (169), (170),
% 139.83/20.24 | | | | | | | | | | | | | | | (189), (201), (203), (206), (207), (217), (226),
% 139.83/20.24 | | | | | | | | | | | | | | | (234), (235), (246), (270), (272), (369), (370),
% 139.83/20.24 | | | | | | | | | | | | | | | (371), (7910), (7919), (7921), (7922), (7924),
% 139.83/20.24 | | | | | | | | | | | | | | | (7946), (7947), (7948), (7951), (7953), (7955),
% 139.83/20.24 | | | | | | | | | | | | | | | (8245), (8248), (8249), (8250), (8254),
% 139.83/20.24 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | #44.
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | (8255) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 139.83/20.24 | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | BETA: splitting (8255) gives:
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | (8256) all_57_14 = e2 & op(e0, e1) = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | ALPHA: (8256) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | (8257) all_57_14 = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | (8258) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | BETA: splitting (8258) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8259) all_57_1 = e2 & op(e3, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | ALPHA: (8259) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8260) all_57_1 = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8261) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | BETA: splitting (8261) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8262) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | ALPHA: (8262) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8263) op(e0, e3) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | (8264) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8264) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8265) all_57_4 = e1 & op(e3, e1) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8265) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8266) all_57_4 = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (8267) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8267) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8268) all_57_0 = e0 & op(e3, e3) = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8268) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8269) op(e3, e3) = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8250), (8269), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8270) all_57_1 = e0 & op(e3, e2) = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8270) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8271) op(e3, e2) = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (97), (8245), (8248), (8263), (8271),
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | #48.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (8272) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8272) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8273) all_57_4 = e0 & op(e3, e1) = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8266), (8273) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | #1100.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8274) all_57_9 = e0 & op(e3, e0) = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8274) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8275) all_57_9 = e0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | (8276) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8276) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8277) all_57_0 = e3 & op(e3, e3) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8277) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8278) op(e3, e3) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8250), (8278), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8279) all_57_1 = e3 & op(e3, e2) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8260), (8279) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | #842.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | (8280) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8280) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8281) all_57_4 = e3 & op(e3, e1) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8281) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8282) all_57_4 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8266), (8282) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8283) e3 = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8), (8283) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8284) $false
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8284) is inconsistent.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8285) all_57_9 = e3 & op(e3, e0) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8285) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | (8286) all_57_9 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8275), (8286) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | | #863.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8287) all_57_5 = e1 & op(e2, e1) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7950), (8287), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | (8288) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8288) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8289) all_57_8 = e1 & op(e1, e1) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8289) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8290) op(e1, e1) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7919), (8290), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8291) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8257), (8291) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | #768.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8292) all_57_13 = e1 & op(e0, e2) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7949), (8292), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8293) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | BETA: splitting (8293) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8294) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8257), (8294) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | #768.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8295) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | ALPHA: (8295) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8296) op(e0, e0) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7921), (8296), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8297) all_57_3 = e2 & op(e2, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | ALPHA: (8297) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8298) op(e2, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (45), (51), (207), (7921),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (7922), (7924), (7955), (8298), (function-axioms)
% 139.83/20.24 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #314.
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | (8299) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.83/20.24 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | BETA: splitting (8299) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8300) all_57_7 = e2 & op(e1, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (8300), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8301) all_57_13 = e2 & op(e0, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (39), (45), (51),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (97), (110), (112), (113), (117), (120), (133),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (134), (135), (145), (158), (159), (160), (162),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (163), (164), (165), (167), (168), (169), (170),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (189), (201), (203), (206), (207), (217), (226),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (234), (235), (246), (270), (272), (369), (370),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (371), (7910), (7919), (7921), (7922), (7924),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (7946), (7947), (7948), (7951), (7953), (7955),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8245), (8248), (8249), (8250), (8301),
% 139.83/20.24 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | #44.
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | (8302) all_57_15 = e2 & op(e0, e0) = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | ALPHA: (8302) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | (8303) op(e0, e0) = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | REF_CLOSE: (45), (7957), (8303), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | inconsistent by sub-proof #1115.
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | (8304) all_24_2 = e2
% 139.83/20.24 | | | | | | | | | | | (8305) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0
% 139.83/20.24 | | | | | | | | | | | & op(e0, e2) = all_24_1 & $i(all_24_0) &
% 139.83/20.24 | | | | | | | | | | | $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2)
% 139.83/20.24 | | | | | | | | | | | = all_24_1 & $i(all_24_1))
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | COMBINE_EQS: (319), (8304) imply:
% 139.83/20.24 | | | | | | | | | | | (8306) all_10_2 = e2
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | SIMP: (8306) implies:
% 139.83/20.24 | | | | | | | | | | | (8307) all_10_2 = e2
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | COMBINE_EQS: (307), (8307) imply:
% 139.83/20.24 | | | | | | | | | | | (8308) all_40_2 = e2
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | REDUCE: (361), (8307) imply:
% 139.83/20.24 | | | | | | | | | | | (8309) ~ (all_52_7 = e2)
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | REDUCE: (370), (8307) imply:
% 139.83/20.24 | | | | | | | | | | | (8310) ~ (all_52_13 = e2)
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | REDUCE: (45), (8307) imply:
% 139.83/20.24 | | | | | | | | | | | (8311) op(e0, e0) = e2
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | BETA: splitting (226) gives:
% 139.83/20.24 | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | (8312) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.83/20.24 | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.83/20.24 | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | BETA: splitting (8312) gives:
% 139.83/20.24 | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | (8313) all_57_2 = e2 & op(e2, e3) = e2
% 139.83/20.24 | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | ALPHA: (8313) implies:
% 139.83/20.24 | | | | | | | | | | | | | (8314) all_57_2 = e2
% 139.83/20.24 | | | | | | | | | | | | | (8315) op(e2, e3) = e2
% 139.83/20.24 | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.83/20.24 | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | (8316) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.83/20.24 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | BETA: splitting (8316) gives:
% 139.83/20.24 | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | (8317) all_57_1 = e2 & op(e3, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | ALPHA: (8317) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | (8318) op(e3, e2) = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 139.83/20.24 | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8315) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | (8319) all_52_1 = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 139.83/20.24 | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8318) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | (8320) all_52_4 = e2
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | REDUCE: (146), (8319) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | (8321) ~ (all_52_9 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | REDUCE: (145), (8319) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | (8322) ~ (all_52_13 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | REDUCE: (343), (8320) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | (8323) ~ (all_14_2 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | SIMP: (8323) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | (8324) ~ (all_14_2 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.83/20.24 | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | (8325) all_54_0 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (8325) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | | (8326) all_14_2 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | REDUCE: (51), (8326) imply:
% 139.83/20.24 | | | | | | | | | | | | | | | | (8327) op(e3, e3) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | (8328) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.24 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.24 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | BETA: splitting (8328) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8329) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | ALPHA: (8329) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8330) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | BETA: splitting (8330) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8331) all_56_11 = e3 & op(e2, e2) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | ALPHA: (8331) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8332) op(e2, e2) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (204), (207), (279), (7919), (7922),
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (7955), (8311), (8324), (8332), (function-axioms)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #42.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8333) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | $i(all_56_3)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | ALPHA: (8333) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8334) ~ (all_56_3 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8335) op(e2, e3) = all_56_3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8315), (8334), (8335), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8336) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | ALPHA: (8336) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8337) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8338) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.24 | | | | | | | | | | | | | | | | | | (8339) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.24 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | BETA: splitting (8337) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8340) all_56_9 = e2 & op(e3, e3) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | ALPHA: (8340) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8341) op(e3, e3) = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8327), (8341), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #450.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8342) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | ALPHA: (8342) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8343) ~ (all_56_0 = e3)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | (8344) op(e3, e2) = all_56_0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | BETA: splitting (8338) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | (8345) all_56_7 = e1 & op(e1, e2) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | ALPHA: (8345) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | (8346) op(e1, e2) = e1
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7948), (8346), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | (8347) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | ALPHA: (8347) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | (8348) ~ (all_56_13 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8339) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8349) all_56_0 = e3 & op(e3, e2) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8349) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8350) op(e3, e2) = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8343), (8344), (8350), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8351) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8351) implies:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8352) ~ (all_56_9 = e2)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | (8353) op(e3, e3) = all_56_9
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (8354) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8352), (8353), (8354),
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | #41.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (8355) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8355) gives:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | (8356) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8311), (8348), (8356), (function-axioms) are
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40.
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.24 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (8357) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (45), (51), (7921), (7922), (7924),
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (7953), (8348), (8357), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #39.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | (8358) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.25 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.25 | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | BETA: splitting (8358) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8359) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | ALPHA: (8359) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8360) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8361) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8362) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8363) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | BETA: splitting (8363) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8364) all_56_4 = e2 & op(e2, e1) = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | ALPHA: (8364) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8365) op(e2, e1) = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (8365), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8366) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | ALPHA: (8366) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8367) ~ (all_56_11 = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8368) op(e2, e2) = all_56_11
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (8360) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8369) all_56_15 = e1 & op(e0, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (8369) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8370) op(e0, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8311), (8370), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8371) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (8371) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8372) ~ (all_56_14 = e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8373) op(e0, e1) = all_56_14
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8374) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8374) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | (8375) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8327), (8375), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #125.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | (8376) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8376), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8377) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (39), (45), (51), (165), (7910), (7921),
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (7922), (7924), (7953), (8360), (8361), (8362),
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8363), (8367), (8368), (8372), (8373), (8377),
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | #38.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8378) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | ALPHA: (8378) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8379) op(e0, e0) = all_56_15
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8380) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8381) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8382) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8383) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8384) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | (8385) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.83/20.25 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | BETA: splitting (8382) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8386) all_56_9 = e0 & op(e3, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | ALPHA: (8386) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8387) op(e3, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (7922), (8387), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1125.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8388) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | ALPHA: (8388) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8389) ~ (all_56_2 = e3)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | (8390) op(e3, e0) = all_56_2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | BETA: splitting (8380) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8391) all_56_13 = e0 & op(e1, e1) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (8391) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8392) op(e1, e1) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (8392), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8393) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | ALPHA: (8393) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8394) ~ (all_56_8 = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | (8395) op(e1, e0) = all_56_8
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8383) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8396) all_56_8 = e1 & op(e1, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8396) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8397) op(e1, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8394), (8395), (8397), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8398) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8398) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8399) ~ (all_56_13 = e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | (8400) op(e1, e1) = all_56_13
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8381) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | (8401) all_56_11 = e0 & op(e2, e2) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8401) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | (8402) op(e2, e2) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8310), (8384), (8402), (function-axioms)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #856.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | (8403) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8403) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | (8404) op(e2, e0) = all_56_5
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8384) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (8405) all_56_5 = e2 & op(e2, e0) = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8405) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (8406) op(e2, e0) = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8310), (8406), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (8407) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8407) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (8408) ~ (all_56_11 = e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | (8409) op(e2, e2) = all_56_11
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8385) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8410) all_56_2 = e3 & op(e3, e0) = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8410) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8411) op(e3, e0) = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8389), (8390), (8411), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #274.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8412) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8412) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8413) ~ (all_56_9 = e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8414) op(e3, e3) = all_56_9
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (8311), (8379)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8415) all_56_15 = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e1, simplifying with (160), (8395)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8416) all_56_8 = all_52_14
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (7919), (8400)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8417) all_56_13 = e2
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | all_56_5, e0, e2, simplifying with (164), (8404)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8418) all_56_5 = all_52_13
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (7953), (8409)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8419) all_56_11 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8327), (8414) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8420) all_56_9 = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8394), (8416) imply:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | (8421) ~ (all_52_14 = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | (8422) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8422) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (8423) all_57_6 = e1 & op(e1, e3) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8423) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (8424) all_57_6 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8425) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8425) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8426) all_57_9 = e1 & op(e3, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8426) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8427) op(e3, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8428) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8428) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8429) all_57_0 = e0 & op(e3, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8429) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8430) op(e3, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (51), (7922), (8430), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1125.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8431) all_57_2 = e0 & op(e2, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8431) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8432) all_57_2 = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8314), (8432) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8433) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8433) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8434) all_57_6 = e0 & op(e1, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8424), (8434) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #427.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8435) all_57_12 = e0 & op(e0, e3) = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8435) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8436) all_57_12 = e0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8437) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8437) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8438) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8438) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8439) all_57_12 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8436), (8439) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1002.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8440) all_57_13 = e1 & op(e0, e2) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (7949), (8440), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8441) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8441) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8442) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8442) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8443) all_57_14 = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8444) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8444) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8445) all_57_12 = e3 & op(e0, e3) = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8445) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8446) all_57_12 = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8436), (8446) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #828.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8447) all_57_13 = e3 & op(e0, e2) = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8447) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8448) op(e0, e2) = e3
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (91) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8449) ~ (all_40_2 = e2)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8308), (8449) imply:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8450) $false
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8450) is inconsistent.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8451) ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_40_1 & $i(all_40_0) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_40_1)) | ( ~ (all_40_1 = e1) & op(e0, e2)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_40_1 & $i(all_40_1))
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8451) gives:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8452) ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_40_1 & $i(all_40_0) &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_40_1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8452) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8453) op(e0, e2) = all_40_1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8305), (8427), (8448), (8453), (function-axioms)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8454) ~ (all_40_1 = e1) & op(e0, e2) = all_40_1 &
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_40_1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8454) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8455) op(e0, e2) = all_40_1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8305), (8427), (8448), (8455), (function-axioms)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #37.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8456) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (8311), (8443), (8456),
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #826.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8457) all_57_15 = e1 & op(e0, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8457) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8458) op(e0, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8311), (8458), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8459) all_57_10 = e1 & op(e2, e0) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (7951), (8459), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8460) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (8311), (8421), (8460),
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | | #36.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (8461) all_57_7 = e1 & op(e1, e2) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8461) implies:
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | (8462) op(e1, e2) = e1
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7948), (8462), (function-axioms) are
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.83/20.25 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | (8463) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (7919), (8421), (8463),
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | #35.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | (8464) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | REF_CLOSE: (279), (7922), (7955), (8324), (8464) are
% 139.83/20.26 | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | (8465) all_57_3 = e2 & op(e2, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | ALPHA: (8465) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | (8466) op(e2, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (45), (51), (207), (7921),
% 139.83/20.26 | | | | | | | | | | | | | | | (7922), (7924), (7955), (8466), (function-axioms)
% 139.83/20.26 | | | | | | | | | | | | | | | are inconsistent by sub-proof #314.
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | (8467) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.83/20.26 | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | BETA: splitting (8467) gives:
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | (8468) all_57_7 = e2 & op(e1, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (8468), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | (8469) all_57_13 = e2 & op(e0, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | REF_CLOSE: (158), (8309), (8469), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | (8470) all_57_3 = e2 & op(e2, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | ALPHA: (8470) implies:
% 139.83/20.26 | | | | | | | | | | | | | (8471) op(e2, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (39), (45), (51), (207), (7921),
% 139.83/20.26 | | | | | | | | | | | | | (7922), (7924), (7955), (8471), (function-axioms)
% 139.83/20.26 | | | | | | | | | | | | | are inconsistent by sub-proof #314.
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | (8472) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.83/20.26 | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | REF_CLOSE: (164), (165), (7910), (8310), (8472),
% 139.83/20.26 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.26 | | | | | | | | | | | | #887.
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | (8473) all_22_2 = e1
% 139.83/20.26 | | | | | | | | | | (8474) ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0
% 139.83/20.26 | | | | | | | | | | & op(e3, e1) = all_22_1 & $i(all_22_0) &
% 139.83/20.26 | | | | | | | | | | $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e3, e1)
% 139.83/20.26 | | | | | | | | | | = all_22_1 & $i(all_22_1))
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | COMBINE_EQS: (321), (8473) imply:
% 139.83/20.26 | | | | | | | | | | (8475) all_14_2 = e1
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | SIMP: (8475) implies:
% 139.83/20.26 | | | | | | | | | | (8476) all_14_2 = e1
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | COMBINE_EQS: (313), (8476) imply:
% 139.83/20.26 | | | | | | | | | | (8477) all_34_2 = e1
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | REDUCE: (339), (8476) imply:
% 139.83/20.26 | | | | | | | | | | (8478) ~ (all_52_2 = e1)
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | REDUCE: (341), (8476) imply:
% 139.83/20.26 | | | | | | | | | | (8479) ~ (all_52_3 = e1)
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | REDUCE: (51), (8476) imply:
% 139.83/20.26 | | | | | | | | | | (8480) op(e3, e3) = e1
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | BETA: splitting (210) gives:
% 139.83/20.26 | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | (8481) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 139.83/20.26 | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | BETA: splitting (8481) gives:
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | (8482) all_57_12 = e1 & op(e0, e3) = e1
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | REF_CLOSE: (159), (8479), (8482), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | inconsistent by sub-proof #350.
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | (8483) all_57_13 = e1 & op(e0, e2) = e1
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | REF_CLOSE: (158), (7949), (8483), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | inconsistent by sub-proof #366.
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | (8484) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 139.83/20.26 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | BETA: splitting (8484) gives:
% 139.83/20.26 | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | (8485) all_57_14 = e1 & op(e0, e1) = e1
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | ALPHA: (8485) implies:
% 139.83/20.26 | | | | | | | | | | | | (8486) all_57_14 = e1
% 139.83/20.26 | | | | | | | | | | | | (8487) op(e0, e1) = e1
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | BETA: splitting (217) gives:
% 139.83/20.26 | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | (8488) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 139.83/20.26 | | | | | | | | | | | | | & op(e1, e2) = e1)
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | REF_CLOSE: (162), (163), (7948), (8478), (8488),
% 139.83/20.26 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.83/20.26 | | | | | | | | | | | | | #85.
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | (8489) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 139.83/20.26 | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | BETA: splitting (8489) gives:
% 139.83/20.26 | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | (8490) all_57_8 = e1 & op(e1, e1) = e1
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | ALPHA: (8490) implies:
% 139.83/20.26 | | | | | | | | | | | | | | (8491) op(e1, e1) = e1
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | REF_CLOSE: (6), (7919), (8491), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | (8492) all_57_11 = e1 & op(e1, e0) = e1
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | ALPHA: (8492) implies:
% 139.83/20.26 | | | | | | | | | | | | | | (8493) all_57_11 = e1
% 139.83/20.26 | | | | | | | | | | | | | | (8494) op(e1, e0) = e1
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.83/20.26 | | | | | | | | | | | | | | e1, e1, e0, simplifying with (157), (8487) gives:
% 139.83/20.26 | | | | | | | | | | | | | | (8495) all_52_11 = e1
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.83/20.26 | | | | | | | | | | | | | | e1, e0, e1, simplifying with (160), (8494) gives:
% 139.83/20.26 | | | | | | | | | | | | | | (8496) all_52_14 = e1
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | REDUCE: (121), (8495) imply:
% 139.83/20.26 | | | | | | | | | | | | | | (8497) ~ (all_52_8 = e1)
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | REDUCE: (112), (8496) imply:
% 139.83/20.26 | | | | | | | | | | | | | | (8498) ~ (all_52_12 = e1)
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | REDUCE: (371), (8496) imply:
% 139.83/20.26 | | | | | | | | | | | | | | (8499) ~ (all_10_2 = e1)
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | REDUCE: (7912), (8496) imply:
% 139.83/20.26 | | | | | | | | | | | | | | (8500) ~ (e2 = e1)
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.83/20.26 | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | (8501) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.26 | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.83/20.26 | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.83/20.26 | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.83/20.26 | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.83/20.26 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.26 | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.26 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.83/20.26 | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.83/20.26 | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.83/20.26 | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.83/20.26 | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.83/20.26 | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.26 | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.26 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.83/20.26 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.83/20.26 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.83/20.26 | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.83/20.26 | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.26 | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.83/20.26 | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | BETA: splitting (8501) gives:
% 139.83/20.26 | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | (8502) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.83/20.26 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.26 | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.26 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.83/20.26 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.83/20.26 | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.26 | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.83/20.26 | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.83/20.26 | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.83/20.26 | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.83/20.26 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | ALPHA: (8502) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | (8503) op(e3, e3) = all_56_9
% 139.83/20.26 | | | | | | | | | | | | | | | | (8504) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.83/20.26 | | | | | | | | | | | | | | | | $i(all_56_10))
% 139.83/20.26 | | | | | | | | | | | | | | | | (8505) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 139.83/20.26 | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 139.83/20.26 | | | | | | | | | | | | | | | | (8506) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.83/20.26 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.26 | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.83/20.26 | | | | | | | | | | | | | | | | (8507) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 139.83/20.26 | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.26 | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.26 | | | | | | | | | | | | | | | | (8508) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11
% 139.83/20.26 | | | | | | | | | | | | | | | | = e3) & op(e2, e2) = all_56_11 &
% 139.83/20.26 | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | BETA: splitting (8505) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | (8509) all_56_11 = e3 & op(e2, e2) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | ALPHA: (8509) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | (8510) op(e2, e2) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (7953), (8510), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | (8511) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.83/20.26 | | | | | | | | | | | | | | | | | $i(all_56_3)
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | ALPHA: (8511) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | (8512) ~ (all_56_3 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | (8513) op(e2, e3) = all_56_3
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | BETA: splitting (8507) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | (8514) all_56_6 = e1 & op(e1, e3) = e1
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | ALPHA: (8514) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | (8515) op(e1, e3) = e1
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (8478), (8515), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #332.
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | (8516) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.83/20.26 | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | ALPHA: (8516) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | (8517) ~ (all_56_13 = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | (8518) op(e1, e1) = all_56_13
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | BETA: splitting (8508) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8519) all_56_3 = e2 & op(e2, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | ALPHA: (8519) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8520) op(e2, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8512), (8513), (8520), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8521) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | ALPHA: (8521) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8522) ~ (all_56_11 = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8523) op(e2, e2) = all_56_11
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (7919), (8518)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8524) all_56_13 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (7953), (8523)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8525) all_56_11 = e1
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1, all_56_9,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8480), (8503) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8526) all_56_9 = e1
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | REDUCE: (8517), (8524) imply:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | (8527) ~ (e3 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | (8528) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8528) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8529) all_57_0 = e2 & op(e3, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8529) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8530) op(e3, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8480), (8530), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8531) all_57_2 = e2 & op(e2, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8531) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8532) op(e2, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8512), (8513), (8532), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | (8533) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8533) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8534) all_57_6 = e2 & op(e1, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8534) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8535) all_57_6 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | (8536) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8536) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8537) all_57_6 = e3 & op(e1, e3) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8535), (8537) are inconsistent by sub-proof
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | #916.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8538) all_57_7 = e3 & op(e1, e2) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8538) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8539) all_57_7 = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (7919), (8493), (8535),
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8539), (function-axioms) are inconsistent by
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #34.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | (8540) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8540) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8541) all_57_8 = e3 & op(e1, e1) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8541) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8542) op(e1, e1) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8517), (8518), (8542), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8543) all_57_11 = e3 & op(e1, e0) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8543) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8544) op(e1, e0) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8494), (8544), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8545) all_57_12 = e2 & op(e0, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8545) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8546) all_57_12 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | (8547) op(e0, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | (8548) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8548) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8549) all_57_2 = e2 & op(e2, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8549) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8550) op(e2, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8512), (8513), (8550), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8551) all_57_3 = e2 & op(e2, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8551) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8552) op(e2, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7953), (8552), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | (8553) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8553) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8554) all_57_5 = e2 & op(e2, e1) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8554) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8555) op(e2, e1) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (8555), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8556) all_57_10 = e2 & op(e2, e0) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8556) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8557) all_57_10 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8558) op(e2, e0) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (8547) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8559) all_52_3 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (8558) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8560) all_52_13 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (370), (8560) imply:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8561) ~ (all_10_2 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8561) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | (8562) ~ (all_10_2 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8506) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8563) all_56_10 = e0 & op(e0, e3) = e0
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8563) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8564) op(e0, e3) = e0
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, e0, e3,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | e0, simplifying with (8547), (8564) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8565) e2 = e0
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (8565) imply:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8566) $false
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8566) is inconsistent.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8567) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8567) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8568) ~ (all_56_15 = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | (8569) op(e0, e0) = all_56_15
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | (8570) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8570) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (8571) all_57_0 = e2 & op(e3, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8571) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (8572) op(e3, e3) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (8546), (8572), (function-axioms) are inconsistent
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #50.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (8573) all_57_1 = e2 & op(e3, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8573) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | (8574) op(e3, e2) = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8504) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8575) all_56_15 = e3 & op(e0, e0) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8575) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8576) op(e0, e0) = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8568), (8569), (8576), (function-axioms) are
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #740.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8577) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8577) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8578) op(e0, e3) = all_56_10
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_10_2,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (45), (8569)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8579) all_56_15 = all_10_2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | all_56_10, e3, e0, simplifying with (8547), (8578)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8580) all_56_10 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8574) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8581) all_52_4 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8568), (8579) imply:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8582) ~ (all_10_2 = e3)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (134), (8581) imply:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8583) ~ (all_52_8 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (133), (8581) imply:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8584) ~ (all_52_12 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8584) implies:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8585) ~ (all_52_12 = e2)
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8586) all_54_15 = e3
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8582), (8586) are inconsistent by
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #755.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8587) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8587) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8588) all_54_15 = e2
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (8562), (8588) are inconsistent by
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #754.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8589) all_54_15 = e1 | all_54_15 = e0
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8589) gives:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8590) all_54_15 = e1
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7921), (8590) are inconsistent by
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8591) all_54_15 = e0
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.26 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (8591) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8592) all_10_2 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8592) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8593) all_10_2 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (369), (8593) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8594) ~ (all_52_12 = e0)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8595) all_54_3 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (270), (8595) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8596) all_52_12 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (120), (8596) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8597) ~ (all_52_8 = e3)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (202) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8598) all_54_2 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (8598) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8599) all_52_8 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8597), (8599) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8600) $false
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8600) is inconsistent.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8601) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8601) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8602) all_54_2 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (8602) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8603) all_52_8 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7909), (8603) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8604) $false
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8604) is inconsistent.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8605) all_54_2 = e1 | all_54_2 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8605) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8606) all_54_2 = e1
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (8606) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8607) all_52_8 = e1
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8497), (8607) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8608) $false
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8608) is inconsistent.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8609) all_54_2 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (271), (8609) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8610) all_52_8 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (169), (8610) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8611) op(e3, e1) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8612) ~ (all_34_2 = e1)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8477), (8612) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8613) $false
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (8613) is inconsistent.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8614) ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e1) = all_34_1 & $i(all_34_0) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_34_1)) | ( ~ (all_34_1 = e0) & op(e3, e1)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_34_1 & $i(all_34_1))
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8474) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8615) ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_22_1 & $i(all_22_0) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8615) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8616) op(e3, e1) = all_22_1
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8547), (8611), (8614), (8616), (function-axioms)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #33.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8617) ~ (all_22_1 = e2) & op(e3, e1) = all_22_1 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_22_1)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8617) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8618) op(e3, e1) = all_22_1
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8547), (8611), (8614), (8618), (function-axioms)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #33.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8619) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (270), (8498), (8585), (8594), (8619) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #157.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | (8620) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8620) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (8621) all_57_4 = e2 & op(e3, e1) = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8621) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (8622) all_57_4 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8623) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8623) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8624) all_57_4 = e0 & op(e3, e1) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8622), (8624) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1013.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8625) all_57_5 = e0 & op(e2, e1) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8625) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8626) all_57_5 = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8627) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8627) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8628) all_57_4 = e3 & op(e3, e1) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8628) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8629) all_57_4 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8622), (8629) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #821.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8630) all_57_5 = e3 & op(e2, e1) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8630) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8631) all_57_5 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8626), (8631) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1041.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8632) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8632) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8633) all_57_8 = e3 & op(e1, e1) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8633) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8634) op(e1, e1) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8517), (8518), (8634), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #230.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8635) all_57_14 = e3 & op(e0, e1) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8635) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8636) all_57_14 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8486), (8636) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1045.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8637) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8637) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8638) all_57_8 = e0 & op(e1, e1) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8638) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8639) op(e1, e1) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (8639), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8640) all_57_14 = e0 & op(e0, e1) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8486), (8640) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #786.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (8641) all_57_9 = e2 & op(e3, e0) = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8641) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | (8642) all_57_9 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8643) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8643) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8644) all_57_9 = e3 & op(e3, e0) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8644) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8645) all_57_9 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8642), (8645) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #581.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8646) all_57_10 = e3 & op(e2, e0) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8646) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8647) all_57_10 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8557), (8647) are inconsistent by sub-proof
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #492.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8648) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8648) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8649) all_57_11 = e3 & op(e1, e0) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8649) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8650) op(e1, e0) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (8494), (8650), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8651) all_57_15 = e3 & op(e0, e0) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8651) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8652) op(e0, e0) = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8568), (8569), (8652), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #740.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | (8653) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.83/20.27 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.83/20.27 | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.83/20.27 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.83/20.27 | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.83/20.27 | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.83/20.27 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.83/20.27 | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.83/20.27 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.83/20.27 | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.83/20.27 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | ALPHA: (8653) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | (8654) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.83/20.27 | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.83/20.27 | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | BETA: splitting (8654) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | (8655) all_56_7 = e1 & op(e1, e2) = e1
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | ALPHA: (8655) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | (8656) op(e1, e2) = e1
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7948), (8656), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | (8657) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | ALPHA: (8657) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | (8658) ~ (all_56_13 = e2)
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (8659) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | BETA: splitting (8659) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (8660) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8480), (8660), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (8661) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8661), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (8662) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.83/20.27 | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.27 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | BETA: splitting (8662) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (8663) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | BETA: splitting (8663) gives:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | (8664) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | ALPHA: (8664) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | (8665) op(e3, e3) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8480), (8665), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | (8666) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | ALPHA: (8666) implies:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | (8667) all_56_13 = e2
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | REDUCE: (8658), (8667) imply:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | (8668) $false
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | | CLOSE: (8668) is inconsistent.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (8669) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (39), (45), (51), (7921), (7922), (7924),
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | (7953), (8658), (8669), (function-axioms) are
% 139.83/20.27 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #39.
% 139.83/20.27 | | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | End of split
% 139.83/20.27 | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | Case 2:
% 139.83/20.27 | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | (8670) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.83/20.27 | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.83/20.27 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.27 | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.83/20.27 | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.83/20.27 | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.83/20.27 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.83/20.27 | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.83/20.27 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.83/20.27 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.83/20.27 | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.83/20.27 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.83/20.27 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.83/20.27 | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.83/20.27 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.83/20.27 | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.83/20.27 | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.83/20.27 | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.83/20.27 | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.83/20.27 | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.83/20.27 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.83/20.27 | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | BETA: splitting (8670) gives:
% 139.83/20.27 | | | | | | | | | | | | | | |
% 139.83/20.27 | | | | | | | | | | | | | | | Case 1:
% 139.83/20.27 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | (8671) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.30 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.86/20.30 | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.86/20.30 | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.86/20.30 | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.86/20.30 | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | ALPHA: (8671) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | (8672) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8673) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8674) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.86/20.30 | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8675) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.86/20.30 | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | BETA: splitting (8672) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8676) all_56_15 = e1 & op(e0, e0) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | ALPHA: (8676) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8677) op(e0, e0) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (7921), (8677), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8678) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | $i(all_56_14)
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | ALPHA: (8678) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8679) ~ (all_56_14 = e0)
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8680) op(e0, e1) = all_56_14
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | BETA: splitting (8675) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8681) all_56_4 = e2 & op(e2, e1) = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | ALPHA: (8681) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8682) op(e2, e1) = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (8682), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8683) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | ALPHA: (8683) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8684) ~ (all_56_11 = e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8685) op(e2, e2) = all_56_11
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8686) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (8686) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8687) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8480), (8687), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8688) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8688), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8689) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (39), (45), (51), (165), (7910), (7921),
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (7922), (7924), (7953), (8672), (8673), (8674),
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8675), (8679), (8680), (8684), (8685), (8689),
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | #38.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | (8690) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.30 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.86/20.30 | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.86/20.30 | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.86/20.30 | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.30 | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.86/20.30 | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.86/20.30 | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.86/20.30 | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | ALPHA: (8690) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | (8691) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.86/20.30 | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (8494), (8691), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | inconsistent by sub-proof #54.
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | (8692) all_57_15 = e1 & op(e0, e0) = e1
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | ALPHA: (8692) implies:
% 139.86/20.30 | | | | | | | | | | | | (8693) op(e0, e0) = e1
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | REF_CLOSE: (45), (7921), (8693), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | inconsistent by sub-proof #237.
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | End of split
% 139.86/20.30 | | | | | | | | |
% 139.86/20.30 | | | | | | | | End of split
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | (8694) all_16_2 = e0
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | COMBINE_EQS: (328), (8694) imply:
% 139.86/20.30 | | | | | | | | (8695) all_6_2 = e0
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | REDUCE: (351), (8695) imply:
% 139.86/20.30 | | | | | | | | (8696) ~ (all_52_4 = e0)
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | REDUCE: (355), (8695) imply:
% 139.86/20.30 | | | | | | | | (8697) ~ (all_52_7 = e0)
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | REDUCE: (357), (8695) imply:
% 139.86/20.30 | | | | | | | | (8698) ~ (all_52_9 = e0)
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | REDUCE: (359), (8695) imply:
% 139.86/20.30 | | | | | | | | (8699) ~ (all_52_13 = e0)
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | REDUCE: (7920), (8695) imply:
% 139.86/20.30 | | | | | | | | (8700) ~ (e3 = e0)
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | REDUCE: (39), (8695) imply:
% 139.86/20.30 | | | | | | | | (8701) op(e2, e2) = e0
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | BETA: splitting (64) gives:
% 139.86/20.30 | | | | | | | |
% 139.86/20.30 | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | |
% 139.86/20.30 | | | | | | | | | (8702) ~ (all_22_2 = e1)
% 139.86/20.30 | | | | | | | | |
% 139.86/20.30 | | | | | | | | | REDUCE: (321), (8702) imply:
% 139.86/20.30 | | | | | | | | | (8703) ~ (all_14_2 = e1)
% 139.86/20.30 | | | | | | | | |
% 139.86/20.30 | | | | | | | | | BETA: splitting (67) gives:
% 139.86/20.30 | | | | | | | | |
% 139.86/20.30 | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | (8704) ~ (all_24_2 = e2)
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | REDUCE: (319), (8704) imply:
% 139.86/20.30 | | | | | | | | | | (8705) ~ (all_10_2 = e2)
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (7921), (7922),
% 139.86/20.30 | | | | | | | | | | (8701), (8703), (8705), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | inconsistent by sub-proof #235.
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | (8706) all_24_2 = e2
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | COMBINE_EQS: (319), (8706) imply:
% 139.86/20.30 | | | | | | | | | | (8707) all_10_2 = e2
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | REDUCE: (370), (8707) imply:
% 139.86/20.30 | | | | | | | | | | (8708) ~ (all_52_13 = e2)
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | REDUCE: (45), (8707) imply:
% 139.86/20.30 | | | | | | | | | | (8709) op(e0, e0) = e2
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | BETA: splitting (226) gives:
% 139.86/20.30 | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | (8710) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.86/20.30 | | | | | | | | | | | & op(e2, e2) = e2)
% 139.86/20.30 | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | BETA: splitting (8710) gives:
% 139.86/20.30 | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | (8711) all_57_2 = e2 & op(e2, e3) = e2
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | ALPHA: (8711) implies:
% 139.86/20.30 | | | | | | | | | | | | (8712) all_57_2 = e2
% 139.86/20.30 | | | | | | | | | | | | (8713) op(e2, e3) = e2
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.86/20.30 | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | (8714) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.86/20.30 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.86/20.30 | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | BETA: splitting (8714) gives:
% 139.86/20.30 | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | (8715) all_57_1 = e2 & op(e3, e2) = e2
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | ALPHA: (8715) implies:
% 139.86/20.30 | | | | | | | | | | | | | | (8716) all_57_1 = e2
% 139.86/20.30 | | | | | | | | | | | | | | (8717) op(e3, e2) = e2
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 139.86/20.30 | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8713) gives:
% 139.86/20.30 | | | | | | | | | | | | | | (8718) all_52_1 = e2
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 139.86/20.30 | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8717) gives:
% 139.86/20.30 | | | | | | | | | | | | | | (8719) all_52_4 = e2
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | REDUCE: (146), (8718) imply:
% 139.86/20.30 | | | | | | | | | | | | | | (8720) ~ (all_52_9 = e2)
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | REDUCE: (145), (8718) imply:
% 139.86/20.30 | | | | | | | | | | | | | | (8721) ~ (all_52_13 = e2)
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | REDUCE: (343), (8719) imply:
% 139.86/20.30 | | | | | | | | | | | | | | (8722) ~ (all_14_2 = e2)
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | SIMP: (8722) implies:
% 139.86/20.30 | | | | | | | | | | | | | | (8723) ~ (all_14_2 = e2)
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.86/20.30 | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | (8724) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.30 | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.86/20.30 | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.86/20.30 | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (8697), (8701), (8709), (8713),
% 139.86/20.30 | | | | | | | | | | | | | | | (8724), (function-axioms) are inconsistent by
% 139.86/20.30 | | | | | | | | | | | | | | | sub-proof #974.
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | (8725) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.86/20.30 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.86/20.30 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.86/20.30 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.86/20.30 | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.86/20.30 | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.86/20.30 | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.86/20.30 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | BETA: splitting (8725) gives:
% 139.86/20.30 | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | (8726) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.30 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.86/20.30 | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.86/20.30 | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.86/20.30 | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.86/20.30 | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.86/20.30 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | ALPHA: (8726) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | (8727) op(e1, e1) = all_56_13
% 139.86/20.30 | | | | | | | | | | | | | | | | (8728) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8729) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.30 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8730) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.86/20.30 | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8731) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 139.86/20.30 | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8732) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.86/20.30 | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.30 | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.86/20.30 | | | | | | | | | | | | | | | | (8733) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.86/20.30 | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | BETA: splitting (8730) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8734) all_56_11 = e1 & op(e2, e2) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | ALPHA: (8734) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8735) all_56_11 = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (8732), (8735), (function-axioms)
% 139.86/20.30 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #91.
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8736) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | $i(all_56_4)
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | ALPHA: (8736) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | (8737) op(e2, e1) = all_56_4
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | BETA: splitting (8728) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8738) all_56_15 = e1 & op(e0, e0) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | ALPHA: (8738) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8739) op(e0, e0) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8709), (8739), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8740) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | ALPHA: (8740) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8741) ~ (all_56_14 = e0)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | (8742) op(e0, e1) = all_56_14
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | BETA: splitting (8732) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8743) all_56_4 = e2 & op(e2, e1) = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | ALPHA: (8743) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8744) op(e2, e1) = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8701), (8730), (8744), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #950.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8745) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | ALPHA: (8745) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8746) ~ (all_56_11 = e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | (8747) op(e2, e2) = all_56_11
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | BETA: splitting (8729) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8748) all_56_14 = e0 & op(e0, e1) = e0
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (8748) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8749) op(e0, e1) = e0
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8741), (8742), (8749), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #973.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8750) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | ALPHA: (8750) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8751) ~ (all_56_15 = e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | (8752) op(e0, e0) = all_56_15
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | BETA: splitting (8731) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (8753) all_56_9 = e1 & op(e3, e3) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8753) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (8754) op(e3, e3) = e1
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (118), (121), (123), (157), (165), (169),
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (190), (198), (247), (261), (7911), (8698),
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (8701), (8730), (8733), (8741), (8742), (8754),
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | #757.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (8755) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | ALPHA: (8755) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (8756) ~ (all_56_1 = e3)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | (8757) op(e3, e1) = all_56_1
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (204) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | (8758) all_54_0 = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (279), (8758) imply:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | (8759) all_14_2 = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (345), (8759) imply:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | (8760) ~ (all_52_8 = e3)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (347), (8759) imply:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | (8761) ~ (all_52_12 = e3)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | (8762) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8762) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | (8763) all_57_0 = e3 & op(e3, e3) = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8763) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | (8764) all_57_0 = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | (8765) op(e3, e3) = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8733) gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8766) all_56_1 = e3 & op(e3, e1) = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8766) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8767) op(e3, e1) = e3
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8760), (8767), (function-axioms) are
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1106.
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8768) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8768) implies:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8769) ~ (all_56_9 = e1)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8770) op(e3, e3) = all_56_9
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (8709), (8752)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8771) all_56_15 = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_14, e1, e0, simplifying with (157), (8742)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8772) all_56_14 = all_52_11
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (7919), (8727)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8773) all_56_13 = e2
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e1, e2, simplifying with (165), (8737)
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | | (8774) all_56_4 = all_52_9
% 139.86/20.30 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e0,
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (8701), (8747)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | (8775) all_56_11 = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, e1, e3, simplifying with (169), (8757)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | (8776) all_56_1 = all_52_8
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_56_9,
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (8765), (8770) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | (8777) all_56_9 = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8746), (8775) imply:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | (8778) ~ (e1 = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8741), (8772) imply:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | (8779) ~ (all_52_11 = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (8780) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8780) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8781) all_57_4 = e0 & op(e3, e1) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8781) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8782) all_57_4 = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8783) op(e3, e1) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8784) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8784) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8785) all_57_0 = e1 & op(e3, e3) = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8785) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8786) op(e3, e3) = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8769), (8770), (8786), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #758.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8787) all_57_1 = e1 & op(e3, e2) = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8787) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8788) all_57_1 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8716), (8788) imply:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8789) e2 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8771), (8789) imply:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8790) all_56_15 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (8729), (8779), (8790), (function-axioms)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #432.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8791) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8791) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8792) all_57_4 = e1 & op(e3, e1) = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8782), (8792) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #74.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8793) all_57_9 = e1 & op(e3, e0) = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8793) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8794) all_57_9 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8795) all_57_15 = e0 & op(e0, e0) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8795) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8796) op(e0, e0) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8709), (8796), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8797) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8797) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8798) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8799) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0) = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8798) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8800) all_57_12 = e0 & op(e0, e3) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8800) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8801) all_57_12 = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8802) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8802) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8803) all_57_6 = e3 & op(e1, e3) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (169), (234), (8712), (8733), (8760),
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8764), (8777), (8801), (8803), (function-axioms)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #895.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8804) all_57_7 = e3 & op(e1, e2) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8804) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8805) op(e1, e2) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (79), (162), (169), (7905), (7906), (8783),
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8805), (function-axioms) are inconsistent by
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #32.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8806) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8806) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8807) all_57_8 = e3 & op(e1, e1) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8807) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8808) op(e1, e1) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8808), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8809) all_57_11 = e3 & op(e1, e0) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8809) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8810) all_57_11 = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8799) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8811) all_57_9 = e0 & op(e3, e0) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8794), (8811) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #813.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8812) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8812) gives:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8813) all_57_10 = e0 & op(e2, e0) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8699), (8813), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1078.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8814) all_57_11 = e0 & op(e1, e0) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8814) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8815) all_57_11 = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8810), (8815) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #858.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8816) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (158), (8697), (8779), (8816),
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #885.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8817) all_57_5 = e0 & op(e2, e1) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8817) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8818) op(e2, e1) = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8698), (8818), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1091.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (8819) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (7919), (8779), (8819),
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | | #60.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | (8820) all_57_1 = e3 & op(e3, e2) = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8716), (8820) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | | #842.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | (8821) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (169), (8760), (8761), (8821),
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | | #1104.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | (8822) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (279), (7922), (8703), (8723), (8822) are
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | (8823) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.31 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.86/20.31 | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.31 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.86/20.31 | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.86/20.31 | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.86/20.31 | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.86/20.31 | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.31 | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.86/20.31 | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.86/20.31 | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.86/20.31 | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.86/20.31 | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.86/20.31 | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.86/20.31 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.86/20.31 | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | ALPHA: (8823) implies:
% 139.86/20.31 | | | | | | | | | | | | | | | | (8824) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.86/20.31 | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.86/20.31 | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.86/20.31 | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8701), (8708), (8824), (function-axioms)
% 139.86/20.31 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #856.
% 139.86/20.31 | | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8825) all_57_3 = e2 & op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | ALPHA: (8825) implies:
% 139.86/20.31 | | | | | | | | | | | | | | (8826) op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (5), (8701), (8826), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | (8827) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.86/20.31 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | BETA: splitting (8827) gives:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8828) all_57_7 = e2 & op(e1, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (8828), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8829) all_57_13 = e2 & op(e0, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 139.86/20.31 | | | | | | | | | | | | | | (212), (8697), (8709), (8829), (function-axioms)
% 139.86/20.31 | | | | | | | | | | | | | | are inconsistent by sub-proof #825.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8830) all_57_3 = e2 & op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | ALPHA: (8830) implies:
% 139.86/20.31 | | | | | | | | | | | | (8831) op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (5), (8701), (8831), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | (8832) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.86/20.31 | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | REF_CLOSE: (164), (165), (7910), (8708), (8832),
% 139.86/20.31 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | #887.
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | (8833) all_22_2 = e1
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | COMBINE_EQS: (321), (8833) imply:
% 139.86/20.31 | | | | | | | | | (8834) all_14_2 = e1
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | REDUCE: (343), (8834) imply:
% 139.86/20.31 | | | | | | | | | (8835) ~ (all_52_4 = e1)
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | REDUCE: (51), (8834) imply:
% 139.86/20.31 | | | | | | | | | (8836) op(e3, e3) = e1
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | BETA: splitting (67) gives:
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | (8837) ~ (all_24_2 = e2)
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | REDUCE: (319), (8837) imply:
% 139.86/20.31 | | | | | | | | | | (8838) ~ (all_10_2 = e2)
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | BETA: splitting (207) gives:
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | (8839) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.86/20.31 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.86/20.31 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.86/20.31 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.86/20.31 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.86/20.31 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.86/20.31 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.86/20.31 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.86/20.31 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.86/20.31 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.86/20.31 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.86/20.31 | | | | | | | | | | | $i(all_56_6))
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | BETA: splitting (8839) gives:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8840) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.86/20.31 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.86/20.31 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.86/20.31 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.86/20.31 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.86/20.31 | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (6), (8836), (8840), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | inconsistent by sub-proof #298.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8841) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 139.86/20.31 | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 139.86/20.31 | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 139.86/20.31 | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 139.86/20.31 | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (9), (7919), (8841), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | inconsistent by sub-proof #76.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | (8842) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.86/20.31 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.86/20.31 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.86/20.31 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.86/20.31 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.86/20.31 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.86/20.31 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.86/20.31 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.86/20.31 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.86/20.31 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.86/20.31 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.86/20.31 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.86/20.31 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.86/20.31 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.86/20.31 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.86/20.31 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.86/20.31 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.86/20.31 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.86/20.31 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.31 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.86/20.31 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.86/20.31 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.31 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.86/20.31 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | BETA: splitting (8842) gives:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8843) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.86/20.31 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.86/20.31 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.86/20.31 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.86/20.31 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (4), (8701), (8836), (8843), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | inconsistent by sub-proof #217.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8844) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.86/20.31 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.86/20.31 | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.86/20.31 | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.86/20.31 | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.86/20.31 | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.86/20.31 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.86/20.31 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.86/20.31 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.86/20.31 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.86/20.31 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.86/20.31 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.31 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.86/20.31 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.31 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (4), (45), (51), (7921), (7922), (8701), (8838),
% 139.86/20.31 | | | | | | | | | | | | (8844), (function-axioms) are inconsistent by
% 139.86/20.31 | | | | | | | | | | | | sub-proof #236.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | (8845) all_24_2 = e2
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | COMBINE_EQS: (319), (8845) imply:
% 139.86/20.31 | | | | | | | | | | (8846) all_10_2 = e2
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | SIMP: (8846) implies:
% 139.86/20.31 | | | | | | | | | | (8847) all_10_2 = e2
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | REDUCE: (370), (8847) imply:
% 139.86/20.31 | | | | | | | | | | (8848) ~ (all_52_13 = e2)
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | REDUCE: (45), (8847) imply:
% 139.86/20.31 | | | | | | | | | | (8849) op(e0, e0) = e2
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | BETA: splitting (226) gives:
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | (8850) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 139.86/20.31 | | | | | | | | | | | & op(e2, e2) = e2)
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | BETA: splitting (8850) gives:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8851) all_57_2 = e2 & op(e2, e3) = e2
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | ALPHA: (8851) implies:
% 139.86/20.31 | | | | | | | | | | | | (8852) op(e2, e3) = e2
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | (8853) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.86/20.31 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | BETA: splitting (8853) gives:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8854) all_57_1 = e2 & op(e3, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | ALPHA: (8854) implies:
% 139.86/20.31 | | | | | | | | | | | | | | (8855) op(e3, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 139.86/20.31 | | | | | | | | | | | | | | e3, e2, simplifying with (167), (8852) gives:
% 139.86/20.31 | | | | | | | | | | | | | | (8856) all_52_1 = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 139.86/20.31 | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8855) gives:
% 139.86/20.31 | | | | | | | | | | | | | | (8857) all_52_4 = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REDUCE: (145), (8856) imply:
% 139.86/20.31 | | | | | | | | | | | | | | (8858) ~ (all_52_13 = e2)
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | (8859) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.31 | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.86/20.31 | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.86/20.31 | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (8697), (8701), (8849), (8852),
% 139.86/20.31 | | | | | | | | | | | | | | | (8859), (function-axioms) are inconsistent by
% 139.86/20.31 | | | | | | | | | | | | | | | sub-proof #974.
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | (8860) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.86/20.31 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.86/20.31 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.86/20.31 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.86/20.31 | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.86/20.31 | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.86/20.31 | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.86/20.31 | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.86/20.31 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (118), (121), (123), (157), (164),
% 139.86/20.31 | | | | | | | | | | | | | | | (165), (169), (190), (198), (247), (261), (7911),
% 139.86/20.31 | | | | | | | | | | | | | | | (8698), (8701), (8836), (8848), (8849), (8860),
% 139.86/20.31 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | | #213.
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8861) all_57_3 = e2 & op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | ALPHA: (8861) implies:
% 139.86/20.31 | | | | | | | | | | | | | | (8862) op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (5), (8701), (8862), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | (8863) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.86/20.31 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | BETA: splitting (8863) gives:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8864) all_57_7 = e2 & op(e1, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (8864), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8865) all_57_13 = e2 & op(e0, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (158), (209), (210),
% 139.86/20.31 | | | | | | | | | | | | | | (212), (8697), (8849), (8865), (function-axioms)
% 139.86/20.31 | | | | | | | | | | | | | | are inconsistent by sub-proof #825.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8866) all_57_3 = e2 & op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | ALPHA: (8866) implies:
% 139.86/20.31 | | | | | | | | | | | | (8867) op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (5), (8701), (8867), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | inconsistent by sub-proof #1076.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | (8868) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 139.86/20.31 | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | REF_CLOSE: (164), (165), (7910), (8848), (8868),
% 139.86/20.31 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | #887.
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | End of split
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | End of split
% 139.86/20.31 | | | | | | | |
% 139.86/20.31 | | | | | | | End of split
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | Case 2:
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | (8869) all_14_2 = e0
% 139.86/20.31 | | | | | | | (8870) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 &
% 139.86/20.31 | | | | | | | op(e3, e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)) |
% 139.86/20.31 | | | | | | | ( ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 &
% 139.86/20.31 | | | | | | | $i(all_14_1))
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | COMBINE_EQS: (315), (8869) imply:
% 139.86/20.31 | | | | | | | (8871) all_28_2 = e0
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | REDUCE: (337), (8869) imply:
% 139.86/20.31 | | | | | | | (8872) ~ (all_52_1 = e0)
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | REDUCE: (339), (8869) imply:
% 139.86/20.31 | | | | | | | (8873) ~ (all_52_2 = e0)
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | REDUCE: (341), (8869) imply:
% 139.86/20.31 | | | | | | | (8874) ~ (all_52_3 = e0)
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | REDUCE: (343), (8869) imply:
% 139.86/20.31 | | | | | | | (8875) ~ (all_52_4 = e0)
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | REDUCE: (345), (8869) imply:
% 139.86/20.31 | | | | | | | (8876) ~ (all_52_8 = e0)
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | REDUCE: (347), (8869) imply:
% 139.86/20.31 | | | | | | | (8877) ~ (all_52_12 = e0)
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | BETA: splitting (232) gives:
% 139.86/20.31 | | | | | | |
% 139.86/20.31 | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | |
% 139.86/20.31 | | | | | | | | (8878) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 139.86/20.31 | | | | | | | | op(e2, e3) = e0)
% 139.86/20.31 | | | | | | | |
% 139.86/20.31 | | | | | | | | BETA: splitting (8878) gives:
% 139.86/20.31 | | | | | | | |
% 139.86/20.31 | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | (8879) all_57_0 = e0 & op(e3, e3) = e0
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | ALPHA: (8879) implies:
% 139.86/20.31 | | | | | | | | | (8880) all_57_0 = e0
% 139.86/20.31 | | | | | | | | | (8881) op(e3, e3) = e0
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | BETA: splitting (55) gives:
% 139.86/20.31 | | | | | | | | |
% 139.86/20.31 | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | (8882) ~ (all_16_2 = e0)
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | REDUCE: (328), (8882) imply:
% 139.86/20.31 | | | | | | | | | | (8883) ~ (all_6_2 = e0)
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | BETA: splitting (61) gives:
% 139.86/20.31 | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | (8884) ~ (all_20_2 = e1)
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | REDUCE: (283), (8884) imply:
% 139.86/20.31 | | | | | | | | | | | (8885) ~ (all_6_2 = e1)
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | BETA: splitting (199) gives:
% 139.86/20.31 | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8886) all_54_5 = e3
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | REF_CLOSE: (268), (7920), (8886) are inconsistent by
% 139.86/20.31 | | | | | | | | | | | | sub-proof #318.
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | (8887) ~ (all_54_5 = e3)
% 139.86/20.31 | | | | | | | | | | | | (8888) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | BETA: splitting (8888) gives:
% 139.86/20.31 | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | (8889) all_54_5 = e2
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | COMBINE_EQS: (268), (8889) imply:
% 139.86/20.31 | | | | | | | | | | | | | (8890) all_6_2 = e2
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | SIMP: (8890) implies:
% 139.86/20.31 | | | | | | | | | | | | | (8891) all_6_2 = e2
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | REDUCE: (348), (8891) imply:
% 139.86/20.31 | | | | | | | | | | | | | (8892) ~ (all_52_1 = e2)
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | REDUCE: (351), (8891) imply:
% 139.86/20.31 | | | | | | | | | | | | | (8893) ~ (all_52_4 = e2)
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | REDUCE: (7920), (8891) imply:
% 139.86/20.31 | | | | | | | | | | | | | (8894) ~ (e3 = e2)
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | REDUCE: (39), (8891) imply:
% 139.86/20.31 | | | | | | | | | | | | | (8895) op(e2, e2) = e2
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.86/20.31 | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8896) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 139.86/20.31 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | REF_CLOSE: (5), (167), (8881), (8892), (8896),
% 139.86/20.31 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.31 | | | | | | | | | | | | | | #707.
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | (8897) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 139.86/20.31 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | BETA: splitting (8897) gives:
% 139.86/20.31 | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | Case 1:
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | (8898) all_57_6 = e2 & op(e1, e3) = e2
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | | REF_CLOSE: (163), (7907), (8898), (function-axioms) are
% 139.86/20.31 | | | | | | | | | | | | | | | inconsistent by sub-proof #79.
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.31 | | | | | | | | | | | | | | Case 2:
% 139.86/20.31 | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | (8899) all_57_12 = e2 & op(e0, e3) = e2
% 139.86/20.32 | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | ALPHA: (8899) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | (8900) all_57_12 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | (8901) op(e0, e3) = e2
% 139.86/20.32 | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | BETA: splitting (237) gives:
% 139.86/20.32 | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | (8902) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | & op(e3, e2) = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | BETA: splitting (8902) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8903) all_57_0 = e2 & op(e3, e3) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | ALPHA: (8903) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8904) op(e3, e3) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8900), (8904), (function-axioms) are inconsistent
% 139.86/20.32 | | | | | | | | | | | | | | | | | by sub-proof #50.
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8905) all_57_1 = e2 & op(e3, e2) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | ALPHA: (8905) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8906) op(e3, e2) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 139.86/20.32 | | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (8906) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8907) all_52_4 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | REDUCE: (8893), (8907) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8908) $false
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | CLOSE: (8908) is inconsistent.
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | (8909) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | & op(e3, e0) = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | BETA: splitting (8909) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8910) all_57_4 = e2 & op(e3, e1) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | ALPHA: (8910) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8911) op(e3, e1) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e2,
% 139.86/20.32 | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (8911) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8912) all_52_8 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | REDUCE: (7909), (8912) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8913) $false
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | CLOSE: (8913) is inconsistent.
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8914) all_57_9 = e2 & op(e3, e0) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | ALPHA: (8914) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8915) all_57_9 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8916) op(e3, e0) = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_3, e2,
% 139.86/20.32 | | | | | | | | | | | | | | | | | e3, e0, simplifying with (159), (8901) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8917) all_52_3 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.86/20.32 | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (168), (8916) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8918) all_52_12 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | REDUCE: (113), (8918) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8919) ~ (all_52_13 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | SIMP: (8919) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8920) ~ (all_52_13 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | REDUCE: (112), (8918) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8921) ~ (all_52_14 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | REDUCE: (369), (8918) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8922) ~ (all_10_2 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | SIMP: (8922) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | (8923) ~ (all_10_2 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | (8924) ~ (all_28_2 = e0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | REDUCE: (8871), (8924) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | (8925) $false
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | CLOSE: (8925) is inconsistent.
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | (8926) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | & op(e3, e0) = all_28_1 & $i(all_28_0) &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | = all_28_1 & $i(all_28_1))
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | BETA: splitting (8926) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (8927) ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_28_1 & $i(all_28_0) &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | ALPHA: (8927) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (8928) ~ (all_28_0 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (8929) op(e3, e0) = all_28_1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (8930) op(all_28_1, e3) = all_28_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (8870) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8931) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_14_1 & $i(all_14_0) &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (8931) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8932) ~ (all_14_0 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8933) op(e3, e0) = all_14_1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8934) op(all_14_1, e3) = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_28_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (8916), (8929) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8935) all_28_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | all_28_1, e0, e3, simplifying with (8929), (8933)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8936) all_28_1 = all_14_1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8935), (8936) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8937) all_14_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (8937) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8938) all_14_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (8930), (8935) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8939) op(e2, e3) = all_28_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (8934), (8938) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8940) op(e2, e3) = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | all_14_0, e3, e2, simplifying with (167), (8940)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8941) all_52_1 = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | all_28_0, e3, e2, simplifying with (167), (8939)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8942) all_52_1 = all_28_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8941), (8942) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8943) all_28_0 = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (8943) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8944) all_28_0 = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (8941) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8945) all_54_4 = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (8941) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8946) ~ (all_52_2 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (8946) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8947) ~ (all_52_2 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (8941) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8948) ~ (all_52_9 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (8948) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8949) ~ (all_52_9 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (8941) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8950) ~ (all_52_13 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (8950) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8951) ~ (all_52_13 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (8872), (8941) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8952) ~ (all_14_0 = e0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (8928), (8944) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (8953) ~ (all_14_0 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (8954) all_54_4 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8945), (8954) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (8955) all_14_0 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | SIMP: (8955) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (8956) all_14_0 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (8947), (8956) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (8957) ~ (all_52_2 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (8949), (8956) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (8958) ~ (all_52_9 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (8951), (8956) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (8959) ~ (all_52_13 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | (8960) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8960) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (8961) all_57_2 = e3 & op(e2, e3) = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8961) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (8962) all_57_2 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | (8963) all_54_8 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8957), (8963) are inconsistent by
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | (8964) ~ (all_54_8 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | (8965) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | (8966) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8966) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8967) all_57_0 = e1 & op(e3, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8967) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8968) op(e3, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8881), (8968), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8969) all_57_2 = e1 & op(e2, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8969) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8970) op(e2, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8932), (8939), (8940), (8970), (function-axioms)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #329.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | (8971) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8971) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8972) all_57_6 = e1 & op(e1, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8972) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8973) all_57_6 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8965) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8974) all_54_8 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7907), (8974) are inconsistent by
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #988.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8975) ~ (all_54_8 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (8976) all_54_8 = e1 | all_54_8 = e0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8976) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8977) all_54_8 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (8977) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8978) all_52_2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8978) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8979) all_52_2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (8979) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8980) ~ (all_52_6 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8980) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8981) ~ (all_52_6 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (8979) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8982) ~ (all_52_14 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8982) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8983) ~ (all_52_14 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (8957), (8979) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8984) ~ (e3 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7907), (8979) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8985) ~ (e2 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (8979) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8986) op(e1, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8987) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (8987) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8988) all_57_9 = e1 & op(e3, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8988) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8989) all_57_9 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8990) op(e3, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8915), (8989) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8991) e2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (8991) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8992) e2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (8900), (8992) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8993) all_57_12 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (73), (163), (168),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (236), (238), (8870), (8871), (8880), (8881),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8973), (8990), (8993), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #606.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8994) all_57_10 = e1 & op(e2, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8994) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8995) all_57_10 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8996) op(e2, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (45), (94), (100), (110),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (118), (126), (157), (159), (162), (163),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (189), (193), (206), (207),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (212), (214), (215), (219), (224),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (234), (246), (250), (297), (303), (370),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371), (7910), (7912), (7919), (7921), (8872),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8881), (8895), (8900), (8901), (8916), (8920),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8923), (8957), (8958), (8959), (8962), (8973),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8981), (8986), (8995), (8996), (function-axioms)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #23.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8997) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (160), (7921), (8983), (8997),
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #22.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8998) all_54_8 = e0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8873), (8998) are inconsistent by
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #792.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (8999) all_57_12 = e1 & op(e0, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (8999) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9000) all_57_12 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8900), (9000) are inconsistent by sub-proof
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | #970.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (9001) all_57_3 = e3 & op(e2, e2) = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9001) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (9002) op(e2, e2) = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8895), (9002), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | (9003) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9003) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (9004) all_57_5 = e3 & op(e2, e1) = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (8958), (9004), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (9005) all_57_10 = e3 & op(e2, e0) = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (8959), (9005), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #81.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9006) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8932), (8945), (8952), (8953), (9006) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9007) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8916), (8929), (9007), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (9008) ~ (all_28_1 = e1) & op(e3, e0) = all_28_1 &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | $i(all_28_1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | ALPHA: (9008) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (9009) ~ (all_28_1 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | (9010) op(e3, e0) = all_28_1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | BETA: splitting (8870) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9011) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | op(e3, e0) = all_14_1 & $i(all_14_0) &
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | ALPHA: (9011) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9012) ~ (all_14_0 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9013) op(e3, e0) = all_14_1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9014) op(all_14_1, e3) = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_28_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (8916), (9010) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9015) all_28_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_14_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | all_28_1, e0, e3, simplifying with (9010), (9013)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9016) all_28_1 = all_14_1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9015), (9016) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9017) all_14_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (9017) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9018) all_14_1 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (9014), (9018) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9019) op(e2, e3) = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1,
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | all_14_0, e3, e2, simplifying with (167), (9019)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9020) all_52_1 = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (269), (9020) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9021) all_54_4 = all_14_0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (149), (9020) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9022) ~ (all_52_2 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (9022) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9023) ~ (all_52_2 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (146), (9020) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9024) ~ (all_52_9 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (9024) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9025) ~ (all_52_9 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (145), (9020) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9026) ~ (all_52_13 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | SIMP: (9026) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9027) ~ (all_52_13 = all_14_0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (8892), (9020) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9028) ~ (all_14_0 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | REDUCE: (8872), (9020) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | (9029) ~ (all_14_0 = e0)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | BETA: splitting (200) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9030) all_54_4 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9021), (9030) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9031) all_14_0 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | SIMP: (9031) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9032) all_14_0 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9023), (9032) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9033) ~ (all_52_2 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9025), (9032) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9034) ~ (all_52_9 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | REDUCE: (9027), (9032) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | (9035) ~ (all_52_13 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (227) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | (9036) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9036) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (9037) all_57_2 = e3 & op(e2, e3) = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9037) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | (9038) all_57_2 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | (9039) all_54_8 = e3
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (9033), (9039) are inconsistent by
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #989.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | (9040) ~ (all_54_8 = e3)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | (9041) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | (9042) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9042) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9043) all_57_0 = e1 & op(e3, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9043) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9044) op(e3, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8881), (9044), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9045) all_57_2 = e1 & op(e2, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9045) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9046) op(e2, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9012), (9019), (9046), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #327.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | (9047) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9047) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9048) all_57_6 = e1 & op(e1, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9048) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | (9049) all_57_6 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9041) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9050) all_54_8 = e2
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (7907), (9050) are inconsistent by
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #988.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9051) ~ (all_54_8 = e2)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9052) all_54_8 = e1 | all_54_8 = e0
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9052) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9053) all_54_8 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (259), (9053) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9054) all_52_2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9054) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9055) all_52_2 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (143), (9055) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9056) ~ (all_52_6 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9056) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9057) ~ (all_52_6 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (141), (9055) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9058) ~ (all_52_14 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9058) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9059) ~ (all_52_14 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9033), (9055) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9060) ~ (e3 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (7907), (9055) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9061) ~ (e2 = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (9055) imply:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9062) op(e1, e3) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9063) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9063) gives:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9064) all_57_9 = e1 & op(e3, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9064) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9065) op(e3, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9009), (9010), (9065), (function-axioms) are
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #685.
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9066) all_57_10 = e1 & op(e2, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9066) implies:
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9067) all_57_10 = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9068) op(e2, e0) = e1
% 139.86/20.32 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (45), (94), (100), (110),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (117), (118), (126), (157), (159), (162), (163),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (164), (165), (167), (189), (193), (206), (207),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (209), (210), (212), (214), (215), (219), (224),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (232), (234), (246), (250), (297), (303), (370),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (371), (7910), (7912), (7919), (7921), (8872),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8881), (8895), (8900), (8901), (8916), (8920),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (8923), (9033), (9034), (9035), (9038), (9049),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9057), (9062), (9067), (9068), (function-axioms)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #23.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9069) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (160), (7921), (9059), (9069),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #22.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9070) all_54_8 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (259), (8873), (9070) are inconsistent by
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #792.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (9071) all_57_12 = e1 & op(e0, e3) = e1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9071) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | (9072) all_57_12 = e1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8900), (9072) are inconsistent by sub-proof
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | | #970.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9073) all_57_3 = e3 & op(e2, e2) = e3
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9073) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9074) op(e2, e2) = e3
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (8895), (9074), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9075) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9075) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9076) all_57_5 = e3 & op(e2, e1) = e3
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9034), (9076), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9077) all_57_10 = e3 & op(e2, e0) = e3
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9035), (9077), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #81.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | (9078) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9012), (9021), (9028), (9029), (9078) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #21.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | (9079) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | $i(all_14_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8916), (9010), (9079), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #328.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | (9080) all_54_5 = e1 | all_54_5 = e0
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | REF_CLOSE: (268), (8883), (8885), (9080) are inconsistent by
% 139.86/20.33 | | | | | | | | | | | | | sub-proof #641.
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | (9081) all_20_2 = e1
% 139.86/20.33 | | | | | | | | | | | (9082) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0
% 139.86/20.33 | | | | | | | | | | | & op(e2, e1) = all_20_1 & $i(all_20_0) &
% 139.86/20.33 | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1)
% 139.86/20.33 | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | COMBINE_EQS: (283), (9081) imply:
% 139.86/20.33 | | | | | | | | | | | (9083) all_6_2 = e1
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | SIMP: (9083) implies:
% 139.86/20.33 | | | | | | | | | | | (9084) all_6_2 = e1
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | COMBINE_EQS: (332), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9085) all_38_2 = e1
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (348), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9086) ~ (all_52_1 = e1)
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (351), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9087) ~ (all_52_4 = e1)
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (353), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9088) ~ (all_52_6 = e1)
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (355), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9089) ~ (all_52_7 = e1)
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (359), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9090) ~ (all_52_13 = e1)
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (7920), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9091) ~ (e3 = e1)
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | REDUCE: (39), (9084) imply:
% 139.86/20.33 | | | | | | | | | | | (9092) op(e2, e2) = e1
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | BETA: splitting (67) gives:
% 139.86/20.33 | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | (9093) ~ (all_24_2 = e2)
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | REDUCE: (319), (9093) imply:
% 139.86/20.33 | | | | | | | | | | | | (9094) ~ (all_10_2 = e2)
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | BETA: splitting (79) gives:
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | (9095) ~ (all_32_2 = e2)
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | REDUCE: (7906), (9095) imply:
% 139.86/20.33 | | | | | | | | | | | | | (9096) $false
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | CLOSE: (9096) is inconsistent.
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | (9097) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0
% 139.86/20.33 | | | | | | | | | | | | | & op(e1, e2) = all_32_1 & $i(all_32_0) &
% 139.86/20.33 | | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2)
% 139.86/20.33 | | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | BETA: splitting (88) gives:
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | (9098) ~ (all_38_2 = e1)
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | REDUCE: (9085), (9098) imply:
% 139.86/20.33 | | | | | | | | | | | | | | (9099) $false
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | CLOSE: (9099) is inconsistent.
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | (9100) ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0
% 139.86/20.33 | | | | | | | | | | | | | | & op(e2, e1) = all_38_1 & $i(all_38_0) &
% 139.86/20.33 | | | | | | | | | | | | | | $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e2, e1)
% 139.86/20.33 | | | | | | | | | | | | | | = all_38_1 & $i(all_38_1))
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | (9101) ~ (all_42_2 = e3)
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | REDUCE: (303), (9101) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | (9102) ~ (all_10_2 = e3)
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | (9103) all_54_15 = e3
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | REF_CLOSE: (246), (9102), (9103) are inconsistent by
% 139.86/20.33 | | | | | | | | | | | | | | | | sub-proof #755.
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | (9104) ~ (all_54_15 = e3)
% 139.86/20.33 | | | | | | | | | | | | | | | | (9105) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | BETA: splitting (9105) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9106) all_54_15 = e2
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (9094), (9106) are inconsistent by
% 139.86/20.33 | | | | | | | | | | | | | | | | | sub-proof #754.
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9107) ~ (all_54_15 = e2)
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9108) all_54_15 = e1 | all_54_15 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | BETA: splitting (9108) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9109) all_54_15 = e1
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7921), (9109) are inconsistent by
% 139.86/20.33 | | | | | | | | | | | | | | | | | | sub-proof #748.
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9110) all_54_15 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (9110) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9111) all_10_2 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | SIMP: (9111) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9112) all_10_2 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | REDUCE: (361), (9112) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9113) ~ (all_52_7 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | REDUCE: (368), (9112) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9114) ~ (all_52_11 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | REDUCE: (9102), (9112) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9115) ~ (e3 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | REDUCE: (9094), (9112) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9116) ~ (e2 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | REDUCE: (7921), (9112) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | (9117) ~ (e1 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | BETA: splitting (228) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | (9118) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (170), (8875), (9092), (9118),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | #1062.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | (9119) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | BETA: splitting (9119) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | (9120) all_57_7 = e0 & op(e1, e2) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (9120) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | (9121) op(e1, e2) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | (9122) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9122) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9123) all_57_4 = e0 & op(e3, e1) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (8876), (9123), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #981.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9124) all_57_5 = e0 & op(e2, e1) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9124) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9125) all_57_5 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9126) op(e2, e1) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | e2, e1, simplifying with (162), (9121) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9127) all_52_6 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (9126) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9128) all_52_9 = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (128), (9127) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | (9129) ~ (all_52_7 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (7905) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9130) ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_4_1 & $i(all_4_0) & $i(all_4_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9130) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9131) op(e1, e2) = all_4_1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9097) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9132) ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_32_1 & $i(all_32_0) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9132) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9133) op(e1, e2) = all_32_1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (134), (135), (158), (169), (191),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (203), (223), (248), (272), (7905), (7919),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (8875), (9082), (9087), (9089), (9100), (9113),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9121), (9125), (9126), (9131), (9133),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | #16.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9134) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9134) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9135) op(e1, e2) = all_32_1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (134), (135), (158), (169), (191),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (203), (223), (248), (272), (7905), (7919),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (8875), (9082), (9087), (9089), (9100), (9113),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9121), (9125), (9126), (9131), (9135),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | #16.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9136) ~ (all_4_1 = e0) & op(e1, e2) = all_4_1 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | $i(all_4_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9136) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9137) ~ (all_4_1 = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | (9138) op(e1, e2) = all_4_1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9097) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9139) ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e2) = all_32_1 & $i(all_32_0) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9139) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9140) op(e1, e2) = all_32_1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9121), (9137), (9138), (9140), (function-axioms)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #58.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9141) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_32_1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9141) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | (9142) op(e1, e2) = all_32_1
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9121), (9137), (9138), (9142), (function-axioms)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #58.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | (9143) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (157), (7919), (9114), (9143),
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | | #60.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | (9144) all_57_13 = e0 & op(e0, e2) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | ALPHA: (9144) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | (9145) op(e0, e2) = e0
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9113), (9145), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #977.
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | (9146) all_42_2 = e3
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | COMBINE_EQS: (303), (9146) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | (9147) all_10_2 = e3
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | REDUCE: (369), (9147) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | (9148) ~ (all_52_12 = e3)
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | REDUCE: (45), (9147) imply:
% 139.86/20.33 | | | | | | | | | | | | | | | (9149) op(e0, e0) = e3
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | (9150) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.33 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.86/20.33 | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.86/20.33 | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | BETA: splitting (9150) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9151) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.86/20.33 | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.86/20.33 | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | ALPHA: (9151) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9152) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8874), (9149), (9152), (function-axioms)
% 139.86/20.33 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9153) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.86/20.33 | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.86/20.33 | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.86/20.33 | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | ALPHA: (9153) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9154) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7919), (9088), (9154), (function-axioms)
% 139.86/20.33 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #30.
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | (9155) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.86/20.33 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.86/20.33 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.86/20.33 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.86/20.33 | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.86/20.33 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | BETA: splitting (9155) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9156) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.86/20.33 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.86/20.33 | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.86/20.33 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.86/20.33 | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | ALPHA: (9156) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9157) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9158) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.33 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9159) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9160) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (165), (7910), (9092), (9149), (9157),
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9158), (9159), (9160), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #45.
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | (9161) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.86/20.33 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.86/20.33 | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.86/20.33 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.86/20.33 | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.86/20.33 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8881), (9148), (9161), (function-axioms)
% 139.86/20.33 | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #15.
% 139.86/20.33 | | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | End of split
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | (9162) all_24_2 = e2
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | COMBINE_EQS: (319), (9162) imply:
% 139.86/20.33 | | | | | | | | | | | | (9163) all_10_2 = e2
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | REDUCE: (45), (9163) imply:
% 139.86/20.33 | | | | | | | | | | | | (9164) op(e0, e0) = e2
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | BETA: splitting (230) gives:
% 139.86/20.33 | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | (9165) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 139.86/20.33 | | | | | | | | | | | | | & op(e2, e2) = e2)
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | BETA: splitting (9165) gives:
% 139.86/20.33 | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | (9166) all_57_1 = e2 & op(e3, e2) = e2
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | ALPHA: (9166) implies:
% 139.86/20.33 | | | | | | | | | | | | | | (9167) op(e3, e2) = e2
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.86/20.33 | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | (9168) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 139.86/20.33 | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | BETA: splitting (9168) gives:
% 139.86/20.33 | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | (9169) all_57_0 = e2 & op(e3, e3) = e2
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | ALPHA: (9169) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | (9170) op(e3, e3) = e2
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8881), (9170), (function-axioms) are
% 139.86/20.33 | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | (9171) all_57_2 = e2 & op(e2, e3) = e2
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | ALPHA: (9171) implies:
% 139.86/20.33 | | | | | | | | | | | | | | | | (9172) op(e2, e3) = e2
% 139.86/20.33 | | | | | | | | | | | | | | | |
% 139.86/20.33 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_1, e2,
% 139.86/20.33 | | | | | | | | | | | | | | | | e3, e2, simplifying with (167), (9172) gives:
% 139.86/20.33 | | | | | | | | | | | | | | | | (9173) all_52_1 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | e2, e3, simplifying with (170), (9167) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | (9174) all_52_4 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | REDUCE: (146), (9173) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | (9175) ~ (all_52_9 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | REDUCE: (145), (9173) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | (9176) ~ (all_52_13 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | SIMP: (9176) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | (9177) ~ (all_52_13 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | REDUCE: (133), (9174) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | (9178) ~ (all_52_12 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | SIMP: (9178) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | (9179) ~ (all_52_12 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | (9180) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.34 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | BETA: splitting (9180) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9181) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ALPHA: (9181) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9182) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | BETA: splitting (9182) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9183) all_56_11 = e3 & op(e2, e2) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9183) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9184) op(e2, e2) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (8881),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9164), (9184), (function-axioms) are inconsistent
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | by sub-proof #14.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9185) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | $i(all_56_3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9185) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9186) ~ (all_56_3 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9187) op(e2, e3) = all_56_3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9172), (9186), (9187), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #979.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9188) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ALPHA: (9188) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9189) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9190) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9191) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | BETA: splitting (9189) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9192) all_56_9 = e2 & op(e3, e3) = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9192) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9193) op(e3, e3) = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8881), (9193), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9194) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9194) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9195) ~ (all_56_0 = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9196) op(e3, e2) = all_56_0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (9190) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9197) all_56_7 = e1 & op(e1, e2) = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (9197) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9198) op(e1, e2) = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9088), (9198), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9199) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (9199) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9200) ~ (all_56_13 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9191) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9201) all_56_0 = e3 & op(e3, e2) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9201) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9202) op(e3, e2) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9195), (9196), (9202), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9203) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9203) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9204) ~ (all_56_9 = e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9205) op(e3, e3) = all_56_9
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9206) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9204), (9205), (9206),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | #41.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9207) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9207) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (9208) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9164), (9200), (9208), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #40.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (9209) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9209) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9210) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9210) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9211) all_56_13 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9200), (9211) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9212) $false
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9212) is inconsistent.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9213) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (9), (9092), (9164), (9213),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | #13.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | (9214) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.86/20.34 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.86/20.34 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | BETA: splitting (9214) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9215) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ALPHA: (9215) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9216) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9217) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9218) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9219) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | BETA: splitting (9219) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9220) all_56_4 = e2 & op(e2, e1) = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9220) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9221) op(e2, e1) = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9221), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9222) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9222) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9223) ~ (all_56_11 = e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9224) op(e2, e2) = all_56_11
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (165), (207), (7910),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (7919), (8881), (9092), (9164), (9216), (9217),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9218), (9219), (9223), (9224), (function-axioms)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #11.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9225) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | ALPHA: (9225) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9226) op(e0, e0) = all_56_15
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9227) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9228) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9229) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 139.86/20.34 | | | | | | | | | | | | | | | | | | (9230) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.86/20.34 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | BETA: splitting (9229) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9231) all_56_5 = e2 & op(e2, e0) = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9231) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9232) op(e2, e0) = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9177), (9232), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1030.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9233) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | ALPHA: (9233) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9234) ~ (all_56_11 = e0)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | (9235) op(e2, e2) = all_56_11
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | BETA: splitting (9227) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9236) all_56_13 = e0 & op(e1, e1) = e0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (9236) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9237) op(e1, e1) = e0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (9237), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9238) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | ALPHA: (9238) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9239) ~ (all_56_8 = e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | (9240) op(e1, e0) = all_56_8
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9230) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9241) all_56_2 = e3 & op(e3, e0) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9241) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9242) op(e3, e0) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9228) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9243) all_56_11 = e0 & op(e2, e2) = e0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9243) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9244) op(e2, e2) = e0
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9234), (9235), (9244), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #857.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9245) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9245) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9246) op(e2, e0) = all_56_5
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (9164), (9226)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9247) all_56_15 = e2
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | all_56_8, e0, e1, simplifying with (160), (9240)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9248) all_56_8 = all_52_14
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | all_56_5, e0, e2, simplifying with (164), (9246)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9249) all_56_5 = all_52_13
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | e3, e0, e3, simplifying with (168), (9242) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9250) all_52_12 = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9239), (9248) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9251) ~ (all_52_14 = e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (113), (9250) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9252) ~ (all_52_13 = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | SIMP: (9252) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9253) ~ (all_52_13 = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (112), (9250) imply:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9254) ~ (all_52_14 = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | SIMP: (9254) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | (9255) ~ (all_52_14 = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (9256) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9256) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9257) all_57_9 = e1 & op(e3, e0) = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9257) implies:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9258) all_57_9 = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | (9259) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9259) gives:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (9260) all_57_9 = e3 & op(e3, e0) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9258), (9260) are inconsistent by sub-proof
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | | #816.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | | (9261) all_57_10 = e3 & op(e2, e0) = e3
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9253), (9261), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #81.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | (9262) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (160), (9164), (9255), (9262),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | | #86.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | (9263) all_57_10 = e1 & op(e2, e0) = e1
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (164), (9090), (9263), (function-axioms) are
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #460.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (9264) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (9164), (9251), (9264),
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | | #36.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | (9265) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8881), (9265), (function-axioms) are inconsistent
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | | by sub-proof #25.
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | End of split
% 139.86/20.34 | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | Case 2:
% 139.86/20.34 | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | (9266) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 139.86/20.34 | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 139.86/20.34 | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | BETA: splitting (9266) gives:
% 139.86/20.34 | | | | | | | | | | | | | | |
% 139.86/20.34 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.34 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9267) all_57_6 = e2 & op(e1, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | ALPHA: (9267) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9268) all_57_6 = e2
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | BETA: splitting (234) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9269) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | & op(e2, e3) = e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (167), (8881), (9086), (9269),
% 139.86/20.35 | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | | | | | | | #325.
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9270) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 =
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1 & op(e0, e3) = e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | BETA: splitting (9270) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9271) all_57_6 = e1 & op(e1, e3) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9268), (9271) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | | | | | | | | #437.
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9272) all_57_12 = e1 & op(e0, e3) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ALPHA: (9272) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9273) all_57_12 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | BETA: splitting (217) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9274) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (9274) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9275) all_57_6 = e1 & op(e1, e3) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (7), (8), (9), (236), (238), (8880),
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (8881), (9273), (9275), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #205.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9276) all_57_7 = e1 & op(e1, e2) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (9276) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9277) op(e1, e2) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (9088), (9277), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9278) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (9278) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9279) all_57_8 = e1 & op(e1, e1) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (9279) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9280) op(e1, e1) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7919), (9280), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1085.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9281) all_57_11 = e1 & op(e1, e0) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (9281) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9282) all_57_11 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9283) op(e1, e0) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | (9284) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9284) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9285) all_57_6 = e3 & op(e1, e3) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9285) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9286) all_57_6 = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9268), (9286) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | #1004.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9287) all_57_7 = e3 & op(e1, e2) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9287) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9288) all_57_7 = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (7), (216), (7919), (9268), (9282),
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9288), (function-axioms) are inconsistent by
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | sub-proof #34.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | (9289) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9289) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9290) all_57_8 = e3 & op(e1, e1) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9290) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9291) op(e1, e1) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9291), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9292) all_57_11 = e3 & op(e1, e0) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9292) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9293) op(e1, e0) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9283), (9293), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #117.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9294) all_57_12 = e2 & op(e0, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | ALPHA: (9294) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9295) all_57_12 = e2
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (210), (212),
% 139.86/20.35 | | | | | | | | | | | | | | | | (9164), (9295), (function-axioms) are inconsistent
% 139.86/20.35 | | | | | | | | | | | | | | | | by sub-proof #28.
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | (9296) all_57_3 = e2 & op(e2, e2) = e2
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | ALPHA: (9296) implies:
% 139.86/20.35 | | | | | | | | | | | | | | (9297) op(e2, e2) = e2
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (9), (207), (8881), (9164), (9297),
% 139.86/20.35 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | | | | #642.
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | (9298) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 139.86/20.35 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | BETA: splitting (9298) gives:
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | (9299) all_57_7 = e2 & op(e1, e2) = e2
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (9299), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | (9300) all_57_13 = e2 & op(e0, e2) = e2
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | ALPHA: (9300) implies:
% 139.86/20.35 | | | | | | | | | | | | | | (9301) all_57_13 = e2
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | (9302) all_57_15 = e0 & op(e0, e0) = e0
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | ALPHA: (9302) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | (9303) op(e0, e0) = e0
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | REF_CLOSE: (5), (9164), (9303), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | inconsistent by sub-proof #1094.
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | (9304) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 139.86/20.35 | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 139.86/20.35 | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 139.86/20.35 | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | ALPHA: (9304) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | (9305) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 139.86/20.35 | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | e1) = e0)
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | BETA: splitting (9305) gives:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9306) all_57_12 = e0 & op(e0, e3) = e0
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | ALPHA: (9306) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9307) op(e0, e3) = e0
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8874), (9307), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | inconsistent by sub-proof #986.
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9308) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 =
% 139.86/20.35 | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | BETA: splitting (9308) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9309) all_57_13 = e0 & op(e0, e2) = e0
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9301), (9309) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | | | | | | | #1060.
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9310) all_57_14 = e0 & op(e0, e1) = e0
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | ALPHA: (9310) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9311) all_57_14 = e0
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (9), (210), (212), (9164),
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9301), (9311), (function-axioms) are inconsistent
% 139.86/20.35 | | | | | | | | | | | | | | | | | by sub-proof #1064.
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | (9312) all_16_2 = e0
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | COMBINE_EQS: (328), (9312) imply:
% 139.86/20.35 | | | | | | | | | | (9313) all_6_2 = e0
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | SIMP: (9313) implies:
% 139.86/20.35 | | | | | | | | | | (9314) all_6_2 = e0
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | REDUCE: (353), (9314) imply:
% 139.86/20.35 | | | | | | | | | | (9315) ~ (all_52_6 = e0)
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | REDUCE: (357), (9314) imply:
% 139.86/20.35 | | | | | | | | | | (9316) ~ (all_52_9 = e0)
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | REDUCE: (7920), (9314) imply:
% 139.86/20.35 | | | | | | | | | | (9317) ~ (e3 = e0)
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | REDUCE: (39), (9314) imply:
% 139.86/20.35 | | | | | | | | | | (9318) op(e2, e2) = e0
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | BETA: splitting (220) gives:
% 139.86/20.35 | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | (9319) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 139.86/20.35 | | | | | | | | | | | & op(e2, e1) = e0)
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | REF_CLOSE: (165), (169), (8876), (9316), (9319),
% 139.86/20.35 | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | #980.
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | (9320) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 139.86/20.35 | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | BETA: splitting (9320) gives:
% 139.86/20.35 | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | (9321) all_57_8 = e0 & op(e1, e1) = e0
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | ALPHA: (9321) implies:
% 139.86/20.35 | | | | | | | | | | | | (9322) op(e1, e1) = e0
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | REF_CLOSE: (5), (7919), (9322), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | inconsistent by sub-proof #61.
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | (9323) all_57_14 = e0 & op(e0, e1) = e0
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | ALPHA: (9323) implies:
% 139.86/20.35 | | | | | | | | | | | | (9324) op(e0, e1) = e0
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | BETA: splitting (216) gives:
% 139.86/20.35 | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | (9325) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 139.86/20.35 | | | | | | | | | | | | | & op(e1, e2) = e0)
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | REF_CLOSE: (162), (163), (8873), (9315), (9325),
% 139.86/20.35 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 139.86/20.35 | | | | | | | | | | | | | #199.
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | (9326) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 139.86/20.35 | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | BETA: splitting (9326) gives:
% 139.86/20.35 | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | (9327) all_57_8 = e0 & op(e1, e1) = e0
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | ALPHA: (9327) implies:
% 139.86/20.35 | | | | | | | | | | | | | | (9328) op(e1, e1) = e0
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (9328), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | (9329) all_57_11 = e0 & op(e1, e0) = e0
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | ALPHA: (9329) implies:
% 139.86/20.35 | | | | | | | | | | | | | | (9330) op(e1, e0) = e0
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 139.86/20.35 | | | | | | | | | | | | | | e0, e1, e0, simplifying with (157), (9324) gives:
% 139.86/20.35 | | | | | | | | | | | | | | (9331) all_52_11 = e0
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 139.86/20.35 | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (9330) gives:
% 139.86/20.35 | | | | | | | | | | | | | | (9332) all_52_14 = e0
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | REDUCE: (125), (9331) imply:
% 139.86/20.35 | | | | | | | | | | | | | | (9333) ~ (all_52_7 = e0)
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | REDUCE: (371), (9332) imply:
% 139.86/20.35 | | | | | | | | | | | | | | (9334) ~ (all_10_2 = e0)
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | SIMP: (9334) implies:
% 139.86/20.35 | | | | | | | | | | | | | | (9335) ~ (all_10_2 = e0)
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | REDUCE: (7912), (9332) imply:
% 139.86/20.35 | | | | | | | | | | | | | | (9336) ~ (e2 = e0)
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 139.86/20.35 | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | (9337) ~ (all_24_2 = e2)
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | REDUCE: (319), (9337) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | (9338) ~ (all_10_2 = e2)
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | BETA: splitting (189) gives:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9339) all_54_15 = e3
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (9339) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9340) all_10_2 = e3
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | SIMP: (9340) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9341) all_10_2 = e3
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | REDUCE: (361), (9341) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9342) ~ (all_52_7 = e3)
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | REDUCE: (369), (9341) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9343) ~ (all_52_12 = e3)
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | REDUCE: (45), (9341) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | | (9344) op(e0, e0) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9345) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.35 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 139.86/20.35 | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | BETA: splitting (9345) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9346) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ALPHA: (9346) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9347) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (159), (8874), (9344), (9347), (function-axioms)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #739.
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9348) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ALPHA: (9348) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9349) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_12))
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9350) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9351) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9352) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9353) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | BETA: splitting (9349) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9354) all_56_15 = e2 & op(e0, e0) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | ALPHA: (9354) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9355) all_56_15 = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (158), (9333), (9350), (9355), (function-axioms)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #976.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9356) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | ALPHA: (9356) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9357) ~ (all_56_12 = e0)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | (9358) op(e0, e2) = all_56_12
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | BETA: splitting (9351) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9359) all_56_9 = e2 & op(e3, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (9359) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9360) op(e3, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8881), (9360), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9361) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | ALPHA: (9361) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9362) ~ (all_56_0 = e3)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | (9363) op(e3, e2) = all_56_0
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9352) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | (9364) all_56_7 = e1 & op(e1, e2) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9364) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | (9365) op(e1, e2) = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9353) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9366) all_56_0 = e3 & op(e3, e2) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9366) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9367) op(e3, e2) = e3
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9362), (9363), (9367), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #670.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (135), (136), (158), (162), (170), (191),
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (203), (248), (272), (8875), (9342), (9357),
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | (9358), (9362), (9363), (9365), (function-axioms)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #10.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | (9368) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7919), (9368), (function-axioms) are inconsistent
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | | by sub-proof #31.
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9369) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 139.86/20.35 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | BETA: splitting (9369) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9370) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ALPHA: (9370) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9371) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9324), (9344), (9371), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #664.
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | (9372) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 139.86/20.35 | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 139.86/20.35 | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 139.86/20.35 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (8881), (9343), (9372), (function-axioms)
% 139.86/20.35 | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #15.
% 139.86/20.35 | | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9373) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | REF_CLOSE: (246), (7921), (9335), (9338), (9373) are
% 139.86/20.35 | | | | | | | | | | | | | | | | inconsistent by sub-proof #198.
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | End of split
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | (9374) all_24_2 = e2
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | COMBINE_EQS: (319), (9374) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | (9375) all_10_2 = e2
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | SIMP: (9375) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | (9376) all_10_2 = e2
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | REDUCE: (370), (9376) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | (9377) ~ (all_52_13 = e2)
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | REDUCE: (45), (9376) imply:
% 139.86/20.35 | | | | | | | | | | | | | | | (9378) op(e0, e0) = e2
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 139.86/20.35 | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | (9379) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | BETA: splitting (9379) gives:
% 139.86/20.35 | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9380) all_57_0 = e2 & op(e3, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | ALPHA: (9380) implies:
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9381) op(e3, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8881), (9381), (function-axioms) are
% 139.86/20.35 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #880.
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | Case 2:
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | (9382) all_57_2 = e2 & op(e2, e3) = e2
% 139.86/20.35 | | | | | | | | | | | | | | | | |
% 139.86/20.35 | | | | | | | | | | | | | | | | | ALPHA: (9382) implies:
% 139.86/20.36 | | | | | | | | | | | | | | | | | (9383) op(e2, e3) = e2
% 139.86/20.36 | | | | | | | | | | | | | | | | |
% 139.86/20.36 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 139.86/20.36 | | | | | | | | | | | | | | | | |
% 139.86/20.36 | | | | | | | | | | | | | | | | | Case 1:
% 139.86/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9384) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 140.52/20.36 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (158), (9318), (9333), (9378), (9383),
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9384), (function-axioms) are inconsistent by
% 140.52/20.36 | | | | | | | | | | | | | | | | | | sub-proof #974.
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9385) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (164), (9318), (9324), (9377), (9378),
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9385), (function-axioms) are inconsistent by
% 140.52/20.36 | | | | | | | | | | | | | | | | | | sub-proof #197.
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | (9386) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 140.52/20.36 | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | BETA: splitting (9386) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9387) all_57_6 = e2 & op(e1, e3) = e2
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (163), (7907), (9387), (function-axioms) are
% 140.52/20.36 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #79.
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9388) all_57_12 = e2 & op(e0, e3) = e2
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | ALPHA: (9388) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9389) all_57_12 = e2
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (209), (210), (212),
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9378), (9389), (function-axioms) are inconsistent
% 140.52/20.36 | | | | | | | | | | | | | | | | | by sub-proof #28.
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | | (9390) all_57_2 = e0 & op(e2, e3) = e0
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | | REF_CLOSE: (167), (8872), (9390), (function-axioms) are
% 140.52/20.36 | | | | | | | | | inconsistent by sub-proof #1028.
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | End of split
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | (9391) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 140.52/20.36 | | | | | | | | op(e0, e3) = e0)
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | REF_CLOSE: (159), (163), (8873), (8874), (9391),
% 140.52/20.36 | | | | | | | | (function-axioms) are inconsistent by sub-proof #196.
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | End of split
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | End of split
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | Case 2:
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | (9392) all_10_2 = e1
% 140.52/20.36 | | | | | | (9393) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0,
% 140.52/20.36 | | | | | | e1) = all_10_1 & $i(all_10_0) & $i(all_10_1)) | ( ~
% 140.52/20.36 | | | | | | (all_10_1 = e3) & op(e0, e1) = all_10_1 & $i(all_10_1))
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | COMBINE_EQS: (309), (9392) imply:
% 140.52/20.36 | | | | | | (9394) all_30_2 = e1
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | REDUCE: (350), (9392) imply:
% 140.52/20.36 | | | | | | (9395) ~ (all_52_3 = e1)
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | REDUCE: (368), (9392) imply:
% 140.52/20.36 | | | | | | (9396) ~ (all_52_11 = e1)
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | REDUCE: (369), (9392) imply:
% 140.52/20.36 | | | | | | (9397) ~ (all_52_12 = e1)
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | REDUCE: (370), (9392) imply:
% 140.52/20.36 | | | | | | (9398) ~ (all_52_13 = e1)
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | REDUCE: (371), (9392) imply:
% 140.52/20.36 | | | | | | (9399) ~ (all_52_14 = e1)
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | BETA: splitting (213) gives:
% 140.52/20.36 | | | | | |
% 140.52/20.36 | | | | | | Case 1:
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | | (9400) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 140.52/20.36 | | | | | | | op(e2, e0) = e1)
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | | BETA: splitting (9400) gives:
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | (9401) all_57_9 = e1 & op(e3, e0) = e1
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | REF_CLOSE: (168), (9397), (9401), (function-axioms) are
% 140.52/20.36 | | | | | | | | inconsistent by sub-proof #461.
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | (9402) all_57_10 = e1 & op(e2, e0) = e1
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | REF_CLOSE: (164), (9398), (9402), (function-axioms) are
% 140.52/20.36 | | | | | | | | inconsistent by sub-proof #460.
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | End of split
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | Case 2:
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | | (9403) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 140.52/20.36 | | | | | | | op(e0, e0) = e1)
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | | BETA: splitting (9403) gives:
% 140.52/20.36 | | | | | | |
% 140.52/20.36 | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | (9404) all_57_11 = e1 & op(e1, e0) = e1
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | ALPHA: (9404) implies:
% 140.52/20.36 | | | | | | | | (9405) op(e1, e0) = e1
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | REF_CLOSE: (160), (9399), (9405), (function-axioms) are
% 140.52/20.36 | | | | | | | | inconsistent by sub-proof #459.
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | (9406) all_57_15 = e1 & op(e0, e0) = e1
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | ALPHA: (9406) implies:
% 140.52/20.36 | | | | | | | | (9407) all_57_15 = e1
% 140.52/20.36 | | | | | | | | (9408) op(e0, e0) = e1
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | BETA: splitting (52) gives:
% 140.52/20.36 | | | | | | | |
% 140.52/20.36 | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | | (9409) ~ (all_14_2 = e0)
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | | BETA: splitting (55) gives:
% 140.52/20.36 | | | | | | | | |
% 140.52/20.36 | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | (9410) ~ (all_16_2 = e0)
% 140.52/20.36 | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | REDUCE: (328), (9410) imply:
% 140.52/20.36 | | | | | | | | | | (9411) ~ (all_6_2 = e0)
% 140.52/20.36 | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | BETA: splitting (61) gives:
% 140.52/20.36 | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | (9412) ~ (all_20_2 = e1)
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | REDUCE: (283), (9412) imply:
% 140.52/20.36 | | | | | | | | | | | (9413) ~ (all_6_2 = e1)
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | (9414) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.36 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.36 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.36 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.36 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.36 | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.36 | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.36 | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.36 | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.36 | | | | | | | | | | | | $i(all_56_6))
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | BETA: splitting (9414) gives:
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | (9415) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.36 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.36 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.36 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.36 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | REF_CLOSE: (39), (7920), (9415), (function-axioms) are
% 140.52/20.36 | | | | | | | | | | | | | inconsistent by sub-proof #1128.
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | (9416) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.52/20.36 | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.52/20.36 | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.52/20.36 | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.52/20.36 | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9416), (function-axioms) are
% 140.52/20.36 | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | (9417) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.36 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.36 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.36 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.36 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.36 | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.36 | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.36 | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.36 | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.36 | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.36 | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.36 | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.36 | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.36 | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.36 | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.36 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.36 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.36 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.36 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | BETA: splitting (9417) gives:
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | (9418) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.36 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.36 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.36 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.36 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | BETA: splitting (9418) gives:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | (9419) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.36 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.52/20.36 | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | ALPHA: (9419) implies:
% 140.52/20.36 | | | | | | | | | | | | | | (9420) op(e0, e0) = e3
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | REF_CLOSE: (8), (9408), (9420), (function-axioms) are
% 140.52/20.36 | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | (9421) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.52/20.36 | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.52/20.36 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | ALPHA: (9421) implies:
% 140.52/20.36 | | | | | | | | | | | | | | (9422) op(e2, e2) = e1
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | REF_CLOSE: (39), (199), (268), (7920), (9411), (9413),
% 140.52/20.36 | | | | | | | | | | | | | | (9422), (function-axioms) are inconsistent by
% 140.52/20.36 | | | | | | | | | | | | | | sub-proof #9.
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | (9423) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.36 | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.36 | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.36 | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.36 | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.36 | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.36 | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.36 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.36 | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.36 | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.36 | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.36 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.36 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.36 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.36 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | BETA: splitting (9423) gives:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | (9424) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.36 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.36 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | ALPHA: (9424) implies:
% 140.52/20.36 | | | | | | | | | | | | | | (9425) op(e2, e2) = e1
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | REF_CLOSE: (39), (199), (268), (7920), (9411), (9413),
% 140.52/20.36 | | | | | | | | | | | | | | (9425), (function-axioms) are inconsistent by
% 140.52/20.36 | | | | | | | | | | | | | | sub-proof #9.
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | (9426) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.36 | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.36 | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.36 | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.36 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.36 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.36 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.36 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.36 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.36 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.36 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.36 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.36 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | BETA: splitting (9426) gives:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | (9427) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.36 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.36 | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | ALPHA: (9427) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | (9428) op(e0, e0) = e2
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | REF_CLOSE: (6), (9408), (9428), (function-axioms) are
% 140.52/20.36 | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | (9429) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.36 | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.36 | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.36 | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.36 | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.36 | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.36 | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.36 | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.36 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.36 | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.36 | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | ALPHA: (9429) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | (9430) op(e0, e0) = all_56_15
% 140.52/20.36 | | | | | | | | | | | | | | | (9431) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.36 | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.36 | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.36 | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.36 | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.36 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.36 | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.36 | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.36 | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.36 | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (39), (7919), (9408), (9411), (9430),
% 140.52/20.36 | | | | | | | | | | | | | | | (9431), (function-axioms) are inconsistent by
% 140.52/20.36 | | | | | | | | | | | | | | | sub-proof #8.
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | End of split
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | (9432) all_20_2 = e1
% 140.52/20.36 | | | | | | | | | | | (9433) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0
% 140.52/20.36 | | | | | | | | | | | & op(e2, e1) = all_20_1 & $i(all_20_0) &
% 140.52/20.36 | | | | | | | | | | | $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1)
% 140.52/20.36 | | | | | | | | | | | = all_20_1 & $i(all_20_1))
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | COMBINE_EQS: (283), (9432) imply:
% 140.52/20.36 | | | | | | | | | | | (9434) all_6_2 = e1
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | SIMP: (9434) implies:
% 140.52/20.36 | | | | | | | | | | | (9435) all_6_2 = e1
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | REDUCE: (353), (9435) imply:
% 140.52/20.36 | | | | | | | | | | | (9436) ~ (all_52_6 = e1)
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | REDUCE: (357), (9435) imply:
% 140.52/20.36 | | | | | | | | | | | (9437) ~ (all_52_9 = e1)
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | REDUCE: (7920), (9435) imply:
% 140.52/20.36 | | | | | | | | | | | (9438) ~ (e3 = e1)
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | REDUCE: (39), (9435) imply:
% 140.52/20.36 | | | | | | | | | | | (9439) op(e2, e2) = e1
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | BETA: splitting (217) gives:
% 140.52/20.36 | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | (9440) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 140.52/20.36 | | | | | | | | | | | | & op(e1, e2) = e1)
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | BETA: splitting (9440) gives:
% 140.52/20.36 | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | (9441) all_57_6 = e1 & op(e1, e3) = e1
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | ALPHA: (9441) implies:
% 140.52/20.36 | | | | | | | | | | | | | (9442) all_57_6 = e1
% 140.52/20.36 | | | | | | | | | | | | | (9443) op(e1, e3) = e1
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | BETA: splitting (221) gives:
% 140.52/20.36 | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | (9444) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 140.52/20.36 | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | BETA: splitting (9444) gives:
% 140.52/20.36 | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | (9445) all_57_4 = e1 & op(e3, e1) = e1
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | ALPHA: (9445) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | (9446) all_57_4 = e1
% 140.52/20.36 | | | | | | | | | | | | | | | (9447) op(e3, e1) = e1
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 140.52/20.36 | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (9443) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | (9448) all_52_2 = e1
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 140.52/20.36 | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (9447) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | (9449) all_52_8 = e1
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | REDUCE: (143), (9448) imply:
% 140.52/20.36 | | | | | | | | | | | | | | | (9450) ~ (all_52_6 = e1)
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | REDUCE: (141), (9448) imply:
% 140.52/20.36 | | | | | | | | | | | | | | | (9451) ~ (all_52_14 = e1)
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | REDUCE: (120), (9449) imply:
% 140.52/20.36 | | | | | | | | | | | | | | | (9452) ~ (all_52_12 = e1)
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | REDUCE: (7909), (9449) imply:
% 140.52/20.36 | | | | | | | | | | | | | | | (9453) ~ (e2 = e1)
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 140.52/20.36 | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | (9454) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 140.52/20.36 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 140.52/20.36 | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 140.52/20.36 | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (7919), (9436), (9443), (9454),
% 140.52/20.36 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.36 | | | | | | | | | | | | | | | | #29.
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | (9455) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 140.52/20.36 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 140.52/20.36 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.52/20.36 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.52/20.36 | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | BETA: splitting (9455) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9456) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 140.52/20.36 | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 140.52/20.36 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.52/20.36 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 140.52/20.36 | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 140.52/20.36 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.52/20.36 | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 140.52/20.36 | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | ALPHA: (9456) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9457) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | $i(all_56_14))
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9458) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.36 | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | $i(all_56_15))
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9459) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 140.52/20.36 | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 140.52/20.36 | | | | | | | | | | | | | | | | | (9460) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 140.52/20.36 | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | $i(all_56_11))
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | BETA: splitting (9460) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9461) all_56_4 = e2 & op(e2, e1) = e2
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ALPHA: (9461) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9462) op(e2, e1) = e2
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9462), (function-axioms) are
% 140.52/20.36 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9463) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | ALPHA: (9463) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9464) ~ (all_56_11 = e1)
% 140.52/20.36 | | | | | | | | | | | | | | | | | | (9465) op(e2, e2) = all_56_11
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | BETA: splitting (9458) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | (9466) all_56_14 = e0 & op(e0, e1) = e0
% 140.52/20.36 | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | ALPHA: (9466) implies:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | (9467) op(e0, e1) = e0
% 140.52/20.36 | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | (9468) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (7919), (9439), (9468),
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | | #47.
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.36 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (9469) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9469) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9470) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9470) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9471) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9471) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9472) op(e0, e0) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9457), (9467), (9472), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #664.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9473) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9473) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9474) all_56_11 = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9475) ~ (all_56_4 = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9460), (9474), (9475) are inconsistent by
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9476) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9476) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9477) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9477) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9478) all_56_11 = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9460), (9478), (function-axioms)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #91.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9479) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9479) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9480) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9480) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9481) op(e0, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9457), (9467), (9481), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #972.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9482) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9482) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9483) op(e0, e0) = all_56_15
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9484) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (7919), (9439), (9457), (9458),
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9459), (9460), (9464), (9465), (9483), (9484),
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | #7.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | (9485) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9408), (9485), (function-axioms) are inconsistent
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | by sub-proof #82.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9486) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 140.52/20.37 | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 140.52/20.37 | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 140.52/20.37 | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | ALPHA: (9486) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9487) op(e0, e0) = all_56_15
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9488) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9489) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9490) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9491) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | $i(all_56_13))
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9492) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e0) & op(e2, e2) = all_56_11 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | $i(all_56_11))
% 140.52/20.37 | | | | | | | | | | | | | | | | | (9493) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.52/20.37 | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 140.52/20.37 | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | BETA: splitting (9490) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9494) all_56_9 = e0 & op(e3, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | ALPHA: (9494) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9495) op(e3, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (110), (112), (113), (160), (164), (168),
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (193), (197), (250), (260), (7912), (9398),
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9399), (9439), (9488), (9489), (9490), (9491),
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9493), (9495), (function-axioms) are inconsistent
% 140.52/20.37 | | | | | | | | | | | | | | | | | | by sub-proof #6.
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9496) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | $i(all_56_2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | ALPHA: (9496) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9497) ~ (all_56_2 = e3)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | (9498) op(e3, e0) = all_56_2
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | BETA: splitting (9488) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | (9499) all_56_13 = e0 & op(e1, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | ALPHA: (9499) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | (9500) op(e1, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (160), (9399), (9491), (9500), (function-axioms)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #98.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | (9501) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | ALPHA: (9501) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | (9502) ~ (all_56_8 = e1)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | (9503) op(e1, e0) = all_56_8
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | BETA: splitting (9491) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (9504) all_56_8 = e1 & op(e1, e0) = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | ALPHA: (9504) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (9505) op(e1, e0) = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9502), (9503), (9505), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #294.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (9506) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | ALPHA: (9506) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (9507) ~ (all_56_13 = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | (9508) op(e1, e1) = all_56_13
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9489) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9509) all_56_11 = e0 & op(e2, e2) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9509) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9510) op(e2, e2) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9439), (9510), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9511) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9511) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9512) ~ (all_56_5 = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | (9513) op(e2, e0) = all_56_5
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9492) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9514) all_56_5 = e2 & op(e2, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9514) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9515) op(e2, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9512), (9513), (9515), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #152.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9516) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9516) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9517) ~ (all_56_11 = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9518) op(e2, e2) = all_56_11
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (9408), (9487)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9519) all_56_15 = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (7919), (9508)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9520) all_56_13 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (9439), (9518)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9521) all_56_11 = e1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | all_56_2, e0, e3, simplifying with (168), (9498)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9522) all_56_2 = all_52_12
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9497), (9522) imply:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | (9523) ~ (all_52_12 = e3)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (214) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9524) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9524) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9525) all_57_9 = e2 & op(e3, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9525) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9526) all_57_9 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9527) op(e3, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (233) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | (9528) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9528) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9529) all_57_0 = e0 & op(e3, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9529) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9530) op(e3, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9493), (9527), (9530), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #24.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9531) all_57_1 = e0 & op(e3, e2) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9531) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9532) all_57_1 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9533) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9533) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9534) all_57_1 = e2 & op(e3, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9532), (9534) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | #353.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9535) all_57_3 = e2 & op(e2, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9535) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9536) op(e2, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9439), (9536), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9537) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9537) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9538) all_57_7 = e2 & op(e1, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (9538), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9539) all_57_13 = e2 & op(e0, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9539) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9540) all_57_13 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9541) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9541) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9542) all_57_2 = e2 & op(e2, e3) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9542) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9543) all_57_2 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (231) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9544) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9544) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9545) all_57_1 = e3 & op(e3, e2) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9532), (9545) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #408.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9546) all_57_3 = e3 & op(e2, e2) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9546) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9547) op(e2, e2) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9439), (9547), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9548) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9548) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9549) all_57_7 = e3 & op(e1, e2) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9549) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9550) op(e1, e2) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (232) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9551) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9551) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9552) all_57_0 = e0 & op(e3, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9552) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9553) op(e3, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9493), (9527), (9553), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #24.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9554) all_57_2 = e0 & op(e2, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9554) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9555) all_57_2 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9543), (9555) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #238.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9556) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e3) = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9556) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9557) all_57_6 = e0 & op(e1, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9557) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9558) all_57_6 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9442), (9558) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1026.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9559) all_57_12 = e0 & op(e0, e3) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9559) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9560) all_57_12 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (212) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9561) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9), (9540), (9560), (9561) are inconsistent
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #827.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9562) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9562) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9563) all_57_14 = e3 & op(e0, e1) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9563) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9564) all_57_14 = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9565) op(e0, e1) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9566) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9566) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9567) all_57_4 = e0 & op(e3, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9567) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9568) op(e3, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (79), (162), (169), (7905), (7906), (9550),
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9568), (function-axioms) are inconsistent by
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #32.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9569) all_57_5 = e0 & op(e2, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9569) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9570) op(e2, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3, e1, e0, simplifying with (157), (9565) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9571) all_52_11 = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9, e0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e2, simplifying with (165), (9570) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9572) all_52_9 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_12,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2, e0, e3, simplifying with (168), (9527) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9573) all_52_12 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9574) ~ (all_30_2 = e1)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9394), (9574) imply:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9575) $false
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9575) is inconsistent.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9576) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e1) = all_30_1 & $i(all_30_0) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | = all_30_1 & $i(all_30_1))
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9393) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9577) ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_10_1 & $i(all_10_0) &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9577) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9578) ~ (all_10_0 = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9579) op(e0, e1) = all_10_1
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9580) op(all_10_1, e0) = all_10_0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9433) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3, all_10_1,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1, e0, simplifying with (9565), (9579) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9581) all_10_1 = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9580), (9581) imply:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9582) op(e3, e0) = all_10_0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_10_0,
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0, e3, simplifying with (9527), (9582) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9583) all_10_0 = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9578), (9583) imply:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9584) $false
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9584) is inconsistent.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9585) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_20_1)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9570), (9585), (function-axioms) are inconsistent
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #17.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9586) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 &
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_10_1)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9565), (9576), (9586), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #371.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9587) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9587) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9588) all_57_8 = e0 & op(e1, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9588) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9589) op(e1, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9507), (9508), (9589), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #140.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9590) all_57_14 = e0 & op(e0, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9590) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9591) all_57_14 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9564), (9591) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1067.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9592) all_57_15 = e3 & op(e0, e0) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9592) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9593) op(e0, e0) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9408), (9593), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9594) all_57_13 = e3 & op(e0, e2) = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9594) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9595) all_57_13 = e3
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9540), (9595) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1068.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9596) all_57_3 = e2 & op(e2, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9596) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9597) op(e2, e2) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9439), (9597), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #749.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9598) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9598) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9599) all_57_5 = e2 & op(e2, e1) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9599) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9600) op(e2, e1) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9600), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9601) all_57_10 = e2 & op(e2, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9601) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9602) op(e2, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9512), (9513), (9602), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #152.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | (9603) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9603) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9604) all_57_4 = e0 & op(e3, e1) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9446), (9604) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | #1100.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9605) all_57_9 = e0 & op(e3, e0) = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9605) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | (9606) all_57_9 = e0
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9526), (9606) are inconsistent by sub-proof
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | | #1018.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9607) all_57_10 = e2 & op(e2, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9607) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9608) op(e2, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9512), (9513), (9608), (function-axioms) are
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #152.
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | (9609) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9609) gives:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9610) all_57_11 = e2 & op(e1, e0) = e2
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9610) implies:
% 140.52/20.37 | | | | | | | | | | | | | | | | | | | | | | | | (9611) all_57_11 = e2
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (215) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | (9612) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9612) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (9613) all_57_9 = e3 & op(e3, e0) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9613) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (9614) op(e3, e0) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (9523), (9614), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1105.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (9615) all_57_10 = e3 & op(e2, e0) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9615) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | (9616) all_57_10 = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9617) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9617) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9618) all_57_6 = e0 & op(e1, e3) = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9618) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9619) all_57_6 = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9442), (9619) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9620) e1 = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9620) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9621) e1 = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9407), (9621) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9622) all_57_15 = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (8), (168), (213), (9397), (9611),
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9616), (9622), (function-axioms) are inconsistent
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #273.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9623) all_57_7 = e0 & op(e1, e2) = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9623) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9624) all_57_7 = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (219) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9625) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9625) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9626) all_57_6 = e3 & op(e1, e3) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9442), (9626) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1093.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9627) all_57_7 = e3 & op(e1, e2) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9624), (9627) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #713.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9628) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9628) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9629) all_57_8 = e3 & op(e1, e1) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9629) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9630) op(e1, e1) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9630), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9631) all_57_11 = e3 & op(e1, e0) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9631) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9632) all_57_11 = e3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9611), (9632) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9633) e3 = e2
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9616), (9633) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9634) all_57_10 = e2
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (168), (215), (9408), (9523), (9611),
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9634), (function-axioms) are inconsistent by
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #188.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9635) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9507), (9508), (9611), (9635),
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | | #135.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | (9636) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (9408), (9611), (9636),
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | | #385.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | (9637) all_57_15 = e2 & op(e0, e0) = e2
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9637) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | (9638) op(e0, e0) = e2
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9408), (9638), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9639) all_57_5 = e1 & op(e2, e1) = e1
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | REF_CLOSE: (165), (9437), (9639), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | (9640) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 140.52/20.38 | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (7919), (9396), (9640),
% 140.52/20.38 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | | | #5.
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | (9641) all_57_7 = e1 & op(e1, e2) = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | ALPHA: (9641) implies:
% 140.52/20.38 | | | | | | | | | | | | | (9642) op(e1, e2) = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REF_CLOSE: (162), (9436), (9642), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | (9643) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 140.52/20.38 | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | REF_CLOSE: (6), (160), (7919), (9399), (9643),
% 140.52/20.38 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | #35.
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | (9644) all_16_2 = e0
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | COMBINE_EQS: (328), (9644) imply:
% 140.52/20.38 | | | | | | | | | | (9645) all_6_2 = e0
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | SIMP: (9645) implies:
% 140.52/20.38 | | | | | | | | | | (9646) all_6_2 = e0
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | REDUCE: (7920), (9646) imply:
% 140.52/20.38 | | | | | | | | | | (9647) ~ (e3 = e0)
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | REDUCE: (39), (9646) imply:
% 140.52/20.38 | | | | | | | | | | (9648) op(e2, e2) = e0
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | (9649) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.38 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.38 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.38 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.38 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.38 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.38 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.38 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.38 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.38 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.38 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.38 | | | | | | | | | | | $i(all_56_6))
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | BETA: splitting (9649) gives:
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | (9650) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.38 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.38 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.38 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.38 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.38 | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | REF_CLOSE: (7), (9648), (9650), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | inconsistent by sub-proof #1118.
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | (9651) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.52/20.38 | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.52/20.38 | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.52/20.38 | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.52/20.38 | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9651), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | (9652) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.38 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.38 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.38 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.38 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.38 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.38 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.38 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.38 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.38 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.38 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.38 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.38 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.38 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.38 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.38 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.38 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | BETA: splitting (9652) gives:
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | (9653) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.38 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.38 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.38 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | REF_CLOSE: (4), (8), (9408), (9648), (9653),
% 140.52/20.38 | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.38 | | | | | | | | | | | | #192.
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | (9654) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.38 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.38 | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.38 | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.38 | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.38 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.38 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.38 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.38 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.38 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | BETA: splitting (9654) gives:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | (9655) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.38 | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.38 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | ALPHA: (9655) implies:
% 140.52/20.38 | | | | | | | | | | | | | (9656) op(e2, e2) = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REF_CLOSE: (4), (9648), (9656), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | (9657) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.38 | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.38 | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.38 | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.38 | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.38 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.38 | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.38 | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.38 | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | BETA: splitting (9657) gives:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | (9658) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.38 | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.38 | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | ALPHA: (9658) implies:
% 140.52/20.38 | | | | | | | | | | | | | | (9659) op(e0, e0) = e2
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | REF_CLOSE: (6), (9408), (9659), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | (9660) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.38 | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.38 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.38 | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.38 | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.38 | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.38 | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | ALPHA: (9660) implies:
% 140.52/20.38 | | | | | | | | | | | | | | (9661) op(e0, e0) = all_56_15
% 140.52/20.38 | | | | | | | | | | | | | | (9662) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.38 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.38 | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.38 | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.38 | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | BETA: splitting (9662) gives:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9663) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.38 | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.38 | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | BETA: splitting (9663) gives:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9664) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.38 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.38 | | | | | | | | | | | | | | | | $i(all_56_10)
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | ALPHA: (9664) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | (9665) op(e3, e3) = e0
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | REF_CLOSE: (51), (9409), (9665), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1125.
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9666) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.52/20.38 | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.38 | | | | | | | | | | | | | | | | $i(all_56_12)
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | ALPHA: (9666) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | (9667) all_56_15 = e2
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | REDUCE: (9661), (9667) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | (9668) op(e0, e0) = e2
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9408), (9668), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9669) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.38 | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.38 | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (9669), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #26.
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | (9670) all_14_2 = e0
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | REDUCE: (337), (9670) imply:
% 140.52/20.38 | | | | | | | | | (9671) ~ (all_52_1 = e0)
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | REDUCE: (341), (9670) imply:
% 140.52/20.38 | | | | | | | | | (9672) ~ (all_52_3 = e0)
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | REDUCE: (343), (9670) imply:
% 140.52/20.38 | | | | | | | | | (9673) ~ (all_52_4 = e0)
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | REDUCE: (345), (9670) imply:
% 140.52/20.38 | | | | | | | | | (9674) ~ (all_52_8 = e0)
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | REDUCE: (347), (9670) imply:
% 140.52/20.38 | | | | | | | | | (9675) ~ (all_52_12 = e0)
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | BETA: splitting (232) gives:
% 140.52/20.38 | | | | | | | | |
% 140.52/20.38 | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | (9676) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0
% 140.52/20.38 | | | | | | | | | | & op(e2, e3) = e0)
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | BETA: splitting (9676) gives:
% 140.52/20.38 | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | (9677) all_57_0 = e0 & op(e3, e3) = e0
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | ALPHA: (9677) implies:
% 140.52/20.38 | | | | | | | | | | | (9678) all_57_0 = e0
% 140.52/20.38 | | | | | | | | | | | (9679) op(e3, e3) = e0
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | BETA: splitting (55) gives:
% 140.52/20.38 | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | (9680) ~ (all_16_2 = e0)
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | REDUCE: (328), (9680) imply:
% 140.52/20.38 | | | | | | | | | | | | (9681) ~ (all_6_2 = e0)
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | BETA: splitting (61) gives:
% 140.52/20.38 | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | (9682) ~ (all_20_2 = e1)
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REDUCE: (283), (9682) imply:
% 140.52/20.38 | | | | | | | | | | | | | (9683) ~ (all_6_2 = e1)
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | (9684) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.38 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.38 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.38 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.38 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.38 | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.38 | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.38 | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.38 | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.38 | | | | | | | | | | | | | | $i(all_56_6))
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | BETA: splitting (9684) gives:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9685) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.38 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.38 | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.38 | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | REF_CLOSE: (5), (9679), (9685), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9686) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.52/20.38 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.52/20.38 | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.52/20.38 | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9686), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | (9687) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.38 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.38 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.38 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.38 | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.38 | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.38 | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.38 | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.38 | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.38 | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.38 | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | BETA: splitting (9687) gives:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9688) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.38 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.38 | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | BETA: splitting (9688) gives:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9689) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.38 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.52/20.38 | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | ALPHA: (9689) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | (9690) op(e0, e0) = e3
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9408), (9690), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | inconsistent by sub-proof #732.
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9691) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.52/20.38 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.52/20.38 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | ALPHA: (9691) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | (9692) op(e2, e2) = e1
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (199), (268), (7920), (9681), (9683),
% 140.52/20.38 | | | | | | | | | | | | | | | | (9692), (function-axioms) are inconsistent by
% 140.52/20.38 | | | | | | | | | | | | | | | | sub-proof #9.
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9693) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.38 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.38 | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.38 | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.38 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.38 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.38 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.38 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | BETA: splitting (9693) gives:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9694) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.38 | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.38 | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | ALPHA: (9694) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | (9695) op(e2, e2) = e1
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | REF_CLOSE: (39), (199), (268), (7920), (9681), (9683),
% 140.52/20.38 | | | | | | | | | | | | | | | | (9695), (function-axioms) are inconsistent by
% 140.52/20.38 | | | | | | | | | | | | | | | | sub-proof #9.
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9696) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.38 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.38 | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.38 | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.38 | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.38 | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.38 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.38 | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.38 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | BETA: splitting (9696) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9697) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | ALPHA: (9697) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9698) op(e0, e0) = e2
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9408), (9698), (function-axioms) are
% 140.52/20.38 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9699) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.38 | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.38 | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.38 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.38 | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.38 | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | ALPHA: (9699) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9700) op(e0, e0) = all_56_15
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9701) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.38 | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.38 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.38 | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (8), (39), (7919), (9408), (9681), (9700),
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9701), (function-axioms) are inconsistent by
% 140.52/20.38 | | | | | | | | | | | | | | | | | sub-proof #8.
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | End of split
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | Case 2:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | (9702) all_20_2 = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | COMBINE_EQS: (283), (9702) imply:
% 140.52/20.38 | | | | | | | | | | | | | (9703) all_6_2 = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | SIMP: (9703) implies:
% 140.52/20.38 | | | | | | | | | | | | | (9704) all_6_2 = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REDUCE: (353), (9704) imply:
% 140.52/20.38 | | | | | | | | | | | | | (9705) ~ (all_52_6 = e1)
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REDUCE: (357), (9704) imply:
% 140.52/20.38 | | | | | | | | | | | | | (9706) ~ (all_52_9 = e1)
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REDUCE: (7920), (9704) imply:
% 140.52/20.38 | | | | | | | | | | | | | (9707) ~ (e3 = e1)
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | REDUCE: (39), (9704) imply:
% 140.52/20.38 | | | | | | | | | | | | | (9708) op(e2, e2) = e1
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | BETA: splitting (217) gives:
% 140.52/20.38 | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | (9709) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 140.52/20.38 | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | BETA: splitting (9709) gives:
% 140.52/20.38 | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | (9710) all_57_6 = e1 & op(e1, e3) = e1
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | ALPHA: (9710) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | (9711) op(e1, e3) = e1
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | BETA: splitting (221) gives:
% 140.52/20.38 | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | (9712) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 140.52/20.38 | | | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | BETA: splitting (9712) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9713) all_57_4 = e1 & op(e3, e1) = e1
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | ALPHA: (9713) implies:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9714) op(e3, e1) = e1
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_2, e1,
% 140.52/20.38 | | | | | | | | | | | | | | | | | e3, e1, simplifying with (163), (9711) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9715) all_52_2 = e1
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e1,
% 140.52/20.38 | | | | | | | | | | | | | | | | | e1, e3, simplifying with (169), (9714) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9716) all_52_8 = e1
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | REDUCE: (143), (9715) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9717) ~ (all_52_6 = e1)
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | REDUCE: (141), (9715) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9718) ~ (all_52_14 = e1)
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | REDUCE: (7909), (9716) imply:
% 140.52/20.38 | | | | | | | | | | | | | | | | | (9719) ~ (e2 = e1)
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 140.52/20.38 | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.38 | | | | | | | | | | | | | | | | | |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | (9720) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 140.52/20.38 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.38 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 140.52/20.38 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 140.52/20.38 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.52/20.38 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 140.52/20.38 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.52/20.38 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 140.52/20.38 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 140.52/20.38 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.52/20.38 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (162), (7919), (9705), (9711), (9720),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | | | | | #29.
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (9721) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | BETA: splitting (9721) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9722) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | ALPHA: (9722) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9723) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9724) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9725) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9726) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (9726) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9727) all_56_4 = e2 & op(e2, e1) = e2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (9727) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9728) op(e2, e1) = e2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9728), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9729) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | ALPHA: (9729) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9730) ~ (all_56_11 = e1)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9731) op(e2, e2) = all_56_11
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (9732) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9732) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (9733) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9679), (9733), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (9734) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9734), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (9735) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9735) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (9736) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9708), (9723), (9724), (9725), (9726),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (9730), (9731), (9736), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #12.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (9737) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9737) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (9738) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9738) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (9739) all_56_11 = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9726), (9739), (function-axioms)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #91.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (9740) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9740) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9741) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9741) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9742) op(e0, e0) = e2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (8), (9), (165), (207), (7910),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (7919), (9679), (9708), (9723), (9724), (9725),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9726), (9730), (9731), (9742), (function-axioms)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #11.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9743) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9743) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9744) op(e0, e0) = all_56_15
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9745) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (8), (7919), (9708), (9723), (9724),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (9725), (9726), (9730), (9731), (9744), (9745),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | | #7.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9746) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | ALPHA: (9746) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9747) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9748) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9749) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9750) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | $i(all_56_13))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9751) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (110), (112), (113), (160), (164), (168),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (193), (197), (250), (260), (7912), (9398),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9399), (9679), (9708), (9747), (9748), (9749),
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9750), (9751), (function-axioms) are inconsistent
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | by sub-proof #6.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | (9752) all_57_5 = e1 & op(e2, e1) = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9706), (9752), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #348.
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | (9753) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | REF_CLOSE: (6), (157), (7919), (9396), (9753),
% 140.52/20.39 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | | | #5.
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | (9754) all_57_7 = e1 & op(e1, e2) = e1
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | ALPHA: (9754) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | (9755) op(e1, e2) = e1
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | REF_CLOSE: (162), (9705), (9755), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | inconsistent by sub-proof #341.
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | (9756) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 140.52/20.39 | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | REF_CLOSE: (6), (160), (7919), (9399), (9756),
% 140.52/20.39 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | #35.
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | (9757) all_16_2 = e0
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | COMBINE_EQS: (328), (9757) imply:
% 140.52/20.39 | | | | | | | | | | | | (9758) all_6_2 = e0
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | REDUCE: (353), (9758) imply:
% 140.52/20.39 | | | | | | | | | | | | (9759) ~ (all_52_6 = e0)
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | REDUCE: (7920), (9758) imply:
% 140.52/20.39 | | | | | | | | | | | | (9760) ~ (e3 = e0)
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | REDUCE: (39), (9758) imply:
% 140.52/20.39 | | | | | | | | | | | | (9761) op(e2, e2) = e0
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | BETA: splitting (216) gives:
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | (9762) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 140.52/20.39 | | | | | | | | | | | | | & op(e1, e2) = e0)
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | BETA: splitting (9762) gives:
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | (9763) all_57_6 = e0 & op(e1, e3) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | ALPHA: (9763) implies:
% 140.52/20.39 | | | | | | | | | | | | | | (9764) all_57_6 = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (234), (236),
% 140.52/20.39 | | | | | | | | | | | | | | (238), (9395), (9678), (9679), (9764),
% 140.52/20.39 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | #322.
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | (9765) all_57_7 = e0 & op(e1, e2) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | ALPHA: (9765) implies:
% 140.52/20.39 | | | | | | | | | | | | | | (9766) op(e1, e2) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | REF_CLOSE: (162), (9759), (9766), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | inconsistent by sub-proof #999.
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | (9767) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 140.52/20.39 | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | BETA: splitting (9767) gives:
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | (9768) all_57_8 = e0 & op(e1, e1) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | ALPHA: (9768) implies:
% 140.52/20.39 | | | | | | | | | | | | | | (9769) op(e1, e1) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (9769), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | inconsistent by sub-proof #61.
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | (9770) all_57_11 = e0 & op(e1, e0) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | ALPHA: (9770) implies:
% 140.52/20.39 | | | | | | | | | | | | | | (9771) op(e1, e0) = e0
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | (9772) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.39 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.39 | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.39 | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.39 | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.39 | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.39 | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.39 | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.39 | | | | | | | | | | | | | | | $i(all_56_6))
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | BETA: splitting (9772) gives:
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | (9773) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.39 | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (9679), (9773), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | inconsistent by sub-proof #753.
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | (9774) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.52/20.39 | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.52/20.39 | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9774), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | (9775) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.39 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.39 | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.39 | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.39 | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.39 | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.39 | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.39 | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.39 | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.39 | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.39 | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.39 | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | BETA: splitting (9775) gives:
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | (9776) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.39 | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (8), (9408), (9761), (9776),
% 140.52/20.39 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | | | #192.
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | (9777) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.39 | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.39 | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.39 | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.39 | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.39 | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.39 | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.39 | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.39 | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | BETA: splitting (9777) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | (9778) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | ALPHA: (9778) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | (9779) op(e2, e2) = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9761), (9779), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1117.
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | (9780) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.39 | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.39 | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.39 | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.39 | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.39 | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.39 | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | BETA: splitting (9780) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (9781) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ALPHA: (9781) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (9782) op(e0, e0) = e2
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9408), (9782), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (9783) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.39 | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | ALPHA: (9783) implies:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (9784) op(e0, e0) = all_56_15
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (9785) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.39 | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.39 | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | BETA: splitting (209) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9786) all_57_15 = e0 & op(e0, e0) = e0
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9407), (9786) are inconsistent by sub-proof
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | #358.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e1,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | all_56_15, e0, e0, simplifying with (9408), (9784)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9787) all_56_15 = e1
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_14,
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | e0, e0, e1, simplifying with (160), (9771) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9788) all_52_14 = e0
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | REDUCE: (7912), (9788) imply:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | (9789) ~ (e2 = e0)
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | BETA: splitting (9785) gives:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9790) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (9787), (9790) are inconsistent by
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | sub-proof #334.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | (9791) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (7919), (9791), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #26.
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | (9792) all_57_2 = e0 & op(e2, e3) = e0
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | REF_CLOSE: (167), (9671), (9792), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | inconsistent by sub-proof #1028.
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | (9793) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 =
% 140.52/20.39 | | | | | | | | | | e0 & op(e0, e3) = e0)
% 140.52/20.39 | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | BETA: splitting (9793) gives:
% 140.52/20.39 | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | Case 1:
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | (9794) all_57_6 = e0 & op(e1, e3) = e0
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | ALPHA: (9794) implies:
% 140.52/20.39 | | | | | | | | | | | (9795) all_57_6 = e0
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (168), (169),
% 140.52/20.39 | | | | | | | | | | | (170), (233), (234), (236), (238), (9395), (9673),
% 140.52/20.39 | | | | | | | | | | | (9674), (9675), (9795), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | inconsistent by sub-proof #321.
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | Case 2:
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | (9796) all_57_12 = e0 & op(e0, e3) = e0
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | ALPHA: (9796) implies:
% 140.52/20.39 | | | | | | | | | | | (9797) op(e0, e3) = e0
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | | REF_CLOSE: (159), (9672), (9797), (function-axioms) are
% 140.52/20.39 | | | | | | | | | | | inconsistent by sub-proof #986.
% 140.52/20.39 | | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | | |
% 140.52/20.39 | | | | | | | | | End of split
% 140.52/20.39 | | | | | | | | |
% 140.52/20.39 | | | | | | | | End of split
% 140.52/20.39 | | | | | | | |
% 140.52/20.39 | | | | | | | End of split
% 140.52/20.39 | | | | | | |
% 140.52/20.39 | | | | | | End of split
% 140.52/20.39 | | | | | |
% 140.52/20.39 | | | | | End of split
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | Case 2:
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | (9798) all_6_2 = e3
% 140.52/20.39 | | | | | (9799) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3)
% 140.52/20.39 | | | | | = all_6_1 & $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 =
% 140.52/20.39 | | | | | e1) & op(e2, e3) = all_6_1 & $i(all_6_1))
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | COMBINE_EQS: (331), (9798) imply:
% 140.52/20.39 | | | | | (9800) all_26_2 = e3
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | REDUCE: (348), (9798) imply:
% 140.52/20.39 | | | | | (9801) ~ (all_52_1 = e3)
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | REDUCE: (351), (9798) imply:
% 140.52/20.39 | | | | | (9802) ~ (all_52_4 = e3)
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | REDUCE: (353), (9798) imply:
% 140.52/20.39 | | | | | (9803) ~ (all_52_6 = e3)
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | REDUCE: (355), (9798) imply:
% 140.52/20.39 | | | | | (9804) ~ (all_52_7 = e3)
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | REDUCE: (357), (9798) imply:
% 140.52/20.39 | | | | | (9805) ~ (all_52_9 = e3)
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | REDUCE: (359), (9798) imply:
% 140.52/20.39 | | | | | (9806) ~ (all_52_13 = e3)
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | BETA: splitting (231) gives:
% 140.52/20.39 | | | | |
% 140.52/20.39 | | | | | Case 1:
% 140.52/20.39 | | | | | |
% 140.52/20.39 | | | | | | (9807) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 140.52/20.39 | | | | | | op(e2, e2) = e3)
% 140.52/20.39 | | | | | |
% 140.52/20.39 | | | | | | BETA: splitting (9807) gives:
% 140.52/20.39 | | | | | |
% 140.52/20.39 | | | | | | Case 1:
% 140.52/20.39 | | | | | | |
% 140.52/20.39 | | | | | | | (9808) all_57_1 = e3 & op(e3, e2) = e3
% 140.52/20.39 | | | | | | |
% 140.52/20.39 | | | | | | | ALPHA: (9808) implies:
% 140.52/20.39 | | | | | | | (9809) op(e3, e2) = e3
% 140.52/20.39 | | | | | | |
% 140.52/20.39 | | | | | | | REF_CLOSE: (170), (9802), (9809), (function-axioms) are
% 140.52/20.39 | | | | | | | inconsistent by sub-proof #1107.
% 140.52/20.39 | | | | | | |
% 140.52/20.39 | | | | | | Case 2:
% 140.52/20.39 | | | | | | |
% 140.52/20.40 | | | | | | | (9810) all_57_3 = e3 & op(e2, e2) = e3
% 140.52/20.40 | | | | | | |
% 140.52/20.40 | | | | | | | ALPHA: (9810) implies:
% 140.52/20.40 | | | | | | | (9811) all_57_3 = e3
% 140.52/20.40 | | | | | | | (9812) op(e2, e2) = e3
% 140.52/20.40 | | | | | | |
% 140.52/20.40 | | | | | | | BETA: splitting (46) gives:
% 140.52/20.40 | | | | | | |
% 140.52/20.40 | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | |
% 140.52/20.40 | | | | | | | | (9813) ~ (all_10_2 = e1)
% 140.52/20.40 | | | | | | | |
% 140.52/20.40 | | | | | | | | BETA: splitting (52) gives:
% 140.52/20.40 | | | | | | | |
% 140.52/20.40 | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | |
% 140.52/20.40 | | | | | | | | | (9814) ~ (all_14_2 = e0)
% 140.52/20.40 | | | | | | | | |
% 140.52/20.40 | | | | | | | | | BETA: splitting (64) gives:
% 140.52/20.40 | | | | | | | | |
% 140.52/20.40 | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | (9815) ~ (all_22_2 = e1)
% 140.52/20.40 | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | REDUCE: (321), (9815) imply:
% 140.52/20.40 | | | | | | | | | | (9816) ~ (all_14_2 = e1)
% 140.52/20.40 | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | BETA: splitting (67) gives:
% 140.52/20.40 | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | (9817) ~ (all_24_2 = e2)
% 140.52/20.40 | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | REDUCE: (319), (9817) imply:
% 140.52/20.40 | | | | | | | | | | | (9818) ~ (all_10_2 = e2)
% 140.52/20.40 | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | BETA: splitting (79) gives:
% 140.52/20.40 | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | (9819) ~ (all_32_2 = e2)
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | REDUCE: (7906), (9819) imply:
% 140.52/20.40 | | | | | | | | | | | | (9820) $false
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | CLOSE: (9820) is inconsistent.
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | (9821) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0
% 140.52/20.40 | | | | | | | | | | | | & op(e1, e2) = all_32_1 & $i(all_32_0) &
% 140.52/20.40 | | | | | | | | | | | | $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2)
% 140.52/20.40 | | | | | | | | | | | | = all_32_1 & $i(all_32_1))
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | BETA: splitting (85) gives:
% 140.52/20.40 | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | (9822) ~ (all_36_2 = e2)
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | REDUCE: (305), (9822) imply:
% 140.52/20.40 | | | | | | | | | | | | | (9823) ~ (all_14_2 = e2)
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | BETA: splitting (204) gives:
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | (9824) all_54_0 = e3
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | COMBINE_EQS: (279), (9824) imply:
% 140.52/20.40 | | | | | | | | | | | | | | (9825) all_14_2 = e3
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | SIMP: (9825) implies:
% 140.52/20.40 | | | | | | | | | | | | | | (9826) all_14_2 = e3
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | REDUCE: (51), (9826) imply:
% 140.52/20.40 | | | | | | | | | | | | | | (9827) op(e3, e3) = e3
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (45), (51), (207), (7919), (9812),
% 140.52/20.40 | | | | | | | | | | | | | | (9813), (9814), (9818), (9827), (function-axioms)
% 140.52/20.40 | | | | | | | | | | | | | | are inconsistent by sub-proof #68.
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | (9828) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | REF_CLOSE: (279), (9814), (9816), (9823), (9828) are
% 140.52/20.40 | | | | | | | | | | | | | | inconsistent by sub-proof #883.
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | (9829) all_36_2 = e2
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | COMBINE_EQS: (305), (9829) imply:
% 140.52/20.40 | | | | | | | | | | | | | (9830) all_14_2 = e2
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | SIMP: (9830) implies:
% 140.52/20.40 | | | | | | | | | | | | | (9831) all_14_2 = e2
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | REDUCE: (337), (9831) imply:
% 140.52/20.40 | | | | | | | | | | | | | (9832) ~ (all_52_1 = e2)
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | REDUCE: (51), (9831) imply:
% 140.52/20.40 | | | | | | | | | | | | | (9833) op(e3, e3) = e2
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | BETA: splitting (226) gives:
% 140.52/20.40 | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | (9834) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 140.52/20.40 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (9812), (9832), (9834),
% 140.52/20.40 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | #154.
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | (9835) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 140.52/20.40 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | BETA: splitting (9835) gives:
% 140.52/20.40 | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | (9836) all_57_5 = e2 & op(e2, e1) = e2
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | ALPHA: (9836) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | (9837) op(e2, e1) = e2
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9837), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | (9838) all_57_10 = e2 & op(e2, e0) = e2
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | ALPHA: (9838) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | (9839) all_57_10 = e2
% 140.52/20.40 | | | | | | | | | | | | | | | (9840) op(e2, e0) = e2
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 140.52/20.40 | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | (9841) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 140.52/20.40 | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 140.52/20.40 | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | BETA: splitting (9841) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9842) all_57_12 = e2 & op(e0, e3) = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | ALPHA: (9842) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9843) all_57_12 = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (232), (234), (238),
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9833), (9843), (function-axioms) are inconsistent
% 140.52/20.40 | | | | | | | | | | | | | | | | | by sub-proof #50.
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9844) all_57_13 = e2 & op(e0, e2) = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | ALPHA: (9844) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9845) all_57_13 = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_13,
% 140.52/20.40 | | | | | | | | | | | | | | | | | e2, e0, e2, simplifying with (164), (9840) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9846) all_52_13 = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | REDUCE: (370), (9846) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9847) ~ (all_10_2 = e2)
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | REDUCE: (9806), (9846) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | (9848) ~ (e3 = e2)
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (9849) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 140.52/20.40 | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | REF_CLOSE: (167), (170), (9802), (9812), (9832), (9833),
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (9849), (function-axioms) are inconsistent by
% 140.52/20.40 | | | | | | | | | | | | | | | | | | sub-proof #177.
% 140.52/20.40 | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (9850) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 140.52/20.40 | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | BETA: splitting (9850) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9851) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | ALPHA: (9851) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9852) op(e1, e1) = all_56_13
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9853) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | $i(all_56_14))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9854) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | $i(all_56_15))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9855) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9856) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9857) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | $i(all_56_11))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | (9858) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 140.52/20.40 | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | BETA: splitting (9853) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | (9859) all_56_15 = e1 & op(e0, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | ALPHA: (9859) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | (9860) op(e0, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9813), (9860), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | (9861) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | ALPHA: (9861) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | (9862) ~ (all_56_14 = e0)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | (9863) op(e0, e1) = all_56_14
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | BETA: splitting (9855) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | (9864) all_56_11 = e1 & op(e2, e2) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9864) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | (9865) all_56_11 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9857), (9865), (function-axioms)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #91.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | (9866) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | $i(all_56_4)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | ALPHA: (9866) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | (9867) ~ (all_56_4 = e2)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | (9868) op(e2, e1) = all_56_4
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9856) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | (9869) all_56_9 = e1 & op(e3, e3) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9869) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | (9870) op(e3, e3) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9833), (9870), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #818.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | (9871) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9871) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | (9872) ~ (all_56_1 = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | (9873) op(e3, e1) = all_56_1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9857) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | (9874) all_56_4 = e2 & op(e2, e1) = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9874) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | (9875) op(e2, e1) = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (9875), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | (9876) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_11)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9876) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | (9877) op(e2, e2) = all_56_11
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9858) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9878) all_56_1 = e3 & op(e3, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9878) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9879) op(e3, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9833), (9856), (9879), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9880) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_56_9)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9880) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9881) ~ (all_56_9 = e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9882) op(e3, e3) = all_56_9
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_11,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_14, e1, e0, simplifying with (157), (9863)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9883) all_56_14 = all_52_11
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_13, e1, e1, simplifying with (7919), (9852)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9884) all_56_13 = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_9,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_4, e1, e2, simplifying with (165), (9868)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9885) all_56_4 = all_52_9
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e3,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_11, e2, e2, simplifying with (9812), (9877)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9886) all_56_11 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | all_56_1, e1, e3, simplifying with (169), (9873)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9887) all_56_1 = all_52_8
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with e2, all_56_9,
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | e3, e3, simplifying with (9833), (9882) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9888) all_56_9 = e2
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9872), (9887) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9889) ~ (all_52_8 = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (9862), (9883) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | (9890) ~ (all_52_11 = e0)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (239) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | (9891) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (170), (9802), (9833), (9891),
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | #180.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | (9892) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9892) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (9893) all_57_4 = e3 & op(e3, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9893) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (9894) op(e3, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9833), (9856), (9894), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (9895) all_57_9 = e3 & op(e3, e0) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9895) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | (9896) all_57_9 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9897) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9897) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9898) all_57_4 = e3 & op(e3, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9898) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9899) op(e3, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (9833), (9856), (9899), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #153.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9900) all_57_5 = e3 & op(e2, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9805), (9900), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | (9901) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9901) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9902) all_57_8 = e3 & op(e1, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9902) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9903) op(e1, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9903), (function-axioms) are
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9904) all_57_14 = e3 & op(e0, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9904) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9905) all_57_14 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9906) op(e0, e1) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (213) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9907) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9907) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9908) all_57_9 = e1 & op(e3, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9908) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9909) all_57_9 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9896), (9909) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9910) e3 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9886), (9910) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9911) all_56_11 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9857), (9867), (9911) are inconsistent by
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9912) all_57_10 = e1 & op(e2, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9839), (9858), (9888), (9889), (9912),
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #90.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9913) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9913) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9914) all_57_11 = e1 & op(e1, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9914) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9915) all_57_11 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9916) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9916) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9917) all_57_12 = e1 & op(e0, e3) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9917) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9918) all_57_12 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (238) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9919) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (9801), (9833), (9919),
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #96.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9920) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9920) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9921) all_57_6 = e3 & op(e1, e3) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9921) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9922) all_57_6 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9923) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9923) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9924) all_57_6 = e0 & op(e1, e3) = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9924) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9925) all_57_6 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9922), (9925) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #873.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9926) all_57_7 = e0 & op(e1, e2) = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7905), (9821), (9906), (9926), (function-axioms)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #56.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9927) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9927) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9928) all_57_8 = e0 & op(e1, e1) = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9928) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9929) all_57_8 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (7918), (9929) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9930) e2 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (9930) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9931) $false
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (9931) is inconsistent.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9932) all_57_11 = e0 & op(e1, e0) = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9932) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9933) all_57_11 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9915), (9933) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9934) e1 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9934) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9935) e1 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9918), (9935) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9936) all_57_12 = e0
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (210) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9916) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (9918), (9936) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1002.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9937) all_57_13 = e1 & op(e0, e2) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9937) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9938) all_57_13 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9845), (9938) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9939) e2 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9888), (9939) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9940) all_56_9 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9858), (9889), (9940), (function-axioms)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #898.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9941) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9941) gives:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9942) all_57_14 = e1 & op(e0, e1) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9942) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9943) all_57_14 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9905), (9943) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9944) e3 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9944) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9945) e3 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9886), (9945) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9946) all_56_11 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9857), (9867), (9946) are inconsistent by
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9947) all_57_15 = e1 & op(e0, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9947) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9948) op(e0, e0) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9853), (9854), (9890), (9948),
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #99.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9949) all_57_12 = e3 & op(e0, e3) = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9949) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9950) all_57_12 = e3
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9918), (9950) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9951) e3 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9886), (9951) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9952) all_56_11 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9857), (9867), (9952) are inconsistent by
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9953) all_57_13 = e1 & op(e0, e2) = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9953) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9954) all_57_13 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9845), (9954) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9955) e2 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (9955) implies:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9956) e2 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9888), (9956) imply:
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9957) all_56_9 = e1
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (169), (9858), (9889), (9957), (function-axioms)
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #898.
% 140.52/20.40 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9958) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (9958) gives:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9959) all_57_14 = e1 & op(e0, e1) = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9959) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9960) all_57_14 = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9905), (9960) imply:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9961) e3 = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (9886), (9961) imply:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9962) all_56_11 = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9857), (9867), (9962) are inconsistent by
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #646.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9963) all_57_15 = e1 & op(e0, e0) = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9963) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9964) op(e0, e0) = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9853), (9854), (9890), (9964),
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #99.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9965) all_57_15 = e1 & op(e0, e0) = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (9965) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (9966) op(e0, e0) = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (157), (9853), (9854), (9890), (9966),
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #99.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9967) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (51), (207), (9813), (9814),
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9816), (9818), (9840), (9967), (function-axioms)
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #151.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | (9968) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | BETA: splitting (9968) gives:
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | (9969) all_57_14 = e2 & op(e0, e1) = e2
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | ALPHA: (9969) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | (9970) all_57_14 = e2
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | (9971) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | BETA: splitting (9971) gives:
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9972) all_57_4 = e3 & op(e3, e1) = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | ALPHA: (9972) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9973) op(e3, e1) = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (45), (51), (167), (170), (206),
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (207), (9802), (9812), (9813), (9814), (9816),
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9818), (9832), (9833), (9840), (9973),
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | #150.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9974) all_57_5 = e3 & op(e2, e1) = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9805), (9974), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | (9975) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 140.52/20.41 | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | BETA: splitting (9975) gives:
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9976) all_57_8 = e3 & op(e1, e1) = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | ALPHA: (9976) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9977) op(e1, e1) = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (9977), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9978) all_57_14 = e3 & op(e0, e1) = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | ALPHA: (9978) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | (9979) all_57_14 = e3
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9970), (9979) are inconsistent by sub-proof
% 140.52/20.41 | | | | | | | | | | | | | | | | | | | #1011.
% 140.52/20.41 | | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | (9980) all_57_15 = e2 & op(e0, e0) = e2
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | ALPHA: (9980) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | | (9981) op(e0, e0) = e2
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9818), (9981), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1115.
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | (9982) all_24_2 = e2
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | COMBINE_EQS: (319), (9982) imply:
% 140.52/20.41 | | | | | | | | | | | (9983) all_10_2 = e2
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | SIMP: (9983) implies:
% 140.52/20.41 | | | | | | | | | | | (9984) all_10_2 = e2
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | REDUCE: (361), (9984) imply:
% 140.52/20.41 | | | | | | | | | | | (9985) ~ (all_52_7 = e2)
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | REDUCE: (45), (9984) imply:
% 140.52/20.41 | | | | | | | | | | | (9986) op(e0, e0) = e2
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | BETA: splitting (230) gives:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (9987) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 140.52/20.41 | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | BETA: splitting (9987) gives:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (9988) all_57_1 = e2 & op(e3, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | ALPHA: (9988) implies:
% 140.52/20.41 | | | | | | | | | | | | | (9989) op(e3, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_4, e2,
% 140.52/20.41 | | | | | | | | | | | | | e2, e3, simplifying with (170), (9989) gives:
% 140.52/20.41 | | | | | | | | | | | | | (9990) all_52_4 = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REDUCE: (343), (9990) imply:
% 140.52/20.41 | | | | | | | | | | | | | (9991) ~ (all_14_2 = e2)
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | SIMP: (9991) implies:
% 140.52/20.41 | | | | | | | | | | | | | (9992) ~ (all_14_2 = e2)
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (6), (51), (204), (207), (279), (7919), (9812),
% 140.52/20.41 | | | | | | | | | | | | | (9814), (9816), (9986), (9992), (function-axioms)
% 140.52/20.41 | | | | | | | | | | | | | are inconsistent by sub-proof #42.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (9993) all_57_3 = e2 & op(e2, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | ALPHA: (9993) implies:
% 140.52/20.41 | | | | | | | | | | | | | (9994) op(e2, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (9), (9812), (9994), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (9995) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 140.52/20.41 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | BETA: splitting (9995) gives:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (9996) all_57_7 = e2 & op(e1, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | ALPHA: (9996) implies:
% 140.52/20.41 | | | | | | | | | | | | | (9997) op(e1, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_6, e2,
% 140.52/20.41 | | | | | | | | | | | | | e2, e1, simplifying with (162), (9997) gives:
% 140.52/20.41 | | | | | | | | | | | | | (9998) all_52_6 = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REDUCE: (7908), (9998) imply:
% 140.52/20.41 | | | | | | | | | | | | | (9999) $false
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | CLOSE: (9999) is inconsistent.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10000) all_57_13 = e2 & op(e0, e2) = e2
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (158), (9985), (10000), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | inconsistent by sub-proof #446.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | (10001) all_22_2 = e1
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | COMBINE_EQS: (321), (10001) imply:
% 140.52/20.41 | | | | | | | | | | (10002) all_14_2 = e1
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | SIMP: (10002) implies:
% 140.52/20.41 | | | | | | | | | | (10003) all_14_2 = e1
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | REDUCE: (51), (10003) imply:
% 140.52/20.41 | | | | | | | | | | (10004) op(e3, e3) = e1
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | (10005) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.41 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.41 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.41 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.41 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.41 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.41 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.41 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.41 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.41 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.41 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.41 | | | | | | | | | | | $i(all_56_6))
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | BETA: splitting (10005) gives:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (10006) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.41 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.41 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.41 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.41 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.41 | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | REF_CLOSE: (6), (10004), (10006), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | inconsistent by sub-proof #298.
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (10007) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.52/20.41 | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.52/20.41 | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.52/20.41 | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.52/20.41 | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | REF_CLOSE: (9), (7919), (10007), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | (10008) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.41 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.41 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.41 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.41 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.41 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.41 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.41 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.41 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.41 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.41 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.41 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.41 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.41 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.41 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.41 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.41 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.41 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | BETA: splitting (10008) gives:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (10009) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.41 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.41 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.41 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.41 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | BETA: splitting (10009) gives:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10010) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.41 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.52/20.41 | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | ALPHA: (10010) implies:
% 140.52/20.41 | | | | | | | | | | | | | (10011) op(e3, e3) = e0
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (4), (10004), (10011), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | inconsistent by sub-proof #840.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10012) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.52/20.41 | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.52/20.41 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | ALPHA: (10012) implies:
% 140.52/20.41 | | | | | | | | | | | | | (10013) op(e2, e2) = e1
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10013), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (10014) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.41 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.41 | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.41 | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.41 | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.41 | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.41 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.41 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.41 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.41 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.41 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | BETA: splitting (10014) gives:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10015) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.41 | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.41 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | ALPHA: (10015) implies:
% 140.52/20.41 | | | | | | | | | | | | | (10016) op(e2, e2) = e1
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10016), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10017) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.41 | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.41 | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.41 | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.41 | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.41 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.41 | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.41 | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.41 | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | BETA: splitting (10017) gives:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | (10018) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.41 | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.41 | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | ALPHA: (10018) implies:
% 140.52/20.41 | | | | | | | | | | | | | | (10019) op(e2, e2) = e0
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | REF_CLOSE: (7), (9812), (10019), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | (10020) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.41 | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.41 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.41 | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.41 | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.41 | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.41 | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.41 | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | ALPHA: (10020) implies:
% 140.52/20.41 | | | | | | | | | | | | | | (10021) op(e0, e0) = all_56_15
% 140.52/20.41 | | | | | | | | | | | | | | (10022) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.41 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.41 | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.41 | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.41 | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | REF_CLOSE: (4), (7), (45), (9812), (9813), (10004), (10021),
% 140.52/20.41 | | | | | | | | | | | | | | (10022), (function-axioms) are inconsistent by
% 140.52/20.41 | | | | | | | | | | | | | | sub-proof #113.
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | (10023) all_14_2 = e0
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | REDUCE: (337), (10023) imply:
% 140.52/20.41 | | | | | | | | | (10024) ~ (all_52_1 = e0)
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | REDUCE: (341), (10023) imply:
% 140.52/20.41 | | | | | | | | | (10025) ~ (all_52_3 = e0)
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | REDUCE: (343), (10023) imply:
% 140.52/20.41 | | | | | | | | | (10026) ~ (all_52_4 = e0)
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | REDUCE: (345), (10023) imply:
% 140.52/20.41 | | | | | | | | | (10027) ~ (all_52_8 = e0)
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | REDUCE: (51), (10023) imply:
% 140.52/20.41 | | | | | | | | | (10028) op(e3, e3) = e0
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | BETA: splitting (67) gives:
% 140.52/20.41 | | | | | | | | |
% 140.52/20.41 | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | (10029) ~ (all_24_2 = e2)
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | REDUCE: (319), (10029) imply:
% 140.52/20.41 | | | | | | | | | | (10030) ~ (all_10_2 = e2)
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | BETA: splitting (70) gives:
% 140.52/20.41 | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | (10031) ~ (all_26_2 = e3)
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | REDUCE: (9800), (10031) imply:
% 140.52/20.41 | | | | | | | | | | | (10032) $false
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | CLOSE: (10032) is inconsistent.
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | (10033) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0
% 140.52/20.41 | | | | | | | | | | | & op(e2, e3) = all_26_1 & $i(all_26_0) &
% 140.52/20.41 | | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3)
% 140.52/20.41 | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | BETA: splitting (94) gives:
% 140.52/20.41 | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | (10034) ~ (all_42_2 = e3)
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | REDUCE: (303), (10034) imply:
% 140.52/20.41 | | | | | | | | | | | | (10035) ~ (all_10_2 = e3)
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | BETA: splitting (207) gives:
% 140.52/20.41 | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10036) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.52/20.41 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.52/20.41 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.52/20.41 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.52/20.41 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.52/20.41 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.52/20.41 | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.52/20.41 | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.52/20.41 | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.52/20.41 | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.52/20.41 | | | | | | | | | | | | | $i(all_56_6))
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10028), (10036), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | (10037) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.41 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.41 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.41 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.41 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.52/20.41 | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.52/20.41 | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.52/20.41 | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.52/20.41 | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.52/20.41 | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.52/20.41 | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.52/20.41 | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.52/20.41 | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.52/20.41 | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.52/20.41 | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | BETA: splitting (10037) gives:
% 140.52/20.41 | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | (10038) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.41 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.52/20.41 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.52/20.41 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.52/20.41 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | BETA: splitting (10038) gives:
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | (10039) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.52/20.41 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.52/20.41 | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | ALPHA: (10039) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | (10040) op(e0, e0) = e3
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | REF_CLOSE: (45), (189), (246), (9813), (10030), (10035),
% 140.52/20.41 | | | | | | | | | | | | | | | (10040), (function-axioms) are inconsistent by
% 140.52/20.41 | | | | | | | | | | | | | | | sub-proof #201.
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | (10041) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.52/20.41 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.52/20.41 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | ALPHA: (10041) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | (10042) op(e2, e2) = e1
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10042), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | End of split
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | (10043) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.41 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.52/20.41 | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.52/20.41 | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.52/20.41 | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.52/20.41 | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.41 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.41 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.41 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.41 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | BETA: splitting (10043) gives:
% 140.52/20.41 | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | (10044) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.52/20.41 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.52/20.41 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | ALPHA: (10044) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | (10045) op(e2, e2) = e1
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10045), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | (10046) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.41 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.52/20.41 | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.52/20.41 | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.52/20.41 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.52/20.41 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.52/20.41 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.52/20.41 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.52/20.41 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.52/20.41 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.52/20.41 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | BETA: splitting (10046) gives:
% 140.52/20.41 | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | (10047) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.52/20.41 | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | ALPHA: (10047) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | (10048) op(e0, e0) = e2
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | REF_CLOSE: (45), (10030), (10048), (function-axioms) are
% 140.52/20.41 | | | | | | | | | | | | | | | | inconsistent by sub-proof #1115.
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | Case 2:
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | (10049) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.52/20.41 | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.52/20.41 | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.52/20.41 | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.52/20.41 | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.52/20.41 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.52/20.41 | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.52/20.41 | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | ALPHA: (10049) implies:
% 140.52/20.41 | | | | | | | | | | | | | | | | (10050) op(e0, e0) = all_56_15
% 140.52/20.41 | | | | | | | | | | | | | | | | (10051) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.41 | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.52/20.41 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.52/20.41 | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | BETA: splitting (10051) gives:
% 140.52/20.41 | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | Case 1:
% 140.52/20.41 | | | | | | | | | | | | | | | | |
% 140.52/20.41 | | | | | | | | | | | | | | | | | (10052) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.52/20.41 | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.52/20.41 | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.52/20.41 | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.52/20.41 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | BETA: splitting (10052) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10053) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | ALPHA: (10053) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10054) all_56_15 = e3
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REDUCE: (10050), (10054) imply:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10055) op(e0, e0) = e3
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (189), (246), (9813), (10030), (10035),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10055), (function-axioms) are inconsistent by
% 140.63/20.42 | | | | | | | | | | | | | | | | | | sub-proof #201.
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10056) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | ALPHA: (10056) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10057) op(e2, e2) = e0
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (9812), (10057), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1119.
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10058) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.63/20.42 | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | BETA: splitting (10058) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10059) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_8)
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | ALPHA: (10059) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10060) all_56_15 = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REDUCE: (10050), (10060) imply:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10061) op(e0, e0) = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9813), (10061), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10062) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_14)
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | ALPHA: (10062) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10063) all_56_15 = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REDUCE: (10050), (10063) imply:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10064) op(e0, e0) = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (9813), (10064), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #237.
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | (10065) all_42_2 = e3
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | COMBINE_EQS: (303), (10065) imply:
% 140.63/20.42 | | | | | | | | | | | | (10066) all_10_2 = e3
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | REDUCE: (368), (10066) imply:
% 140.63/20.42 | | | | | | | | | | | | (10067) ~ (all_52_11 = e3)
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | REDUCE: (45), (10066) imply:
% 140.63/20.42 | | | | | | | | | | | | (10068) op(e0, e0) = e3
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | BETA: splitting (223) gives:
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | (10069) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 140.63/20.42 | | | | | | | | | | | | | & op(e2, e1) = e3)
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | BETA: splitting (10069) gives:
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | (10070) all_57_4 = e3 & op(e3, e1) = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | ALPHA: (10070) implies:
% 140.63/20.42 | | | | | | | | | | | | | | (10071) all_57_4 = e3
% 140.63/20.42 | | | | | | | | | | | | | | (10072) op(e3, e1) = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | GROUND_INST: instantiating (function-axioms) with all_52_8, e3,
% 140.63/20.42 | | | | | | | | | | | | | | e1, e3, simplifying with (169), (10072) gives:
% 140.63/20.42 | | | | | | | | | | | | | | (10073) all_52_8 = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | REDUCE: (120), (10073) imply:
% 140.63/20.42 | | | | | | | | | | | | | | (10074) ~ (all_52_12 = e3)
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | SIMP: (10074) implies:
% 140.63/20.42 | | | | | | | | | | | | | | (10075) ~ (all_52_12 = e3)
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | (10076) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 140.63/20.42 | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 140.63/20.42 | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 140.63/20.42 | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | BETA: splitting (10076) gives:
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | (10077) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 140.63/20.42 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 140.63/20.42 | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 140.63/20.42 | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 140.63/20.42 | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | ALPHA: (10077) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | (10078) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_15))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | REF_CLOSE: (159), (10025), (10068), (10078),
% 140.63/20.42 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.42 | | | | | | | | | | | | | | | | #739.
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | (10079) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 140.63/20.42 | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 140.63/20.42 | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 140.63/20.42 | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 140.63/20.42 | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | ALPHA: (10079) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | (10080) op(e2, e2) = all_56_11
% 140.63/20.42 | | | | | | | | | | | | | | | | (10081) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_12))
% 140.63/20.42 | | | | | | | | | | | | | | | | (10082) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7
% 140.63/20.42 | | | | | | | | | | | | | | | | = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))
% 140.63/20.42 | | | | | | | | | | | | | | | | (10083) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_15))
% 140.63/20.42 | | | | | | | | | | | | | | | | (10084) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 140.63/20.42 | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 140.63/20.42 | | | | | | | | | | | | | | | | (10085) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13
% 140.63/20.42 | | | | | | | | | | | | | | | | = e2) & op(e1, e1) = all_56_13 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_13))
% 140.63/20.42 | | | | | | | | | | | | | | | | (10086) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 140.63/20.42 | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | BETA: splitting (10081) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10087) all_56_15 = e2 & op(e0, e0) = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | ALPHA: (10087) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10088) op(e0, e0) = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (10068), (10088), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1066.
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10089) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | $i(all_56_12)
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | ALPHA: (10089) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10090) ~ (all_56_12 = e0)
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10091) op(e0, e2) = all_56_12
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | BETA: splitting (10083) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10092) all_56_12 = e0 & op(e0, e2) = e0
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | ALPHA: (10092) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10093) op(e0, e2) = e0
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (10090), (10091), (10093), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #738.
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10094) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_15)
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | ALPHA: (10094) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10095) ~ (all_56_15 = e2)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10096) op(e0, e0) = all_56_15
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | BETA: splitting (10084) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10097) all_56_9 = e2 & op(e3, e3) = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | ALPHA: (10097) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10098) all_56_9 = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (170), (9802), (10086), (10098), (function-axioms)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #345.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10099) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | $i(all_56_0)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | ALPHA: (10099) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10100) ~ (all_56_0 = e3)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10101) op(e3, e2) = all_56_0
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (10085) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10102) all_56_7 = e1 & op(e1, e2) = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (10102) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10103) op(e1, e2) = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10082) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (128), (135), (136), (158), (162), (170), (191),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (203), (248), (272), (9804), (10026), (10090),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10091), (10100), (10101), (10103),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | #10.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10104) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | $i(all_56_7)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10104) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10105) ~ (all_56_7 = e1)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10106) op(e1, e2) = all_56_7
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (158), (159), (167),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (169), (170), (209), (220), (221), (222), (223),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (224), (225), (227), (228), (9799), (9802),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (9811), (9812), (10024), (10025), (10026),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10027), (10028), (10033), (10068), (10071),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10080), (10083), (10084), (10085), (10086),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10090), (10091), (10095), (10096), (10105),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | (10106), (function-axioms) are inconsistent by
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | | sub-proof #109.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10107) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (10107) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10108) ~ (all_56_13 = e2)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10109) op(e1, e1) = all_56_13
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (8), (36), (158), (159), (167),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (169), (170), (209), (220), (221), (222), (223),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (224), (225), (227), (228), (9799), (9811),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (9812), (10024), (10025), (10026), (10027),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10028), (10033), (10068), (10071), (10080),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10083), (10086), (10090), (10091), (10095),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10096), (10100), (10101), (10108), (10109),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | #110.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | (10110) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 140.63/20.42 | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.63/20.42 | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 140.63/20.42 | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.63/20.42 | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | BETA: splitting (10110) gives:
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | (10111) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 140.63/20.42 | | | | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 140.63/20.42 | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.63/20.42 | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.63/20.42 | | | | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 140.63/20.42 | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.63/20.42 | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | REF_CLOSE: (4), (10028), (10072), (10111), (function-axioms)
% 140.63/20.42 | | | | | | | | | | | | | | | | are inconsistent by sub-proof #733.
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | (10112) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.63/20.42 | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 140.63/20.42 | | | | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 140.63/20.42 | | | | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.63/20.42 | | | | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 140.63/20.42 | | | | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 140.63/20.42 | | | | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 140.63/20.42 | | | | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 140.63/20.42 | | | | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 140.63/20.42 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | ALPHA: (10112) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | (10113) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 140.63/20.42 | | | | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | BETA: splitting (10113) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10114) all_56_2 = e3 & op(e3, e0) = e3
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | ALPHA: (10114) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10115) op(e3, e0) = e3
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10075), (10115), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1105.
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10116) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | $i(all_56_9)
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | ALPHA: (10116) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | (10117) ~ (all_56_9 = e0)
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | BETA: splitting (207) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10118) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.42 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.63/20.42 | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (10028), (10118), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #752.
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (10119) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.42 | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.63/20.42 | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.63/20.42 | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | BETA: splitting (10119) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10120) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (10120) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10121) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (10121) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10122) all_56_9 = e0
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | REDUCE: (10117), (10122) imply:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10123) $false
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | CLOSE: (10123) is inconsistent.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10124) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (10124) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10125) op(e2, e2) = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10125), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (10126) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | BETA: splitting (10126) gives:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10127) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | ALPHA: (10127) implies:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10128) op(e2, e2) = e1
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10128), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (10129) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10068), (10117), (10129),
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | | #645.
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | (10130) all_57_5 = e3 & op(e2, e1) = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | REF_CLOSE: (165), (9805), (10130), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | (10131) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 140.63/20.42 | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | BETA: splitting (10131) gives:
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | (10132) all_57_8 = e3 & op(e1, e1) = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | ALPHA: (10132) implies:
% 140.63/20.42 | | | | | | | | | | | | | | (10133) all_57_8 = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | COMBINE_EQS: (7918), (10133) imply:
% 140.63/20.42 | | | | | | | | | | | | | | (10134) e3 = e2
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | REDUCE: (9), (10134) imply:
% 140.63/20.42 | | | | | | | | | | | | | | (10135) $false
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | CLOSE: (10135) is inconsistent.
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | (10136) all_57_14 = e3 & op(e0, e1) = e3
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | REF_CLOSE: (157), (10067), (10136), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | | | | | inconsistent by sub-proof #184.
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | (10137) all_24_2 = e2
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | COMBINE_EQS: (319), (10137) imply:
% 140.63/20.42 | | | | | | | | | | (10138) all_10_2 = e2
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | REDUCE: (45), (10138) imply:
% 140.63/20.42 | | | | | | | | | | (10139) op(e0, e0) = e2
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (9812),
% 140.63/20.42 | | | | | | | | | | (10028), (10139), (function-axioms) are
% 140.63/20.42 | | | | | | | | | | inconsistent by sub-proof #14.
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | End of split
% 140.63/20.42 | | | | | | | | |
% 140.63/20.42 | | | | | | | | End of split
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | (10140) all_10_2 = e1
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | REDUCE: (350), (10140) imply:
% 140.63/20.42 | | | | | | | | (10141) ~ (all_52_3 = e1)
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | REDUCE: (369), (10140) imply:
% 140.63/20.42 | | | | | | | | (10142) ~ (all_52_12 = e1)
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | REDUCE: (370), (10140) imply:
% 140.63/20.42 | | | | | | | | (10143) ~ (all_52_13 = e1)
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | REDUCE: (45), (10140) imply:
% 140.63/20.42 | | | | | | | | (10144) op(e0, e0) = e1
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | BETA: splitting (52) gives:
% 140.63/20.42 | | | | | | | |
% 140.63/20.42 | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | |
% 140.63/20.42 | | | | | | | | | (10145) ~ (all_14_2 = e0)
% 140.63/20.42 | | | | | | | | |
% 140.63/20.42 | | | | | | | | | BETA: splitting (64) gives:
% 140.63/20.42 | | | | | | | | |
% 140.63/20.42 | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | (10146) ~ (all_22_2 = e1)
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | REDUCE: (321), (10146) imply:
% 140.63/20.42 | | | | | | | | | | (10147) ~ (all_14_2 = e1)
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | BETA: splitting (85) gives:
% 140.63/20.42 | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | (10148) ~ (all_36_2 = e2)
% 140.63/20.42 | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | REDUCE: (305), (10148) imply:
% 140.63/20.42 | | | | | | | | | | | (10149) ~ (all_14_2 = e2)
% 140.63/20.42 | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | BETA: splitting (207) gives:
% 140.63/20.42 | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | (10150) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.42 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.42 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.42 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.42 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.63/20.42 | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.63/20.42 | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.63/20.42 | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.63/20.42 | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.63/20.42 | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.63/20.42 | | | | | | | | | | | | $i(all_56_6))
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | BETA: splitting (10150) gives:
% 140.63/20.42 | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | (10151) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.42 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.42 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.42 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.42 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.42 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | BETA: splitting (10151) gives:
% 140.63/20.42 | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | Case 1:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | (10152) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.42 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0 &
% 140.63/20.42 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_0)
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | ALPHA: (10152) implies:
% 140.63/20.42 | | | | | | | | | | | | | | (10153) op(e3, e3) = e2
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | REF_CLOSE: (51), (204), (279), (10145), (10147), (10149),
% 140.63/20.42 | | | | | | | | | | | | | | (10153), (function-axioms) are inconsistent by
% 140.63/20.42 | | | | | | | | | | | | | | sub-proof #182.
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | Case 2:
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | (10154) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 =
% 140.63/20.42 | | | | | | | | | | | | | | e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 &
% 140.63/20.42 | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_3)
% 140.63/20.42 | | | | | | | | | | | | | |
% 140.63/20.42 | | | | | | | | | | | | | | ALPHA: (10154) implies:
% 140.63/20.43 | | | | | | | | | | | | | | (10155) op(e3, e3) = e2
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | REF_CLOSE: (51), (204), (279), (10145), (10147), (10149),
% 140.63/20.43 | | | | | | | | | | | | | | (10155), (function-axioms) are inconsistent by
% 140.63/20.43 | | | | | | | | | | | | | | sub-proof #182.
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10156) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.63/20.43 | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.63/20.43 | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.63/20.43 | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (10156), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10157) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.43 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.43 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.43 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.63/20.43 | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.63/20.43 | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.63/20.43 | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.63/20.43 | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.63/20.43 | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.63/20.43 | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.63/20.43 | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.63/20.43 | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.63/20.43 | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | BETA: splitting (10157) gives:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10158) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.43 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.43 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.43 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10144), (10158), (function-axioms)
% 140.63/20.43 | | | | | | | | | | | | | are inconsistent by sub-proof #4.
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10159) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.43 | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.63/20.43 | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.63/20.43 | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.63/20.43 | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.43 | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.43 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.43 | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.43 | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.43 | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | BETA: splitting (10159) gives:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10160) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.43 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.63/20.43 | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | ALPHA: (10160) implies:
% 140.63/20.43 | | | | | | | | | | | | | | (10161) op(e2, e2) = e1
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10161), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10162) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.43 | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.63/20.43 | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.63/20.43 | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.43 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.43 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.43 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.43 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.43 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | BETA: splitting (10162) gives:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | (10163) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.43 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.63/20.43 | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | ALPHA: (10163) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | (10164) op(e0, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | REF_CLOSE: (6), (51), (204), (207), (279), (7919), (9812),
% 140.63/20.43 | | | | | | | | | | | | | | | (10145), (10147), (10149), (10164),
% 140.63/20.43 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | | #42.
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | (10165) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.63/20.43 | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.63/20.43 | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.63/20.43 | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.43 | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.63/20.43 | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.63/20.43 | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.63/20.43 | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.63/20.43 | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.63/20.43 | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.63/20.43 | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (7919), (9812), (10144), (10165),
% 140.63/20.43 | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | | #3.
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10166) all_36_2 = e2
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | COMBINE_EQS: (305), (10166) imply:
% 140.63/20.43 | | | | | | | | | | | (10167) all_14_2 = e2
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | REDUCE: (337), (10167) imply:
% 140.63/20.43 | | | | | | | | | | | (10168) ~ (all_52_1 = e2)
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | REDUCE: (51), (10167) imply:
% 140.63/20.43 | | | | | | | | | | | (10169) op(e3, e3) = e2
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | BETA: splitting (211) gives:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10170) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 140.63/20.43 | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | BETA: splitting (10170) gives:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10171) all_57_12 = e2 & op(e0, e3) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | ALPHA: (10171) implies:
% 140.63/20.43 | | | | | | | | | | | | | (10172) all_57_12 = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (232), (234),
% 140.63/20.43 | | | | | | | | | | | | | (238), (10141), (10169), (10172),
% 140.63/20.43 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | #2.
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10173) all_57_13 = e2 & op(e0, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | ALPHA: (10173) implies:
% 140.63/20.43 | | | | | | | | | | | | | (10174) op(e0, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | BETA: splitting (226) gives:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10175) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 140.63/20.43 | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (9812), (10168), (10175),
% 140.63/20.43 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | #154.
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10176) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 140.63/20.43 | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | BETA: splitting (10176) gives:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | (10177) all_57_5 = e2 & op(e2, e1) = e2
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | ALPHA: (10177) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | (10178) op(e2, e1) = e2
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (10178), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | (10179) all_57_10 = e2 & op(e2, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | ALPHA: (10179) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | (10180) op(e2, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | REF_CLOSE: (7), (117), (118), (121), (125), (145), (157),
% 140.63/20.43 | | | | | | | | | | | | | | | (158), (164), (165), (167), (169), (170), (206),
% 140.63/20.43 | | | | | | | | | | | | | | | (220), (223), (7919), (9802), (9805), (9806),
% 140.63/20.43 | | | | | | | | | | | | | | | (9812), (10143), (10144), (10169), (10174),
% 140.63/20.43 | | | | | | | | | | | | | | | (10180), (function-axioms) are inconsistent by
% 140.63/20.43 | | | | | | | | | | | | | | | sub-proof #1.
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10181) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 140.63/20.43 | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | BETA: splitting (10181) gives:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10182) all_57_14 = e2 & op(e0, e1) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | ALPHA: (10182) implies:
% 140.63/20.43 | | | | | | | | | | | | | (10183) all_57_14 = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | BETA: splitting (212) gives:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10184) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 140.63/20.43 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | BETA: splitting (10184) gives:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | (10185) all_57_12 = e3 & op(e0, e3) = e3
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | ALPHA: (10185) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | (10186) all_57_12 = e3
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | BETA: splitting (226) gives:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | (10187) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (167), (9812), (10168), (10187),
% 140.63/20.43 | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | | | #154.
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | (10188) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 140.63/20.43 | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | BETA: splitting (10188) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | (10189) all_57_5 = e2 & op(e2, e1) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | ALPHA: (10189) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | (10190) op(e2, e1) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (7910), (10190), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | | | inconsistent by sub-proof #890.
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | (10191) all_57_10 = e2 & op(e2, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | ALPHA: (10191) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | (10192) op(e2, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | BETA: splitting (223) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | (10193) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e3)
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | BETA: splitting (10193) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10194) all_57_4 = e3 & op(e3, e1) = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | ALPHA: (10194) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10195) all_57_4 = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | (10196) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10196) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10197) all_57_1 = e2 & op(e3, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10197) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10198) all_57_1 = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | (10199) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (10169), (10198), (10199), (function-axioms)
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #142.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | (10200) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (10200) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | | (10201) all_57_4 = e1 & op(e3, e1) = e1
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (10195), (10201) are inconsistent by
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #143.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | | (10202) all_57_9 = e1 & op(e3, e0) = e1
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (168), (10142), (10202), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #461.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10203) all_57_3 = e2 & op(e2, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10203) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10204) op(e2, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (9812), (10204), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #728.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | (10205) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | BETA: splitting (10205) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10206) all_57_7 = e2 & op(e1, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (162), (7908), (10206), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #78.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10207) all_57_13 = e2 & op(e0, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | ALPHA: (10207) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10208) op(e0, e2) = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (117), (118), (121), (125), (145), (157),
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (158), (164), (165), (167), (169), (170), (206),
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (220), (223), (7919), (9802), (9805), (9806),
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (9812), (10143), (10144), (10169), (10192),
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | (10208), (function-axioms) are inconsistent by
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | | sub-proof #1.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10209) all_57_5 = e3 & op(e2, e1) = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (165), (9805), (10209), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #320.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | (10210) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 140.63/20.43 | | | | | | | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | BETA: splitting (10210) gives:
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10211) all_57_8 = e3 & op(e1, e1) = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | ALPHA: (10211) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10212) op(e1, e1) = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (7919), (10212), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #77.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10213) all_57_14 = e3 & op(e0, e1) = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | ALPHA: (10213) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10214) all_57_14 = e3
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10183), (10214) imply:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10215) e3 = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | SIMP: (10215) implies:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10216) e3 = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10186), (10216) imply:
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (10217) all_57_12 = e2
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (159), (232), (234),
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (238), (10141), (10169), (10217),
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | | | | | | #2.
% 140.63/20.43 | | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | (10218) all_57_13 = e3 & op(e0, e2) = e3
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | | REF_CLOSE: (158), (9804), (10218), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | | inconsistent by sub-proof #80.
% 140.63/20.43 | | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10219) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 140.63/20.43 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (10144), (10183), (10219),
% 140.63/20.43 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | #413.
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10220) all_57_15 = e2 & op(e0, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | ALPHA: (10220) implies:
% 140.63/20.43 | | | | | | | | | | | | | (10221) op(e0, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | REF_CLOSE: (6), (10144), (10221), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | (10222) all_22_2 = e1
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | COMBINE_EQS: (321), (10222) imply:
% 140.63/20.43 | | | | | | | | | | (10223) all_14_2 = e1
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | REDUCE: (51), (10223) imply:
% 140.63/20.43 | | | | | | | | | | (10224) op(e3, e3) = e1
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | BETA: splitting (207) gives:
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10225) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.43 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.43 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.43 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.43 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.63/20.43 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.63/20.43 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.63/20.43 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.63/20.43 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.63/20.43 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.63/20.43 | | | | | | | | | | | $i(all_56_6))
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | BETA: splitting (10225) gives:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10226) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.43 | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.43 | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.43 | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.43 | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | REF_CLOSE: (6), (10224), (10226), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | inconsistent by sub-proof #298.
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10227) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.63/20.43 | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.63/20.43 | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.63/20.43 | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | REF_CLOSE: (9), (7919), (10227), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10228) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.43 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.43 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.43 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.43 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.63/20.43 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.63/20.43 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.63/20.43 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.63/20.43 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.63/20.43 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.63/20.43 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.63/20.43 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.63/20.43 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.63/20.43 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.63/20.43 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.63/20.43 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | BETA: splitting (10228) gives:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10229) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.43 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.43 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.43 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10144), (10229), (function-axioms)
% 140.63/20.43 | | | | | | | | | | | | are inconsistent by sub-proof #4.
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10230) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.43 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.63/20.43 | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.63/20.43 | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.63/20.43 | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.43 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.43 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.43 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.43 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.43 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | BETA: splitting (10230) gives:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10231) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.43 | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.63/20.43 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | ALPHA: (10231) implies:
% 140.63/20.43 | | | | | | | | | | | | | (10232) op(e2, e2) = e1
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10232), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10233) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.43 | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.63/20.43 | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.63/20.43 | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.43 | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.43 | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.43 | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.43 | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.43 | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | BETA: splitting (10233) gives:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10234) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.43 | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.63/20.43 | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | ALPHA: (10234) implies:
% 140.63/20.43 | | | | | | | | | | | | | | (10235) op(e0, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | REF_CLOSE: (6), (10144), (10235), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | | inconsistent by sub-proof #1070.
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | (10236) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.63/20.43 | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.63/20.43 | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.63/20.43 | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.43 | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.63/20.43 | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.63/20.43 | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.63/20.43 | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.63/20.43 | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.63/20.43 | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.63/20.43 | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (7919), (9812), (10144), (10236),
% 140.63/20.43 | | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.43 | | | | | | | | | | | | | | #3.
% 140.63/20.43 | | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | |
% 140.63/20.43 | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | |
% 140.63/20.43 | | | | | | | | | (10237) all_14_2 = e0
% 140.63/20.43 | | | | | | | | |
% 140.63/20.43 | | | | | | | | | REDUCE: (51), (10237) imply:
% 140.63/20.43 | | | | | | | | | (10238) op(e3, e3) = e0
% 140.63/20.43 | | | | | | | | |
% 140.63/20.43 | | | | | | | | | BETA: splitting (207) gives:
% 140.63/20.43 | | | | | | | | |
% 140.63/20.43 | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | (10239) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.43 | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.43 | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.43 | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.43 | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.63/20.43 | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.63/20.43 | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.63/20.43 | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.63/20.43 | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.63/20.43 | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.63/20.43 | | | | | | | | | | $i(all_56_6))
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | BETA: splitting (10239) gives:
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10240) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.63/20.43 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.63/20.43 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.63/20.43 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.63/20.43 | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | REF_CLOSE: (5), (10238), (10240), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | inconsistent by sub-proof #753.
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10241) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.63/20.43 | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.63/20.43 | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.63/20.43 | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.63/20.43 | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.63/20.43 | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | REF_CLOSE: (9), (7919), (10241), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | inconsistent by sub-proof #76.
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | End of split
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | (10242) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.43 | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.43 | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.43 | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.43 | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.63/20.43 | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.63/20.43 | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.63/20.43 | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.63/20.43 | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.63/20.43 | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.63/20.43 | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.63/20.43 | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.63/20.43 | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.63/20.43 | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.63/20.43 | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.63/20.43 | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | BETA: splitting (10242) gives:
% 140.63/20.43 | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10243) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.63/20.43 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.63/20.43 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.63/20.43 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.63/20.43 | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | REF_CLOSE: (8), (9812), (10144), (10243), (function-axioms)
% 140.63/20.43 | | | | | | | | | | | are inconsistent by sub-proof #4.
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | (10244) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.43 | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.63/20.43 | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.63/20.43 | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.63/20.43 | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.63/20.43 | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.63/20.43 | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.43 | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.43 | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.43 | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.43 | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.43 | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | BETA: splitting (10244) gives:
% 140.63/20.43 | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10245) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.63/20.43 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.63/20.43 | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | ALPHA: (10245) implies:
% 140.63/20.43 | | | | | | | | | | | | (10246) op(e2, e2) = e1
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | REF_CLOSE: (8), (9812), (10246), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | inconsistent by sub-proof #69.
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | (10247) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.43 | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.63/20.43 | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.63/20.43 | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.63/20.43 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.63/20.43 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.43 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.63/20.43 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.63/20.43 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.63/20.43 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.43 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.43 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | BETA: splitting (10247) gives:
% 140.63/20.43 | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 1:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10248) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.63/20.43 | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.63/20.43 | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | ALPHA: (10248) implies:
% 140.63/20.43 | | | | | | | | | | | | | (10249) op(e0, e0) = e2
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | REF_CLOSE: (4), (5), (6), (7), (8), (9), (207), (9812),
% 140.63/20.43 | | | | | | | | | | | | | (10238), (10249), (function-axioms) are
% 140.63/20.43 | | | | | | | | | | | | | inconsistent by sub-proof #14.
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | Case 2:
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.43 | | | | | | | | | | | | | (10250) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.63/20.43 | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.63/20.43 | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.63/20.43 | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.43 | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.63/20.43 | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.63/20.43 | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.63/20.43 | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.63/20.43 | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.63/20.43 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.63/20.43 | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.63/20.43 | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.63/20.43 | | | | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | | | | REF_CLOSE: (5), (7), (8), (7919), (9812), (10144), (10250),
% 140.63/20.44 | | | | | | | | | | | | | (function-axioms) are inconsistent by sub-proof
% 140.63/20.44 | | | | | | | | | | | | | #3.
% 140.63/20.44 | | | | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | | | End of split
% 140.63/20.44 | | | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | | End of split
% 140.63/20.44 | | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | End of split
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | End of split
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | End of split
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | End of split
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | End of split
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | Case 2:
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | (10251) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 140.63/20.44 | | | | | | op(e0, e2) = e3)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | BETA: splitting (10251) gives:
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | Case 1:
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | (10252) all_57_7 = e3 & op(e1, e2) = e3
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | REF_CLOSE: (162), (9803), (10252), (function-axioms) are
% 140.63/20.44 | | | | | | | inconsistent by sub-proof #27.
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | Case 2:
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | (10253) all_57_13 = e3 & op(e0, e2) = e3
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | REF_CLOSE: (158), (9804), (10253), (function-axioms) are
% 140.63/20.44 | | | | | | | inconsistent by sub-proof #80.
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | End of split
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | End of split
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | End of split
% 140.63/20.44 | | | |
% 140.63/20.44 | | | Case 2:
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | (10254) all_57_11 = e2 & op(e1, e0) = e2
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | ALPHA: (10254) implies:
% 140.63/20.44 | | | | (10255) op(e1, e0) = e2
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | GROUND_INST: instantiating (function-axioms) with all_52_14, e2, e0, e1,
% 140.63/20.44 | | | | simplifying with (160), (10255) gives:
% 140.63/20.44 | | | | (10256) all_52_14 = e2
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | REDUCE: (7912), (10256) imply:
% 140.63/20.44 | | | | (10257) $false
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | CLOSE: (10257) is inconsistent.
% 140.63/20.44 | | | |
% 140.63/20.44 | | | End of split
% 140.63/20.44 | | |
% 140.63/20.44 | | End of split
% 140.63/20.44 | |
% 140.63/20.44 | End of split
% 140.63/20.44 |
% 140.63/20.44 End of proof
% 140.63/20.44
% 140.63/20.44 Sub-proof #1 shows that the following formulas are inconsistent:
% 140.63/20.44 ----------------------------------------------------------------
% 140.63/20.44 (1) ~ (all_52_8 = all_52_11)
% 140.63/20.44 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 140.63/20.44 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 140.63/20.44 (3) ~ (all_52_13 = e3)
% 140.63/20.44 (4) ~ (all_52_9 = all_52_13)
% 140.63/20.44 (5) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.63/20.44 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.63/20.44 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.63/20.44 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.63/20.44 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 140.63/20.44 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 140.63/20.44 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 140.63/20.44 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 140.63/20.44 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 140.63/20.44 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 140.63/20.44 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 140.63/20.44 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.63/20.44 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.63/20.44 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 140.63/20.44 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.63/20.44 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 140.63/20.44 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.63/20.44 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 140.63/20.44 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 140.63/20.44 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 140.63/20.44 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 140.63/20.44 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.63/20.44 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.63/20.44 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 140.63/20.44 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.63/20.44 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.63/20.44 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 140.63/20.44 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 140.63/20.44 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 140.63/20.44 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 140.63/20.44 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 140.63/20.44 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.63/20.44 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.63/20.44 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 140.63/20.44 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.63/20.44 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 140.63/20.44 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 140.63/20.44 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 140.63/20.44 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 140.63/20.44 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 140.63/20.44 (6) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 140.63/20.44 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 140.63/20.44 (7) ~ (all_52_9 = all_52_11)
% 140.63/20.44 (8) op(e3, e3) = e2
% 140.63/20.44 (9) ~ (e3 = e0)
% 140.63/20.44 (10) ~ (all_52_4 = e3)
% 140.63/20.44 (11) op(e3, e1) = all_52_8
% 140.63/20.44 (12) ~ (all_52_1 = all_52_13)
% 140.63/20.44 (13) op(e0, e0) = e1
% 140.63/20.44 (14) op(e2, e3) = all_52_1
% 140.63/20.44 (15) op(e1, e1) = e2
% 140.63/20.44 (16) op(e3, e2) = all_52_4
% 140.63/20.44 (17) ~ (all_52_7 = all_52_11)
% 140.63/20.44 (18) op(e0, e1) = all_52_11
% 140.63/20.44 (19) op(e2, e2) = e3
% 140.63/20.44 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.44 (21) ~ (all_52_9 = e3)
% 140.63/20.44 (22) op(e0, e2) = all_52_7
% 140.63/20.44 (23) op(e2, e1) = all_52_9
% 140.63/20.44 (24) op(e0, e2) = e2
% 140.63/20.44 (25) ~ (all_52_13 = e1)
% 140.63/20.44 (26) op(e2, e0) = e2
% 140.63/20.44 (27) op(e2, e0) = all_52_13
% 140.63/20.44
% 140.63/20.44 Begin of proof
% 140.63/20.44 |
% 140.63/20.44 | GROUND_INST: instantiating (20) with all_52_7, e2, e2, e0, simplifying with
% 140.63/20.44 | (22), (24) gives:
% 140.63/20.44 | (28) all_52_7 = e2
% 140.63/20.44 |
% 140.63/20.44 | GROUND_INST: instantiating (20) with all_52_13, e2, e0, e2, simplifying with
% 140.63/20.44 | (26), (27) gives:
% 140.63/20.44 | (29) all_52_13 = e2
% 140.63/20.44 |
% 140.63/20.44 | REDUCE: (12), (29) imply:
% 140.63/20.44 | (30) ~ (all_52_1 = e2)
% 140.63/20.44 |
% 140.63/20.44 | REDUCE: (17), (28) imply:
% 140.63/20.44 | (31) ~ (all_52_11 = e2)
% 140.63/20.44 |
% 140.63/20.44 | SIMP: (31) implies:
% 140.63/20.44 | (32) ~ (all_52_11 = e2)
% 140.63/20.44 |
% 140.63/20.44 | REDUCE: (4), (29) imply:
% 140.63/20.44 | (33) ~ (all_52_9 = e2)
% 140.63/20.44 |
% 140.63/20.44 | REDUCE: (3), (29) imply:
% 140.63/20.44 | (34) ~ (e3 = e2)
% 140.63/20.44 |
% 140.63/20.44 | SIMP: (34) implies:
% 140.63/20.44 | (35) ~ (e3 = e2)
% 140.63/20.44 |
% 140.63/20.44 | REDUCE: (25), (29) imply:
% 140.63/20.44 | (36) ~ (e2 = e1)
% 140.63/20.44 |
% 140.63/20.44 | BETA: splitting (5) gives:
% 140.63/20.44 |
% 140.63/20.44 | Case 1:
% 140.63/20.44 | |
% 140.63/20.44 | | (37) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 140.63/20.44 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.63/20.44 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.63/20.44 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.63/20.44 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 140.63/20.44 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 140.63/20.44 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 140.63/20.44 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.63/20.44 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.63/20.44 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 140.63/20.44 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 140.63/20.44 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 140.63/20.44 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.63/20.44 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.63/20.44 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 140.63/20.44 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.63/20.44 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 140.63/20.44 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.63/20.44 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 140.63/20.44 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 140.63/20.44 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 140.63/20.44 | | $i(all_56_12))))
% 140.63/20.44 | |
% 140.63/20.44 | | REF_CLOSE: (8), (10), (14), (16), (19), (20), (30), (37) are inconsistent by
% 140.63/20.44 | | sub-proof #177.
% 140.63/20.44 | |
% 140.63/20.44 | Case 2:
% 140.63/20.44 | |
% 140.63/20.44 | | (38) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 140.63/20.44 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.63/20.44 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 140.63/20.44 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.63/20.44 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 140.63/20.44 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.63/20.44 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.63/20.44 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.63/20.44 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.63/20.44 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.63/20.44 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 140.63/20.44 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | (
% 140.63/20.44 | | ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.63/20.44 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 140.63/20.44 | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 140.63/20.44 | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.63/20.44 | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 140.63/20.44 | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 140.63/20.44 | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 140.63/20.44 | | e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 140.63/20.44 | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 140.63/20.44 | | $i(all_56_8))))
% 140.63/20.44 | |
% 140.63/20.44 | | BETA: splitting (38) gives:
% 140.63/20.44 | |
% 140.63/20.44 | | Case 1:
% 140.63/20.44 | | |
% 140.63/20.44 | | | (39) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 140.63/20.44 | | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 140.63/20.44 | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 140.63/20.44 | | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.63/20.44 | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 140.63/20.44 | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 140.63/20.44 | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.63/20.44 | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 140.63/20.44 | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.63/20.44 | | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.63/20.44 | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 140.63/20.44 | | |
% 140.63/20.44 | | | ALPHA: (39) implies:
% 140.63/20.44 | | | (40) op(e1, e1) = all_56_13
% 140.63/20.44 | | | (41) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 140.63/20.44 | | | e0) = all_56_15 & $i(all_56_15))
% 140.63/20.44 | | | (42) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 140.63/20.44 | | | e1) = all_56_4 & $i(all_56_4))
% 140.63/20.44 | | | (43) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 140.63/20.44 | | | e1) = all_56_1 & $i(all_56_1))
% 140.63/20.44 | | | (44) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.63/20.44 | | | e2) = all_56_11 & $i(all_56_11))
% 140.63/20.44 | | |
% 140.63/20.44 | | | BETA: splitting (42) gives:
% 140.63/20.44 | | |
% 140.63/20.44 | | | Case 1:
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | (45) all_56_11 = e1 & op(e2, e2) = e1
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | ALPHA: (45) implies:
% 140.63/20.44 | | | | (46) all_56_11 = e1
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | REF_CLOSE: (20), (23), (33), (44), (46) are inconsistent by sub-proof
% 140.63/20.44 | | | | #91.
% 140.63/20.44 | | | |
% 140.63/20.44 | | | Case 2:
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | (47) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | ALPHA: (47) implies:
% 140.63/20.44 | | | | (48) op(e2, e1) = all_56_4
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | BETA: splitting (43) gives:
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | Case 1:
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | (49) all_56_9 = e1 & op(e3, e3) = e1
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | ALPHA: (49) implies:
% 140.63/20.44 | | | | | (50) op(e3, e3) = e1
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | REF_CLOSE: (8), (20), (36), (50) are inconsistent by sub-proof #818.
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | Case 2:
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | (51) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1)
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | ALPHA: (51) implies:
% 140.63/20.44 | | | | | (52) ~ (all_56_1 = e3)
% 140.63/20.44 | | | | | (53) op(e3, e1) = all_56_1
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | BETA: splitting (41) gives:
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | | Case 1:
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | (54) all_56_14 = e0 & op(e0, e1) = e0
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | ALPHA: (54) implies:
% 140.63/20.44 | | | | | | (55) op(e0, e1) = e0
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | GROUND_INST: instantiating (20) with all_52_11, e0, e1, e0,
% 140.63/20.44 | | | | | | simplifying with (18), (55) gives:
% 140.63/20.44 | | | | | | (56) all_52_11 = e0
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | GROUND_INST: instantiating (20) with e2, all_56_13, e1, e1,
% 140.63/20.44 | | | | | | simplifying with (15), (40) gives:
% 140.63/20.44 | | | | | | (57) all_56_13 = e2
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | GROUND_INST: instantiating (20) with all_52_9, all_56_4, e1, e2,
% 140.63/20.44 | | | | | | simplifying with (23), (48) gives:
% 140.63/20.44 | | | | | | (58) all_56_4 = all_52_9
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | GROUND_INST: instantiating (20) with all_52_8, all_56_1, e1, e3,
% 140.63/20.44 | | | | | | simplifying with (11), (53) gives:
% 140.63/20.44 | | | | | | (59) all_56_1 = all_52_8
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | REDUCE: (52), (59) imply:
% 140.63/20.44 | | | | | | (60) ~ (all_52_8 = e3)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | REDUCE: (1), (56) imply:
% 140.63/20.44 | | | | | | (61) ~ (all_52_8 = e0)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | REDUCE: (7), (56) imply:
% 140.63/20.44 | | | | | | (62) ~ (all_52_9 = e0)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | REDUCE: (32), (56) imply:
% 140.63/20.44 | | | | | | (63) ~ (e2 = e0)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | SIMP: (63) implies:
% 140.63/20.44 | | | | | | (64) ~ (e2 = e0)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | BETA: splitting (2) gives:
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | Case 1:
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | (65) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 140.63/20.44 | | | | | | | op(e2, e1) = e3)
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | REF_CLOSE: (11), (20), (21), (23), (60), (65) are inconsistent by
% 140.63/20.44 | | | | | | | sub-proof #319.
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | Case 2:
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | (66) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 140.63/20.44 | | | | | | | op(e0, e1) = e3)
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | BETA: splitting (66) gives:
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | | Case 1:
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | (67) all_57_8 = e3 & op(e1, e1) = e3
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | ALPHA: (67) implies:
% 140.63/20.44 | | | | | | | | (68) op(e1, e1) = e3
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | REF_CLOSE: (15), (20), (35), (68) are inconsistent by sub-proof
% 140.63/20.44 | | | | | | | | #77.
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | Case 2:
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | (69) all_57_14 = e3 & op(e0, e1) = e3
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | ALPHA: (69) implies:
% 140.63/20.44 | | | | | | | | (70) all_57_14 = e3
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | BETA: splitting (6) gives:
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | | Case 1:
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | | (71) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 140.63/20.44 | | | | | | | | | op(e2, e1) = e0)
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | | REF_CLOSE: (11), (20), (23), (61), (62), (71) are inconsistent
% 140.63/20.44 | | | | | | | | | by sub-proof #980.
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | Case 2:
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | | (72) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 140.63/20.44 | | | | | | | | | op(e0, e1) = e0)
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | | BETA: splitting (72) gives:
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | | Case 1:
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | (73) all_57_8 = e0 & op(e1, e1) = e0
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | ALPHA: (73) implies:
% 140.63/20.44 | | | | | | | | | | (74) op(e1, e1) = e0
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | REF_CLOSE: (15), (20), (64), (74) are inconsistent by
% 140.63/20.44 | | | | | | | | | | sub-proof #61.
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | Case 2:
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | (75) all_57_14 = e0 & op(e0, e1) = e0
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | | REF_CLOSE: (9), (70), (75) are inconsistent by sub-proof
% 140.63/20.44 | | | | | | | | | | #626.
% 140.63/20.44 | | | | | | | | | |
% 140.63/20.44 | | | | | | | | | End of split
% 140.63/20.44 | | | | | | | | |
% 140.63/20.44 | | | | | | | | End of split
% 140.63/20.44 | | | | | | | |
% 140.63/20.44 | | | | | | | End of split
% 140.63/20.44 | | | | | | |
% 140.63/20.44 | | | | | | End of split
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | Case 2:
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | (76) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | | REF_CLOSE: (13), (20), (76) are inconsistent by sub-proof #82.
% 140.63/20.44 | | | | | |
% 140.63/20.44 | | | | | End of split
% 140.63/20.44 | | | | |
% 140.63/20.44 | | | | End of split
% 140.63/20.44 | | | |
% 140.63/20.44 | | | End of split
% 140.63/20.44 | | |
% 140.63/20.44 | | Case 2:
% 140.63/20.44 | | |
% 140.63/20.44 | | | (77) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 140.63/20.44 | | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 140.63/20.44 | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 140.63/20.44 | | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.63/20.44 | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 140.63/20.44 | | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.63/20.44 | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 140.63/20.44 | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.63/20.44 | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 140.63/20.44 | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 140.63/20.44 | | | e0) = all_56_8 & $i(all_56_8)))
% 140.63/20.44 | | |
% 140.63/20.44 | | | ALPHA: (77) implies:
% 140.63/20.44 | | | (78) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 140.63/20.44 | | | e0) = all_56_5 & $i(all_56_5))
% 140.63/20.44 | | |
% 140.63/20.44 | | | BETA: splitting (78) gives:
% 140.63/20.44 | | |
% 140.63/20.44 | | | Case 1:
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | (79) all_56_11 = e0 & op(e2, e2) = e0
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | ALPHA: (79) implies:
% 140.63/20.44 | | | | (80) op(e2, e2) = e0
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | REF_CLOSE: (9), (19), (20), (80) are inconsistent by sub-proof #1119.
% 140.63/20.44 | | | |
% 140.63/20.44 | | | Case 2:
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | (81) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5)
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | ALPHA: (81) implies:
% 140.63/20.44 | | | | (82) ~ (all_56_5 = e2)
% 140.63/20.44 | | | | (83) op(e2, e0) = all_56_5
% 140.63/20.44 | | | |
% 140.63/20.44 | | | | REF_CLOSE: (20), (26), (82), (83) are inconsistent by sub-proof #152.
% 140.63/20.44 | | | |
% 140.63/20.44 | | | End of split
% 140.63/20.44 | | |
% 140.63/20.44 | | End of split
% 140.63/20.44 | |
% 140.63/20.44 | End of split
% 140.63/20.44 |
% 140.63/20.44 End of proof
% 140.63/20.44
% 140.63/20.44 Sub-proof #2 shows that the following formulas are inconsistent:
% 140.63/20.44 ----------------------------------------------------------------
% 140.63/20.44 (1) ~ (e2 = e1)
% 140.63/20.44 (2) op(e0, e3) = all_52_3
% 140.63/20.44 (3) op(e3, e3) = e2
% 140.63/20.44 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.63/20.44 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.63/20.44 (5) ~ (e3 = e0)
% 140.63/20.44 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 140.63/20.44 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 140.63/20.44 (7) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.63/20.44 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.63/20.44 (8) ~ (e1 = e0)
% 140.63/20.44 (9) ~ (all_52_3 = e1)
% 140.63/20.44 (10) ~ (e2 = e0)
% 140.63/20.44 (11) ~ (e3 = e2)
% 140.63/20.44 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.44 (13) ~ (e3 = e1)
% 140.63/20.44 (14) all_57_12 = e2
% 140.63/20.44
% 140.63/20.44 Begin of proof
% 140.63/20.44 |
% 140.63/20.44 | BETA: splitting (6) gives:
% 140.63/20.44 |
% 140.63/20.44 | Case 1:
% 140.63/20.44 | |
% 140.63/20.44 | | (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 140.63/20.44 | | e3)
% 140.63/20.44 | |
% 140.63/20.44 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (10), (11), (12), (13), (14), (15)
% 140.63/20.44 | | are inconsistent by sub-proof #52.
% 140.63/20.44 | |
% 140.63/20.44 | Case 2:
% 140.63/20.44 | |
% 140.63/20.44 | | (16) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 140.63/20.44 | | e3)
% 140.63/20.44 | |
% 140.63/20.44 | | BETA: splitting (16) gives:
% 140.63/20.44 | |
% 140.63/20.44 | | Case 1:
% 140.63/20.44 | | |
% 140.63/20.44 | | | (17) all_57_6 = e3 & op(e1, e3) = e3
% 140.63/20.44 | | |
% 140.63/20.44 | | | ALPHA: (17) implies:
% 140.63/20.44 | | | (18) all_57_6 = e3
% 140.63/20.44 | | |
% 140.63/20.44 | | | BETA: splitting (7) gives:
% 140.63/20.44 | | |
% 140.63/20.44 | | | Case 1:
% 140.63/20.44 | | | |
% 140.63/20.45 | | | | (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 140.63/20.45 | | | | = e1)
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | REF_CLOSE: (1), (3), (4), (5), (8), (10), (12), (14), (18), (19) are
% 140.63/20.45 | | | | inconsistent by sub-proof #51.
% 140.63/20.45 | | | |
% 140.63/20.45 | | | Case 2:
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | (20) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 140.63/20.45 | | | | = e1)
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | BETA: splitting (20) gives:
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | Case 1:
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | (21) all_57_6 = e1 & op(e1, e3) = e1
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | REF_CLOSE: (13), (18), (21) are inconsistent by sub-proof #865.
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | Case 2:
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | (22) all_57_12 = e1 & op(e0, e3) = e1
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | REF_CLOSE: (2), (9), (12), (22) are inconsistent by sub-proof #350.
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | End of split
% 140.63/20.45 | | | |
% 140.63/20.45 | | | End of split
% 140.63/20.45 | | |
% 140.63/20.45 | | Case 2:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (23) all_57_12 = e3 & op(e0, e3) = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (23) implies:
% 140.63/20.45 | | | (24) all_57_12 = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (11), (14), (24) are inconsistent by sub-proof #772.
% 140.63/20.45 | | |
% 140.63/20.45 | | End of split
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #3 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.63/20.45 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.63/20.45 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.63/20.45 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.63/20.45 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0
% 140.63/20.45 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.63/20.45 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14
% 140.63/20.45 & $i(all_56_14)))
% 140.63/20.45 (2) ~ (e3 = e0)
% 140.63/20.45 (3) op(e0, e0) = e1
% 140.63/20.45 (4) op(e1, e1) = e2
% 140.63/20.45 (5) ~ (e2 = e0)
% 140.63/20.45 (6) op(e2, e2) = e3
% 140.63/20.45 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (8) ~ (e3 = e1)
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | ALPHA: (1) implies:
% 140.63/20.45 | (9) op(e0, e0) = all_56_15
% 140.63/20.45 | (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.63/20.45 | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.45 | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 140.63/20.45 | = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.63/20.45 | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 140.63/20.45 | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 140.63/20.45 | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (10) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.63/20.45 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.45 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.45 | | e2) = all_56_12 & $i(all_56_12))
% 140.63/20.45 | |
% 140.63/20.45 | | BETA: splitting (11) gives:
% 140.63/20.45 | |
% 140.63/20.45 | | Case 1:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (12) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 140.63/20.45 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (12) implies:
% 140.63/20.45 | | | (13) all_56_15 = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REDUCE: (9), (13) imply:
% 140.63/20.45 | | | (14) op(e0, e0) = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (3), (7), (8), (14) are inconsistent by sub-proof #732.
% 140.63/20.45 | | |
% 140.63/20.45 | | Case 2:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (15) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.63/20.45 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (15) implies:
% 140.63/20.45 | | | (16) op(e2, e2) = e0
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (2), (6), (7), (16) are inconsistent by sub-proof #1119.
% 140.63/20.45 | | |
% 140.63/20.45 | | End of split
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (17) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 140.63/20.45 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.63/20.45 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.45 | | e1) = all_56_14 & $i(all_56_14))
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (4), (5), (7), (17) are inconsistent by sub-proof #26.
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #4 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) op(e0, e0) = e1
% 140.63/20.45 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 140.63/20.45 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.63/20.45 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 140.63/20.45 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.63/20.45 (3) op(e2, e2) = e3
% 140.63/20.45 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (5) ~ (e3 = e1)
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (2) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (6) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 140.63/20.45 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 140.63/20.45 | |
% 140.63/20.45 | | ALPHA: (6) implies:
% 140.63/20.45 | | (7) op(e0, e0) = e3
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #732.
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (8) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.63/20.45 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 140.63/20.45 | |
% 140.63/20.45 | | ALPHA: (8) implies:
% 140.63/20.45 | | (9) op(e2, e2) = e1
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #69.
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #5 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) ~ (e2 = e1)
% 140.63/20.45 (2) ~ (all_52_11 = e1)
% 140.63/20.45 (3) op(e1, e1) = e2
% 140.63/20.45 (4) op(e0, e1) = all_52_11
% 140.63/20.45 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (6) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (6) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 140.63/20.45 | |
% 140.63/20.45 | | ALPHA: (7) implies:
% 140.63/20.45 | | (8) op(e1, e1) = e1
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #1085.
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (9) all_57_14 = e1 & op(e0, e1) = e1
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #347.
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #6 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) ~ (all_52_14 = e2)
% 140.63/20.45 (2) ~ (all_52_14 = e1)
% 140.63/20.45 (3) all_54_11 = all_52_14
% 140.63/20.45 (4) all_54_7 = all_52_13
% 140.63/20.45 (5) op(e2, e2) = e1
% 140.63/20.45 (6) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 140.63/20.45 all_56_8 & $i(all_56_8))
% 140.63/20.45 (7) ~ (all_52_12 = all_52_14)
% 140.63/20.45 (8) ~ (all_52_13 = all_52_14)
% 140.63/20.45 (9) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 140.63/20.45 (10) ~ (e1 = e0)
% 140.63/20.45 (11) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 140.63/20.45 all_56_13 & $i(all_56_13))
% 140.63/20.45 (12) op(e3, e0) = all_52_12
% 140.63/20.45 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (14) ~ (all_52_12 = all_52_13)
% 140.63/20.45 (15) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 140.63/20.45 all_56_2 & $i(all_56_2))
% 140.63/20.45 (16) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 140.63/20.45 (17) op(e3, e3) = e0
% 140.63/20.45 (18) ~ (all_52_13 = e1)
% 140.63/20.45 (19) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 140.63/20.45 all_56_9 & $i(all_56_9))
% 140.63/20.45 (20) op(e2, e0) = all_52_13
% 140.63/20.45 (21) op(e1, e0) = all_52_14
% 140.63/20.45 (22) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 140.63/20.45 all_56_5 & $i(all_56_5))
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (6) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (23) all_56_13 = e0 & op(e1, e1) = e0
% 140.63/20.45 | |
% 140.63/20.45 | | ALPHA: (23) implies:
% 140.63/20.45 | | (24) op(e1, e1) = e0
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (2), (11), (13), (21), (24) are inconsistent by sub-proof #98.
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (25) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8)
% 140.63/20.45 | |
% 140.63/20.45 | | ALPHA: (25) implies:
% 140.63/20.45 | | (26) ~ (all_56_8 = e1)
% 140.63/20.45 | | (27) op(e1, e0) = all_56_8
% 140.63/20.45 | |
% 140.63/20.45 | | BETA: splitting (19) gives:
% 140.63/20.45 | |
% 140.63/20.45 | | Case 1:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (28) all_56_2 = e3 & op(e3, e0) = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (28) implies:
% 140.63/20.45 | | | (29) op(e3, e0) = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | BETA: splitting (22) gives:
% 140.63/20.45 | | |
% 140.63/20.45 | | | Case 1:
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | (30) all_56_11 = e0 & op(e2, e2) = e0
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | ALPHA: (30) implies:
% 140.63/20.45 | | | | (31) op(e2, e2) = e0
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | REF_CLOSE: (5), (10), (13), (31) are inconsistent by sub-proof #1117.
% 140.63/20.45 | | | |
% 140.63/20.45 | | | Case 2:
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | (32) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5)
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | ALPHA: (32) implies:
% 140.63/20.45 | | | | (33) ~ (all_56_5 = e2)
% 140.63/20.45 | | | | (34) op(e2, e0) = all_56_5
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | BETA: splitting (15) gives:
% 140.63/20.45 | | | |
% 140.63/20.45 | | | | Case 1:
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | GROUND_INST: instantiating (13) with all_52_14, all_56_8, e0, e1,
% 140.63/20.45 | | | | | simplifying with (21), (27) gives:
% 140.63/20.45 | | | | | (35) all_56_8 = all_52_14
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | GROUND_INST: instantiating (13) with all_52_13, all_56_5, e0, e2,
% 140.63/20.45 | | | | | simplifying with (20), (34) gives:
% 140.63/20.45 | | | | | (36) all_56_5 = all_52_13
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | GROUND_INST: instantiating (13) with all_52_12, e3, e0, e3,
% 140.63/20.45 | | | | | simplifying with (12), (29) gives:
% 140.63/20.45 | | | | | (37) all_52_12 = e3
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | REDUCE: (33), (36) imply:
% 140.63/20.45 | | | | | (38) ~ (all_52_13 = e2)
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | REDUCE: (14), (37) imply:
% 140.63/20.45 | | | | | (39) ~ (all_52_13 = e3)
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | SIMP: (39) implies:
% 140.63/20.45 | | | | | (40) ~ (all_52_13 = e3)
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | REDUCE: (7), (37) imply:
% 140.63/20.45 | | | | | (41) ~ (all_52_14 = e3)
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | SIMP: (41) implies:
% 140.63/20.45 | | | | | (42) ~ (all_52_14 = e3)
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | BETA: splitting (9) gives:
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | Case 1:
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | | (43) all_54_11 = e3
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | | REF_CLOSE: (3), (42), (43) are inconsistent by sub-proof #216.
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | Case 2:
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | | (44) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | | BETA: splitting (44) gives:
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | | Case 1:
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | | (45) all_54_11 = e2
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | | REF_CLOSE: (1), (3), (45) are inconsistent by sub-proof #215.
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | Case 2:
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | | (46) all_54_11 = e1 | all_54_11 = e0
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | | BETA: splitting (46) gives:
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | | Case 1:
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | (47) all_54_11 = e1
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | REF_CLOSE: (2), (3), (47) are inconsistent by sub-proof #942.
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | Case 2:
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | (48) all_54_11 = e0
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | COMBINE_EQS: (3), (48) imply:
% 140.63/20.45 | | | | | | | | (49) all_52_14 = e0
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | SIMP: (49) implies:
% 140.63/20.45 | | | | | | | | (50) all_52_14 = e0
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | REDUCE: (8), (50) imply:
% 140.63/20.45 | | | | | | | | (51) ~ (all_52_13 = e0)
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | BETA: splitting (16) gives:
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | | Case 1:
% 140.63/20.45 | | | | | | | | |
% 140.63/20.45 | | | | | | | | | (52) all_54_7 = e3
% 140.63/20.45 | | | | | | | | |
% 140.63/20.45 | | | | | | | | | REF_CLOSE: (4), (40), (52) are inconsistent by sub-proof
% 140.63/20.45 | | | | | | | | | #1007.
% 140.63/20.45 | | | | | | | | |
% 140.63/20.45 | | | | | | | | Case 2:
% 140.63/20.45 | | | | | | | | |
% 140.63/20.45 | | | | | | | | | (53) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 140.63/20.45 | | | | | | | | |
% 140.63/20.45 | | | | | | | | | REF_CLOSE: (4), (18), (38), (51), (53) are inconsistent by
% 140.63/20.45 | | | | | | | | | sub-proof #59.
% 140.63/20.45 | | | | | | | | |
% 140.63/20.45 | | | | | | | | End of split
% 140.63/20.45 | | | | | | | |
% 140.63/20.45 | | | | | | | End of split
% 140.63/20.45 | | | | | | |
% 140.63/20.45 | | | | | | End of split
% 140.63/20.45 | | | | | |
% 140.63/20.45 | | | | | End of split
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | Case 2:
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | (54) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2)
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | ALPHA: (54) implies:
% 140.63/20.45 | | | | | (55) ~ (all_56_2 = e3)
% 140.63/20.45 | | | | | (56) op(e3, e0) = all_56_2
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | | REF_CLOSE: (13), (29), (55), (56) are inconsistent by sub-proof #274.
% 140.63/20.45 | | | | |
% 140.63/20.45 | | | | End of split
% 140.63/20.45 | | | |
% 140.63/20.45 | | | End of split
% 140.63/20.45 | | |
% 140.63/20.45 | | Case 2:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (57) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (13), (17), (57) are inconsistent by sub-proof #25.
% 140.63/20.45 | | |
% 140.63/20.45 | | End of split
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #7 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.63/20.45 all_56_11 & $i(all_56_11))
% 140.63/20.45 (2) op(e2, e2) = all_56_11
% 140.63/20.45 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.63/20.45 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.63/20.45 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.63/20.45 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 140.63/20.45 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 140.63/20.45 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.45 e1) = all_56_14 & $i(all_56_14))
% 140.63/20.45 (4) op(e2, e2) = e1
% 140.63/20.45 (5) ~ (e1 = e0)
% 140.63/20.45 (6) op(e1, e1) = e2
% 140.63/20.45 (7) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.63/20.45 all_56_14 & $i(all_56_14))
% 140.63/20.45 (8) ~ (e2 = e0)
% 140.63/20.45 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (10) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 140.63/20.45 all_56_4 & $i(all_56_4))
% 140.63/20.45 (11) ~ (e3 = e1)
% 140.63/20.45 (12) op(e0, e0) = all_56_15
% 140.63/20.45 (13) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.63/20.45 all_56_15 & $i(all_56_15))
% 140.63/20.45 (14) ~ (all_56_11 = e1)
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (3) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (15) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.63/20.45 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.45 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.45 | | e2) = all_56_12 & $i(all_56_12))
% 140.63/20.45 | |
% 140.63/20.45 | | BETA: splitting (15) gives:
% 140.63/20.45 | |
% 140.63/20.45 | | Case 1:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (16) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 140.63/20.45 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (16) implies:
% 140.63/20.45 | | | (17) all_56_15 = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REDUCE: (12), (17) imply:
% 140.63/20.45 | | | (18) op(e0, e0) = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (1), (2), (4), (7), (9), (10), (11), (13), (14), (18) are
% 140.63/20.45 | | | inconsistent by sub-proof #533.
% 140.63/20.45 | | |
% 140.63/20.45 | | Case 2:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (19) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.63/20.45 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (19) implies:
% 140.63/20.45 | | | (20) op(e2, e2) = e0
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (4), (5), (9), (20) are inconsistent by sub-proof #1117.
% 140.63/20.45 | | |
% 140.63/20.45 | | End of split
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (21) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 140.63/20.45 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.63/20.45 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.45 | | e1) = all_56_14 & $i(all_56_14))
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (6), (8), (9), (21) are inconsistent by sub-proof #26.
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #8 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.63/20.45 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.63/20.45 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.63/20.45 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 140.63/20.45 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 140.63/20.45 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.45 e1) = all_56_14 & $i(all_56_14))
% 140.63/20.45 (2) op(e0, e0) = e1
% 140.63/20.45 (3) op(e1, e1) = e2
% 140.63/20.45 (4) ~ (e2 = e0)
% 140.63/20.45 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (6) ~ (e3 = e1)
% 140.63/20.45 (7) op(e0, e0) = all_56_15
% 140.63/20.45 (8) op(e2, e2) = all_6_2
% 140.63/20.45 (9) ~ (all_6_2 = e0)
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (1) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.63/20.45 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.63/20.45 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.63/20.45 | | e2) = all_56_12 & $i(all_56_12))
% 140.63/20.45 | |
% 140.63/20.45 | | BETA: splitting (10) gives:
% 140.63/20.45 | |
% 140.63/20.45 | | Case 1:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (11) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 140.63/20.45 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (11) implies:
% 140.63/20.45 | | | (12) all_56_15 = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REDUCE: (7), (12) imply:
% 140.63/20.45 | | | (13) op(e0, e0) = e3
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (2), (5), (6), (13) are inconsistent by sub-proof #732.
% 140.63/20.45 | | |
% 140.63/20.45 | | Case 2:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (14) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.63/20.45 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 140.63/20.45 | | |
% 140.63/20.45 | | | ALPHA: (14) implies:
% 140.63/20.45 | | | (15) op(e2, e2) = e0
% 140.63/20.45 | | |
% 140.63/20.45 | | | REF_CLOSE: (5), (8), (9), (15) are inconsistent by sub-proof #1122.
% 140.63/20.45 | | |
% 140.63/20.45 | | End of split
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (16) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 140.63/20.45 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.63/20.45 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.63/20.45 | | e1) = all_56_14 & $i(all_56_14))
% 140.63/20.45 | |
% 140.63/20.45 | | REF_CLOSE: (3), (4), (5), (16) are inconsistent by sub-proof #26.
% 140.63/20.45 | |
% 140.63/20.45 | End of split
% 140.63/20.45 |
% 140.63/20.45 End of proof
% 140.63/20.45
% 140.63/20.45 Sub-proof #9 shows that the following formulas are inconsistent:
% 140.63/20.45 ----------------------------------------------------------------
% 140.63/20.45 (1) all_54_5 = e3 | all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 140.63/20.45 (2) ~ (all_6_2 = e1)
% 140.63/20.45 (3) op(e2, e2) = e1
% 140.63/20.45 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.45 (5) all_54_5 = all_6_2
% 140.63/20.45 (6) ~ (all_6_2 = e3)
% 140.63/20.45 (7) op(e2, e2) = all_6_2
% 140.63/20.45 (8) ~ (all_6_2 = e0)
% 140.63/20.45
% 140.63/20.45 Begin of proof
% 140.63/20.45 |
% 140.63/20.45 | BETA: splitting (1) gives:
% 140.63/20.45 |
% 140.63/20.45 | Case 1:
% 140.63/20.45 | |
% 140.63/20.45 | | (9) all_54_5 = e3
% 140.63/20.45 | |
% 140.63/20.45 | | COMBINE_EQS: (5), (9) imply:
% 140.63/20.45 | | (10) all_6_2 = e3
% 140.63/20.45 | |
% 140.63/20.45 | | REDUCE: (6), (10) imply:
% 140.63/20.45 | | (11) $false
% 140.63/20.45 | |
% 140.63/20.45 | | CLOSE: (11) is inconsistent.
% 140.63/20.45 | |
% 140.63/20.45 | Case 2:
% 140.63/20.45 | |
% 140.63/20.45 | | (12) all_54_5 = e2 | all_54_5 = e1 | all_54_5 = e0
% 140.63/20.45 | |
% 140.63/20.45 | | BETA: splitting (12) gives:
% 140.63/20.45 | |
% 140.63/20.45 | | Case 1:
% 140.63/20.45 | | |
% 140.63/20.45 | | | (13) all_54_5 = e2
% 140.63/20.46 | | |
% 140.63/20.46 | | | COMBINE_EQS: (5), (13) imply:
% 140.63/20.46 | | | (14) all_6_2 = e2
% 140.63/20.46 | | |
% 140.63/20.46 | | | REDUCE: (2), (14) imply:
% 140.63/20.46 | | | (15) ~ (e2 = e1)
% 140.63/20.46 | | |
% 140.63/20.46 | | | REDUCE: (7), (14) imply:
% 140.63/20.46 | | | (16) op(e2, e2) = e2
% 140.63/20.46 | | |
% 140.63/20.46 | | | REF_CLOSE: (3), (4), (15), (16) are inconsistent by sub-proof #749.
% 140.63/20.46 | | |
% 140.63/20.46 | | Case 2:
% 140.63/20.46 | | |
% 140.63/20.46 | | | (17) all_54_5 = e1 | all_54_5 = e0
% 140.63/20.46 | | |
% 140.63/20.46 | | | REF_CLOSE: (2), (5), (8), (17) are inconsistent by sub-proof #641.
% 140.63/20.46 | | |
% 140.63/20.46 | | End of split
% 140.63/20.46 | |
% 140.63/20.46 | End of split
% 140.63/20.46 |
% 140.63/20.46 End of proof
% 140.63/20.46
% 140.63/20.46 Sub-proof #10 shows that the following formulas are inconsistent:
% 140.63/20.46 ----------------------------------------------------------------
% 140.63/20.46 (1) ~ (all_52_4 = all_52_7)
% 140.63/20.46 (2) op(e1, e2) = all_52_6
% 140.63/20.46 (3) ~ (all_52_4 = e0)
% 140.63/20.46 (4) all_54_13 = all_52_7
% 140.63/20.46 (5) ~ (all_52_7 = e3)
% 140.63/20.46 (6) op(e1, e2) = e1
% 140.63/20.46 (7) ~ (all_52_4 = all_52_6)
% 140.63/20.46 (8) all_54_1 = all_52_4
% 140.63/20.46 (9) ~ (all_52_6 = all_52_7)
% 140.63/20.46 (10) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.63/20.46 (11) op(e3, e2) = all_52_4
% 140.63/20.46 (12) op(e3, e2) = all_56_0
% 140.63/20.46 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.63/20.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.63/20.46 (14) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.63/20.46 (15) op(e0, e2) = all_52_7
% 140.63/20.46 (16) op(e0, e2) = all_56_12
% 140.63/20.46 (17) ~ (all_56_0 = e3)
% 140.63/20.46 (18) ~ (all_56_12 = e0)
% 140.63/20.46
% 140.63/20.46 Begin of proof
% 140.63/20.46 |
% 140.63/20.46 | GROUND_INST: instantiating (13) with all_52_7, all_56_12, e2, e0, simplifying
% 140.63/20.46 | with (15), (16) gives:
% 140.63/20.46 | (19) all_56_12 = all_52_7
% 140.63/20.46 |
% 140.63/20.46 | GROUND_INST: instantiating (13) with all_52_6, e1, e2, e1, simplifying with
% 140.63/20.46 | (2), (6) gives:
% 140.63/20.46 | (20) all_52_6 = e1
% 140.63/20.46 |
% 140.63/20.46 | GROUND_INST: instantiating (13) with all_52_4, all_56_0, e2, e3, simplifying
% 140.63/20.46 | with (11), (12) gives:
% 140.63/20.46 | (21) all_56_0 = all_52_4
% 140.63/20.46 |
% 140.63/20.46 | REDUCE: (17), (21) imply:
% 140.63/20.46 | (22) ~ (all_52_4 = e3)
% 140.63/20.46 |
% 140.63/20.46 | REDUCE: (18), (19) imply:
% 140.63/20.46 | (23) ~ (all_52_7 = e0)
% 140.63/20.46 |
% 140.63/20.46 | REDUCE: (7), (20) imply:
% 140.63/20.46 | (24) ~ (all_52_4 = e1)
% 140.63/20.46 |
% 140.63/20.46 | REDUCE: (9), (20) imply:
% 140.63/20.46 | (25) ~ (all_52_7 = e1)
% 140.63/20.46 |
% 140.63/20.46 | SIMP: (25) implies:
% 140.63/20.46 | (26) ~ (all_52_7 = e1)
% 140.63/20.46 |
% 140.63/20.46 | BETA: splitting (10) gives:
% 140.63/20.46 |
% 140.63/20.46 | Case 1:
% 140.63/20.46 | |
% 140.63/20.46 | | (27) all_54_1 = e3
% 140.63/20.46 | |
% 140.63/20.46 | | REF_CLOSE: (8), (22), (27) are inconsistent by sub-proof #424.
% 140.63/20.46 | |
% 140.63/20.46 | Case 2:
% 140.63/20.46 | |
% 140.63/20.46 | | (28) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.63/20.46 | |
% 140.63/20.46 | | BETA: splitting (28) gives:
% 140.63/20.46 | |
% 140.63/20.46 | | Case 1:
% 140.63/20.46 | | |
% 140.63/20.46 | | | (29) all_54_1 = e2
% 140.63/20.46 | | |
% 140.63/20.46 | | | COMBINE_EQS: (8), (29) imply:
% 140.63/20.46 | | | (30) all_52_4 = e2
% 140.63/20.46 | | |
% 140.63/20.46 | | | SIMP: (30) implies:
% 140.63/20.46 | | | (31) all_52_4 = e2
% 140.63/20.46 | | |
% 140.63/20.46 | | | REDUCE: (1), (31) imply:
% 140.63/20.46 | | | (32) ~ (all_52_7 = e2)
% 140.63/20.46 | | |
% 140.63/20.46 | | | SIMP: (32) implies:
% 140.63/20.46 | | | (33) ~ (all_52_7 = e2)
% 140.63/20.46 | | |
% 140.63/20.46 | | | BETA: splitting (14) gives:
% 140.63/20.46 | | |
% 140.63/20.46 | | | Case 1:
% 140.63/20.46 | | | |
% 140.63/20.46 | | | | (34) all_54_13 = e3
% 140.63/20.46 | | | |
% 140.63/20.46 | | | | REF_CLOSE: (4), (5), (34) are inconsistent by sub-proof #364.
% 140.63/20.46 | | | |
% 140.63/20.46 | | | Case 2:
% 140.63/20.46 | | | |
% 140.63/20.46 | | | | (35) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.63/20.46 | | | |
% 140.63/20.46 | | | | BETA: splitting (35) gives:
% 140.63/20.46 | | | |
% 140.63/20.46 | | | | Case 1:
% 140.63/20.46 | | | | |
% 140.63/20.46 | | | | | (36) all_54_13 = e2
% 140.63/20.46 | | | | |
% 140.63/20.46 | | | | | REF_CLOSE: (4), (33), (36) are inconsistent by sub-proof #67.
% 140.63/20.46 | | | | |
% 140.63/20.46 | | | | Case 2:
% 140.63/20.46 | | | | |
% 140.63/20.46 | | | | | (37) all_54_13 = e1 | all_54_13 = e0
% 140.63/20.46 | | | | |
% 140.63/20.46 | | | | | REF_CLOSE: (4), (23), (26), (37) are inconsistent by sub-proof #362.
% 140.63/20.46 | | | | |
% 140.63/20.46 | | | | End of split
% 140.63/20.46 | | | |
% 140.63/20.46 | | | End of split
% 140.63/20.46 | | |
% 140.63/20.46 | | Case 2:
% 140.63/20.46 | | |
% 140.63/20.46 | | | (38) all_54_1 = e1 | all_54_1 = e0
% 140.63/20.46 | | |
% 140.63/20.46 | | | REF_CLOSE: (3), (8), (24), (38) are inconsistent by sub-proof #20.
% 140.63/20.46 | | |
% 140.72/20.46 | | End of split
% 140.72/20.46 | |
% 140.72/20.46 | End of split
% 140.72/20.46 |
% 140.72/20.46 End of proof
% 140.72/20.46
% 140.72/20.46 Sub-proof #11 shows that the following formulas are inconsistent:
% 140.72/20.46 ----------------------------------------------------------------
% 140.72/20.46 (1) ~ (e2 = e1)
% 140.72/20.46 (2) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.72/20.46 all_56_11 & $i(all_56_11))
% 140.72/20.46 (3) op(e2, e2) = all_56_11
% 140.72/20.46 (4) op(e2, e2) = e1
% 140.72/20.46 (5) ~ (all_52_9 = e2)
% 140.72/20.46 (6) ~ (e1 = e0)
% 140.72/20.46 (7) op(e1, e1) = e2
% 140.72/20.46 (8) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.72/20.46 all_56_14 & $i(all_56_14))
% 140.72/20.46 (9) ~ (e2 = e0)
% 140.72/20.46 (10) ~ (e3 = e2)
% 140.72/20.46 (11) op(e0, e0) = e2
% 140.72/20.46 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.46 (13) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 140.72/20.46 all_56_4 & $i(all_56_4))
% 140.72/20.46 (14) ~ (e3 = e1)
% 140.72/20.46 (15) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.46 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.46 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.72/20.46 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.46 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.46 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.72/20.46 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.72/20.46 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.72/20.46 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.72/20.46 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.72/20.46 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.46 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.46 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.72/20.46 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.72/20.46 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.46 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.46 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.46 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.46 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.46 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.46 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.46 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.46 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.46 $i(all_56_14))))
% 140.72/20.46 (16) op(e3, e3) = e0
% 140.72/20.46 (17) op(e2, e1) = all_52_9
% 140.72/20.46 (18) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.72/20.46 all_56_15 & $i(all_56_15))
% 140.72/20.46 (19) ~ (all_56_11 = e1)
% 140.72/20.46
% 140.72/20.46 Begin of proof
% 140.72/20.46 |
% 140.72/20.46 | BETA: splitting (15) gives:
% 140.72/20.46 |
% 140.72/20.46 | Case 1:
% 140.72/20.46 | |
% 140.72/20.46 | | (20) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.72/20.46 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.72/20.46 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.72/20.46 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 140.72/20.46 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 140.72/20.46 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.46 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 140.72/20.46 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.46 | |
% 140.72/20.46 | | BETA: splitting (20) gives:
% 140.72/20.46 | |
% 140.72/20.46 | | Case 1:
% 140.72/20.46 | | |
% 140.72/20.46 | | | (21) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 140.72/20.46 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.72/20.46 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 140.72/20.46 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 140.72/20.46 | | |
% 140.72/20.46 | | | REF_CLOSE: (9), (12), (16), (21) are inconsistent by sub-proof #753.
% 140.72/20.46 | | |
% 140.72/20.46 | | Case 2:
% 140.72/20.46 | | |
% 140.72/20.46 | | | (22) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.72/20.46 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.46 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 140.72/20.46 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.46 | | |
% 140.72/20.46 | | | REF_CLOSE: (7), (10), (12), (22) are inconsistent by sub-proof #76.
% 140.72/20.46 | | |
% 140.72/20.46 | | End of split
% 140.72/20.46 | |
% 140.72/20.46 | Case 2:
% 140.72/20.46 | |
% 140.72/20.46 | | (23) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 140.72/20.46 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.72/20.46 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.72/20.46 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 140.72/20.46 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 140.72/20.46 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.46 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.72/20.46 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.46 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.46 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.46 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.46 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.46 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.46 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.46 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.72/20.46 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.72/20.46 | | all_56_14 & $i(all_56_14))))
% 140.72/20.46 | |
% 140.72/20.46 | | BETA: splitting (23) gives:
% 140.72/20.46 | |
% 140.72/20.46 | | Case 1:
% 140.72/20.46 | | |
% 140.72/20.46 | | | (24) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 140.72/20.46 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.72/20.46 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 140.72/20.46 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.46 | | |
% 140.72/20.46 | | | REF_CLOSE: (2), (3), (4), (8), (12), (13), (14), (18), (19), (24) are
% 140.72/20.46 | | | inconsistent by sub-proof #12.
% 140.72/20.46 | | |
% 140.72/20.46 | | Case 2:
% 140.72/20.46 | | |
% 140.72/20.46 | | | (25) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.72/20.46 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.46 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 140.72/20.46 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.46 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.46 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.46 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.46 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.46 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.46 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.72/20.46 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.46 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.46 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.46 | | |
% 140.72/20.46 | | | BETA: splitting (25) gives:
% 140.72/20.46 | | |
% 140.72/20.46 | | | Case 1:
% 140.72/20.46 | | | |
% 140.72/20.46 | | | | (26) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 140.72/20.46 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.72/20.46 | | | | $i(all_56_7)
% 140.72/20.46 | | | |
% 140.72/20.46 | | | | ALPHA: (26) implies:
% 140.72/20.46 | | | | (27) all_56_11 = e1
% 140.72/20.46 | | | |
% 140.72/20.46 | | | | REF_CLOSE: (2), (5), (12), (17), (27) are inconsistent by sub-proof #91.
% 140.72/20.46 | | | |
% 140.72/20.46 | | | Case 2:
% 140.72/20.46 | | | |
% 140.72/20.46 | | | | (28) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 140.72/20.46 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 140.72/20.46 | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.72/20.46 | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.46 | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 140.72/20.46 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 140.72/20.46 | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.72/20.46 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 140.72/20.46 | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.46 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 140.72/20.46 | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.46 | | | | $i(all_56_14))))
% 140.72/20.46 | | | |
% 140.72/20.46 | | | | REF_CLOSE: (1), (4), (6), (10), (11), (12), (28) are inconsistent by
% 140.72/20.46 | | | | sub-proof #13.
% 140.72/20.46 | | | |
% 140.72/20.46 | | | End of split
% 140.72/20.46 | | |
% 140.72/20.46 | | End of split
% 140.72/20.46 | |
% 140.72/20.46 | End of split
% 140.72/20.46 |
% 140.72/20.46 End of proof
% 140.72/20.46
% 140.72/20.46 Sub-proof #12 shows that the following formulas are inconsistent:
% 140.72/20.46 ----------------------------------------------------------------
% 140.72/20.46 (1) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.72/20.46 all_56_11 & $i(all_56_11))
% 140.72/20.46 (2) op(e2, e2) = all_56_11
% 140.72/20.46 (3) op(e2, e2) = e1
% 140.72/20.46 (4) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 140.72/20.46 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.72/20.46 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 140.72/20.46 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.46 (5) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.72/20.46 all_56_14 & $i(all_56_14))
% 140.72/20.46 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.46 (7) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 140.72/20.46 all_56_4 & $i(all_56_4))
% 140.72/20.46 (8) ~ (e3 = e1)
% 140.72/20.46 (9) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.72/20.46 all_56_15 & $i(all_56_15))
% 140.72/20.46 (10) ~ (all_56_11 = e1)
% 140.72/20.46
% 140.72/20.46 Begin of proof
% 140.72/20.46 |
% 140.72/20.46 | BETA: splitting (4) gives:
% 140.72/20.46 |
% 140.72/20.46 | Case 1:
% 140.72/20.46 | |
% 140.72/20.46 | | (11) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 140.72/20.46 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 140.72/20.46 | |
% 140.72/20.46 | | ALPHA: (11) implies:
% 140.72/20.46 | | (12) op(e0, e0) = e3
% 140.72/20.46 | |
% 140.72/20.46 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (12) are
% 140.72/20.46 | | inconsistent by sub-proof #533.
% 140.72/20.46 | |
% 140.72/20.46 | Case 2:
% 140.72/20.46 | |
% 140.72/20.46 | | (13) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.72/20.46 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 140.72/20.46 | |
% 140.72/20.46 | | ALPHA: (13) implies:
% 140.72/20.46 | | (14) all_56_11 = e1
% 140.72/20.46 | | (15) ~ (all_56_4 = e2)
% 140.72/20.46 | |
% 140.72/20.46 | | REF_CLOSE: (1), (14), (15) are inconsistent by sub-proof #646.
% 140.72/20.46 | |
% 140.72/20.46 | End of split
% 140.72/20.46 |
% 140.72/20.46 End of proof
% 140.72/20.46
% 140.72/20.46 Sub-proof #13 shows that the following formulas are inconsistent:
% 140.72/20.46 ----------------------------------------------------------------
% 140.72/20.46 (1) ~ (e2 = e1)
% 140.72/20.46 (2) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 140.72/20.46 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.72/20.46 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 140.72/20.46 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.46 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.72/20.46 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.46 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 140.72/20.46 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.46 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 140.72/20.46 = all_56_14 & $i(all_56_14))))
% 140.72/20.46 (3) op(e2, e2) = e1
% 140.72/20.46 (4) ~ (e1 = e0)
% 140.72/20.46 (5) ~ (e3 = e2)
% 140.72/20.46 (6) op(e0, e0) = e2
% 140.72/20.46 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.46
% 140.72/20.46 Begin of proof
% 140.72/20.46 |
% 140.72/20.46 | BETA: splitting (2) gives:
% 140.72/20.46 |
% 140.72/20.46 | Case 1:
% 140.72/20.46 | |
% 140.72/20.46 | | (8) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.72/20.46 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 140.72/20.46 | |
% 140.72/20.46 | | ALPHA: (8) implies:
% 140.72/20.46 | | (9) op(e2, e2) = e0
% 140.72/20.46 | |
% 140.72/20.46 | | REF_CLOSE: (3), (4), (7), (9) are inconsistent by sub-proof #1117.
% 140.72/20.46 | |
% 140.72/20.46 | Case 2:
% 140.72/20.46 | |
% 140.72/20.46 | | (10) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 140.72/20.46 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.72/20.46 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 140.72/20.46 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.72/20.46 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 140.72/20.46 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 140.72/20.46 | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.72/20.46 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.46 | | $i(all_56_14)))
% 140.72/20.46 | |
% 140.72/20.46 | | ALPHA: (10) implies:
% 140.72/20.46 | | (11) op(e0, e0) = all_56_15
% 140.72/20.46 | | (12) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.72/20.46 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.46 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.72/20.46 | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.46 | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.72/20.46 | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.72/20.46 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.46 | | $i(all_56_14))
% 140.72/20.46 | |
% 140.72/20.46 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (12) are inconsistent by
% 140.72/20.46 | | sub-proof #526.
% 140.72/20.46 | |
% 140.72/20.46 | End of split
% 140.72/20.46 |
% 140.72/20.46 End of proof
% 140.72/20.46
% 140.72/20.46 Sub-proof #14 shows that the following formulas are inconsistent:
% 140.72/20.46 ----------------------------------------------------------------
% 140.72/20.46 (1) ~ (e2 = e1)
% 140.72/20.46 (2) ~ (e3 = e0)
% 140.72/20.46 (3) ~ (e1 = e0)
% 140.72/20.46 (4) ~ (e2 = e0)
% 140.72/20.46 (5) ~ (e3 = e2)
% 140.72/20.46 (6) op(e2, e2) = e3
% 140.72/20.46 (7) op(e0, e0) = e2
% 140.72/20.46 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.46 (9) ~ (e3 = e1)
% 140.72/20.46 (10) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.46 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.46 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.72/20.46 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.46 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.46 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.72/20.46 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.72/20.46 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.72/20.46 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.72/20.46 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.72/20.46 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.46 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.46 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.72/20.46 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.72/20.46 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.46 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.46 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.46 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.46 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.46 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.46 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.46 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.46 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.46 $i(all_56_14))))
% 140.72/20.46 (11) op(e3, e3) = e0
% 140.72/20.46
% 140.72/20.46 Begin of proof
% 140.72/20.46 |
% 140.72/20.46 | BETA: splitting (10) gives:
% 140.72/20.46 |
% 140.72/20.46 | Case 1:
% 140.72/20.46 | |
% 140.72/20.46 | | (12) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.72/20.46 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.72/20.46 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.72/20.46 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 140.72/20.46 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 140.72/20.46 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.46 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 140.72/20.46 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.46 | |
% 140.72/20.46 | | REF_CLOSE: (3), (4), (8), (11), (12) are inconsistent by sub-proof #752.
% 140.72/20.46 | |
% 140.72/20.46 | Case 2:
% 140.72/20.46 | |
% 140.72/20.46 | | (13) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 140.72/20.46 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.72/20.46 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.72/20.46 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 140.72/20.46 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 140.72/20.46 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.46 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.72/20.46 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.46 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.46 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.46 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.46 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.46 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.46 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.46 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.72/20.46 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.72/20.46 | | all_56_14 & $i(all_56_14))))
% 140.72/20.46 | |
% 140.72/20.46 | | BETA: splitting (13) gives:
% 140.72/20.46 | |
% 140.72/20.46 | | Case 1:
% 140.72/20.46 | | |
% 140.72/20.46 | | | (14) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 140.72/20.46 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.72/20.46 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 140.72/20.46 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.46 | | |
% 140.72/20.46 | | | REF_CLOSE: (5), (6), (7), (8), (9), (14) are inconsistent by sub-proof
% 140.72/20.46 | | | #43.
% 140.72/20.46 | | |
% 140.72/20.46 | | Case 2:
% 140.72/20.46 | | |
% 140.72/20.46 | | | (15) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.72/20.46 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.46 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 140.72/20.46 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.46 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.46 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.46 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.46 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.46 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.46 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.72/20.46 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.46 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.46 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.46 | | |
% 140.72/20.46 | | | BETA: splitting (15) gives:
% 140.72/20.46 | | |
% 140.72/20.46 | | | Case 1:
% 140.72/20.46 | | | |
% 140.72/20.47 | | | | (16) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 140.72/20.47 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.72/20.47 | | | | $i(all_56_7)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | ALPHA: (16) implies:
% 140.72/20.47 | | | | (17) op(e2, e2) = e1
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | REF_CLOSE: (6), (8), (9), (17) are inconsistent by sub-proof #69.
% 140.72/20.47 | | | |
% 140.72/20.47 | | | Case 2:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (18) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 140.72/20.47 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 140.72/20.47 | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.72/20.47 | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.47 | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 140.72/20.47 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 140.72/20.47 | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.72/20.47 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 140.72/20.47 | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.47 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 140.72/20.47 | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.47 | | | | $i(all_56_14))))
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (18) are inconsistent by
% 140.72/20.47 | | | | sub-proof #107.
% 140.72/20.47 | | | |
% 140.72/20.47 | | | End of split
% 140.72/20.47 | | |
% 140.72/20.47 | | End of split
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #15 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 140.72/20.47 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.72/20.47 ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 140.72/20.47 all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 140.72/20.47 ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.47 ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 140.72/20.47 all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.72/20.47 (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 140.72/20.47 ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 140.72/20.47 all_56_8 & $i(all_56_8)))
% 140.72/20.47 (2) ~ (all_52_12 = e3)
% 140.72/20.47 (3) op(e3, e0) = all_52_12
% 140.72/20.47 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.47 (5) op(e3, e3) = e0
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | ALPHA: (1) implies:
% 140.72/20.47 | (6) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 140.72/20.47 | all_56_9 & $i(all_56_9))
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (6) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (7) all_56_2 = e3 & op(e3, e0) = e3
% 140.72/20.47 | |
% 140.72/20.47 | | ALPHA: (7) implies:
% 140.72/20.47 | | (8) op(e3, e0) = e3
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1105.
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (9) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #25.
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #16 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) ~ (all_52_4 = all_52_7)
% 140.72/20.47 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 140.72/20.47 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 140.72/20.47 (3) ~ (all_52_7 = e1)
% 140.72/20.47 (4) ~ (all_52_4 = e0)
% 140.72/20.47 (5) ~ (all_52_4 = all_52_8)
% 140.72/20.47 (6) ~ (all_52_4 = e1)
% 140.72/20.47 (7) ~ (all_52_7 = e0)
% 140.72/20.47 (8) all_57_5 = e0
% 140.72/20.47 (9) all_54_13 = all_52_7
% 140.72/20.47 (10) op(e1, e2) = all_4_1
% 140.72/20.47 (11) all_54_1 = all_52_4
% 140.72/20.47 (12) ~ (e3 = e0)
% 140.72/20.47 (13) op(e1, e2) = e0
% 140.72/20.47 (14) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 140.72/20.47 all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2,
% 140.72/20.47 e1) = all_20_1 & $i(all_20_1))
% 140.72/20.47 (15) op(e3, e1) = all_52_8
% 140.72/20.47 (16) op(e1, e2) = all_32_1
% 140.72/20.47 (17) ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 140.72/20.47 all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e2,
% 140.72/20.47 e1) = all_38_1 & $i(all_38_1))
% 140.72/20.47 (18) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.72/20.47 (19) op(e1, e1) = e2
% 140.72/20.47 (20) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.72/20.47 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.72/20.47 & $i(all_4_1))
% 140.72/20.47 (21) ~ (e3 = e2)
% 140.72/20.47 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.47 (23) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.72/20.47 (24) op(e0, e2) = all_52_7
% 140.72/20.47 (25) op(e2, e1) = e0
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (14) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (26) ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 140.72/20.47 | | all_20_1 & $i(all_20_0) & $i(all_20_1)
% 140.72/20.47 | |
% 140.72/20.47 | | ALPHA: (26) implies:
% 140.72/20.47 | | (27) ~ (all_20_0 = e3)
% 140.72/20.47 | | (28) op(e2, e1) = all_20_1
% 140.72/20.47 | | (29) op(all_20_1, e2) = all_20_0
% 140.72/20.47 | |
% 140.72/20.47 | | BETA: splitting (17) gives:
% 140.72/20.47 | |
% 140.72/20.47 | | Case 1:
% 140.72/20.47 | | |
% 140.72/20.47 | | | (30) ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 140.72/20.47 | | | all_38_1 & $i(all_38_0) & $i(all_38_1)
% 140.72/20.47 | | |
% 140.72/20.47 | | | ALPHA: (30) implies:
% 140.72/20.47 | | | (31) op(e2, e1) = all_38_1
% 140.72/20.47 | | | (32) op(all_38_1, e2) = all_38_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with e0, all_32_1, e2, e1, simplifying
% 140.72/20.47 | | | with (13), (16) gives:
% 140.72/20.47 | | | (33) all_32_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_4_1, all_32_1, e2, e1,
% 140.72/20.47 | | | simplifying with (10), (16) gives:
% 140.72/20.47 | | | (34) all_32_1 = all_4_1
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with e0, all_38_1, e1, e2, simplifying
% 140.72/20.47 | | | with (25), (31) gives:
% 140.72/20.47 | | | (35) all_38_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_20_1, all_38_1, e1, e2,
% 140.72/20.47 | | | simplifying with (28), (31) gives:
% 140.72/20.47 | | | (36) all_38_1 = all_20_1
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (35), (36) imply:
% 140.72/20.47 | | | (37) all_20_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (33), (34) imply:
% 140.72/20.47 | | | (38) all_4_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | SIMP: (38) implies:
% 140.72/20.47 | | | (39) all_4_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (32), (35) imply:
% 140.72/20.47 | | | (40) op(e0, e2) = all_38_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (29), (37) imply:
% 140.72/20.47 | | | (41) op(e0, e2) = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_52_7, all_20_0, e2, e0,
% 140.72/20.47 | | | simplifying with (24), (41) gives:
% 140.72/20.47 | | | (42) all_52_7 = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_52_7, all_38_0, e2, e0,
% 140.72/20.47 | | | simplifying with (24), (40) gives:
% 140.72/20.47 | | | (43) all_52_7 = all_38_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (42), (43) imply:
% 140.72/20.47 | | | (44) all_38_0 = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (9), (42) imply:
% 140.72/20.47 | | | (45) all_54_13 = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (1), (42) imply:
% 140.72/20.47 | | | (46) ~ (all_52_4 = all_20_0)
% 140.72/20.47 | | |
% 140.72/20.47 | | | BETA: splitting (2) gives:
% 140.72/20.47 | | |
% 140.72/20.47 | | | Case 1:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (47) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 140.72/20.47 | | | | = e3)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | BETA: splitting (47) gives:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | Case 1:
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | (48) all_57_4 = e3 & op(e3, e1) = e3
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (11), (15), (18), (22), (23),
% 140.72/20.47 | | | | | (27), (45), (46), (48) are inconsistent by sub-proof #19.
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | Case 2:
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | (49) all_57_5 = e3 & op(e2, e1) = e3
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | ALPHA: (49) implies:
% 140.72/20.47 | | | | | (50) all_57_5 = e3
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | REF_CLOSE: (8), (12), (50) are inconsistent by sub-proof #1041.
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | End of split
% 140.72/20.47 | | | |
% 140.72/20.47 | | | Case 2:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (51) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 140.72/20.47 | | | | = e3)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | REF_CLOSE: (13), (16), (19), (20), (21), (22), (51) are inconsistent by
% 140.72/20.47 | | | | sub-proof #18.
% 140.72/20.47 | | | |
% 140.72/20.47 | | | End of split
% 140.72/20.47 | | |
% 140.72/20.47 | | Case 2:
% 140.72/20.47 | | |
% 140.72/20.47 | | | (52) ~ (all_38_1 = e3) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 140.72/20.47 | | |
% 140.72/20.47 | | | ALPHA: (52) implies:
% 140.72/20.47 | | | (53) ~ (all_38_1 = e3)
% 140.72/20.47 | | | (54) op(e2, e1) = all_38_1
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with e0, all_32_1, e2, e1, simplifying
% 140.72/20.47 | | | with (13), (16) gives:
% 140.72/20.47 | | | (55) all_32_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_4_1, all_32_1, e2, e1,
% 140.72/20.47 | | | simplifying with (10), (16) gives:
% 140.72/20.47 | | | (56) all_32_1 = all_4_1
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with e0, all_38_1, e1, e2, simplifying
% 140.72/20.47 | | | with (25), (54) gives:
% 140.72/20.47 | | | (57) all_38_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_20_1, all_38_1, e1, e2,
% 140.72/20.47 | | | simplifying with (28), (54) gives:
% 140.72/20.47 | | | (58) all_38_1 = all_20_1
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (57), (58) imply:
% 140.72/20.47 | | | (59) all_20_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (55), (56) imply:
% 140.72/20.47 | | | (60) all_4_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | SIMP: (60) implies:
% 140.72/20.47 | | | (61) all_4_1 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (29), (59) imply:
% 140.72/20.47 | | | (62) op(e0, e2) = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | GROUND_INST: instantiating (22) with all_52_7, all_20_0, e2, e0,
% 140.72/20.47 | | | simplifying with (24), (62) gives:
% 140.72/20.47 | | | (63) all_52_7 = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (9), (63) imply:
% 140.72/20.47 | | | (64) all_54_13 = all_20_0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (1), (63) imply:
% 140.72/20.47 | | | (65) ~ (all_52_4 = all_20_0)
% 140.72/20.47 | | |
% 140.72/20.47 | | | BETA: splitting (2) gives:
% 140.72/20.47 | | |
% 140.72/20.47 | | | Case 1:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (66) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 140.72/20.47 | | | | = e3)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | BETA: splitting (66) gives:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | Case 1:
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | (67) all_57_4 = e3 & op(e3, e1) = e3
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | REF_CLOSE: (3), (4), (5), (6), (7), (9), (11), (15), (18), (22), (23),
% 140.72/20.47 | | | | | (27), (64), (65), (67) are inconsistent by sub-proof #19.
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | Case 2:
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | (68) all_57_5 = e3 & op(e2, e1) = e3
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | ALPHA: (68) implies:
% 140.72/20.47 | | | | | (69) op(e2, e1) = e3
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | REF_CLOSE: (22), (28), (53), (54), (69) are inconsistent by sub-proof
% 140.72/20.47 | | | | | #360.
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | End of split
% 140.72/20.47 | | | |
% 140.72/20.47 | | | Case 2:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (70) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 140.72/20.47 | | | | = e3)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | REF_CLOSE: (13), (16), (19), (20), (21), (22), (70) are inconsistent by
% 140.72/20.47 | | | | sub-proof #18.
% 140.72/20.47 | | | |
% 140.72/20.47 | | | End of split
% 140.72/20.47 | | |
% 140.72/20.47 | | End of split
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (71) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (22), (25), (71) are inconsistent by sub-proof #17.
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #17 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 140.72/20.47 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.47 (3) op(e2, e1) = e0
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | ALPHA: (1) implies:
% 140.72/20.47 | (4) ~ (all_20_1 = e0)
% 140.72/20.47 | (5) op(e2, e1) = all_20_1
% 140.72/20.47 |
% 140.72/20.47 | GROUND_INST: instantiating (2) with e0, all_20_1, e1, e2, simplifying with
% 140.72/20.47 | (3), (5) gives:
% 140.72/20.47 | (6) all_20_1 = e0
% 140.72/20.47 |
% 140.72/20.47 | REDUCE: (4), (6) imply:
% 140.72/20.47 | (7) $false
% 140.72/20.47 |
% 140.72/20.47 | CLOSE: (7) is inconsistent.
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #18 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) op(e1, e2) = e0
% 140.72/20.47 (2) op(e1, e2) = all_32_1
% 140.72/20.47 (3) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 140.72/20.47 (4) op(e1, e1) = e2
% 140.72/20.47 (5) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.72/20.47 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.72/20.47 & $i(all_4_1))
% 140.72/20.47 (6) ~ (e3 = e2)
% 140.72/20.47 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (3) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (8) all_57_8 = e3 & op(e1, e1) = e3
% 140.72/20.47 | |
% 140.72/20.47 | | ALPHA: (8) implies:
% 140.72/20.47 | | (9) op(e1, e1) = e3
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (4), (6), (7), (9) are inconsistent by sub-proof #77.
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (10) all_57_14 = e3 & op(e0, e1) = e3
% 140.72/20.47 | |
% 140.72/20.47 | | ALPHA: (10) implies:
% 140.72/20.47 | | (11) op(e0, e1) = e3
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (1), (2), (5), (7), (11) are inconsistent by sub-proof #57.
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #19 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) ~ (all_52_7 = e1)
% 140.72/20.47 (2) ~ (all_52_4 = e0)
% 140.72/20.47 (3) ~ (all_52_4 = all_52_8)
% 140.72/20.47 (4) ~ (all_52_4 = e1)
% 140.72/20.47 (5) ~ (all_52_7 = e0)
% 140.72/20.47 (6) all_54_13 = all_52_7
% 140.72/20.47 (7) all_54_13 = all_20_0
% 140.72/20.47 (8) all_54_1 = all_52_4
% 140.72/20.47 (9) all_57_4 = e3 & op(e3, e1) = e3
% 140.72/20.47 (10) op(e3, e1) = all_52_8
% 140.72/20.47 (11) ~ (all_52_4 = all_20_0)
% 140.72/20.47 (12) ~ (all_20_0 = e3)
% 140.72/20.47 (13) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.72/20.47 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.47 (15) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | ALPHA: (9) implies:
% 140.72/20.47 | (16) op(e3, e1) = e3
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (15) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (17) all_54_13 = e3
% 140.72/20.47 | |
% 140.72/20.47 | | COMBINE_EQS: (7), (17) imply:
% 140.72/20.47 | | (18) all_20_0 = e3
% 140.72/20.47 | |
% 140.72/20.47 | | REDUCE: (12), (18) imply:
% 140.72/20.47 | | (19) $false
% 140.72/20.47 | |
% 140.72/20.47 | | CLOSE: (19) is inconsistent.
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (20) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.72/20.47 | |
% 140.72/20.47 | | BETA: splitting (20) gives:
% 140.72/20.47 | |
% 140.72/20.47 | | Case 1:
% 140.72/20.47 | | |
% 140.72/20.47 | | | (21) all_54_13 = e2
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (7), (21) imply:
% 140.72/20.47 | | | (22) all_20_0 = e2
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (11), (22) imply:
% 140.72/20.47 | | | (23) ~ (all_52_4 = e2)
% 140.72/20.47 | | |
% 140.72/20.47 | | | BETA: splitting (13) gives:
% 140.72/20.47 | | |
% 140.72/20.47 | | | Case 1:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (24) all_54_1 = e3
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | COMBINE_EQS: (8), (24) imply:
% 140.72/20.47 | | | | (25) all_52_4 = e3
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | SIMP: (25) implies:
% 140.72/20.47 | | | | (26) all_52_4 = e3
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | REDUCE: (3), (26) imply:
% 140.72/20.47 | | | | (27) ~ (all_52_8 = e3)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | SIMP: (27) implies:
% 140.72/20.47 | | | | (28) ~ (all_52_8 = e3)
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | REF_CLOSE: (10), (14), (16), (28) are inconsistent by sub-proof #1106.
% 140.72/20.47 | | | |
% 140.72/20.47 | | | Case 2:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | (29) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | BETA: splitting (29) gives:
% 140.72/20.47 | | | |
% 140.72/20.47 | | | | Case 1:
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | (30) all_54_1 = e2
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | REF_CLOSE: (8), (23), (30) are inconsistent by sub-proof #423.
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | Case 2:
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | (31) all_54_1 = e1 | all_54_1 = e0
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | | REF_CLOSE: (2), (4), (8), (31) are inconsistent by sub-proof #20.
% 140.72/20.47 | | | | |
% 140.72/20.47 | | | | End of split
% 140.72/20.47 | | | |
% 140.72/20.47 | | | End of split
% 140.72/20.47 | | |
% 140.72/20.47 | | Case 2:
% 140.72/20.47 | | |
% 140.72/20.47 | | | (32) all_54_13 = e1 | all_54_13 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REF_CLOSE: (1), (5), (6), (32) are inconsistent by sub-proof #362.
% 140.72/20.47 | | |
% 140.72/20.47 | | End of split
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #20 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) all_54_1 = e1 | all_54_1 = e0
% 140.72/20.47 (2) all_54_1 = all_52_4
% 140.72/20.47 (3) ~ (all_52_4 = e1)
% 140.72/20.47 (4) ~ (all_52_4 = e0)
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (1) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (5) all_54_1 = e1
% 140.72/20.47 | |
% 140.72/20.47 | | COMBINE_EQS: (2), (5) imply:
% 140.72/20.47 | | (6) all_52_4 = e1
% 140.72/20.47 | |
% 140.72/20.47 | | REDUCE: (3), (6) imply:
% 140.72/20.47 | | (7) $false
% 140.72/20.47 | |
% 140.72/20.47 | | CLOSE: (7) is inconsistent.
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (8) all_54_1 = e0
% 140.72/20.47 | |
% 140.72/20.47 | | COMBINE_EQS: (2), (8) imply:
% 140.72/20.47 | | (9) all_52_4 = e0
% 140.72/20.47 | |
% 140.72/20.47 | | REDUCE: (4), (9) imply:
% 140.72/20.47 | | (10) $false
% 140.72/20.47 | |
% 140.72/20.47 | | CLOSE: (10) is inconsistent.
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #21 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) all_54_4 = all_14_0
% 140.72/20.47 (2) ~ (all_14_0 = e2)
% 140.72/20.47 (3) ~ (all_14_0 = e1)
% 140.72/20.47 (4) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 140.72/20.47 (5) ~ (all_14_0 = e0)
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (4) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (6) all_54_4 = e2
% 140.72/20.47 | |
% 140.72/20.47 | | COMBINE_EQS: (1), (6) imply:
% 140.72/20.47 | | (7) all_14_0 = e2
% 140.72/20.47 | |
% 140.72/20.47 | | SIMP: (7) implies:
% 140.72/20.47 | | (8) all_14_0 = e2
% 140.72/20.47 | |
% 140.72/20.47 | | REDUCE: (2), (8) imply:
% 140.72/20.47 | | (9) $false
% 140.72/20.47 | |
% 140.72/20.47 | | CLOSE: (9) is inconsistent.
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (10) all_54_4 = e1 | all_54_4 = e0
% 140.72/20.47 | |
% 140.72/20.47 | | BETA: splitting (10) gives:
% 140.72/20.47 | |
% 140.72/20.47 | | Case 1:
% 140.72/20.47 | | |
% 140.72/20.47 | | | (11) all_54_4 = e1
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (1), (11) imply:
% 140.72/20.47 | | | (12) all_14_0 = e1
% 140.72/20.47 | | |
% 140.72/20.47 | | | SIMP: (12) implies:
% 140.72/20.47 | | | (13) all_14_0 = e1
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (3), (13) imply:
% 140.72/20.47 | | | (14) $false
% 140.72/20.47 | | |
% 140.72/20.47 | | | CLOSE: (14) is inconsistent.
% 140.72/20.47 | | |
% 140.72/20.47 | | Case 2:
% 140.72/20.47 | | |
% 140.72/20.47 | | | (15) all_54_4 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | COMBINE_EQS: (1), (15) imply:
% 140.72/20.47 | | | (16) all_14_0 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | SIMP: (16) implies:
% 140.72/20.47 | | | (17) all_14_0 = e0
% 140.72/20.47 | | |
% 140.72/20.47 | | | REDUCE: (5), (17) imply:
% 140.72/20.47 | | | (18) $false
% 140.72/20.47 | | |
% 140.72/20.47 | | | CLOSE: (18) is inconsistent.
% 140.72/20.47 | | |
% 140.72/20.47 | | End of split
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #22 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) ~ (all_52_14 = e1)
% 140.72/20.47 (2) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 140.72/20.47 (3) ~ (all_10_2 = e1)
% 140.72/20.47 (4) op(e0, e0) = all_10_2
% 140.72/20.47 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.47 (6) op(e1, e0) = all_52_14
% 140.72/20.47
% 140.72/20.47 Begin of proof
% 140.72/20.47 |
% 140.72/20.47 | BETA: splitting (2) gives:
% 140.72/20.47 |
% 140.72/20.47 | Case 1:
% 140.72/20.47 | |
% 140.72/20.47 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 140.72/20.47 | |
% 140.72/20.47 | | ALPHA: (7) implies:
% 140.72/20.47 | | (8) op(e1, e0) = e1
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #459.
% 140.72/20.47 | |
% 140.72/20.47 | Case 2:
% 140.72/20.47 | |
% 140.72/20.47 | | (9) all_57_15 = e1 & op(e0, e0) = e1
% 140.72/20.47 | |
% 140.72/20.47 | | ALPHA: (9) implies:
% 140.72/20.47 | | (10) op(e0, e0) = e1
% 140.72/20.47 | |
% 140.72/20.47 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #237.
% 140.72/20.47 | |
% 140.72/20.47 | End of split
% 140.72/20.47 |
% 140.72/20.47 End of proof
% 140.72/20.47
% 140.72/20.47 Sub-proof #23 shows that the following formulas are inconsistent:
% 140.72/20.47 ----------------------------------------------------------------
% 140.72/20.47 (1) ~ (all_10_2 = e2)
% 140.72/20.47 (2) ~ (all_52_14 = e2)
% 140.72/20.47 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 140.72/20.47 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 140.72/20.47 (4) ~ (all_52_13 = all_10_2)
% 140.72/20.47 (5) op(e1, e3) = all_52_2
% 140.72/20.47 (6) op(e0, e3) = e2
% 140.72/20.47 (7) op(e1, e2) = all_52_6
% 140.72/20.47 (8) ~ (all_52_6 = e1)
% 140.72/20.47 (9) ~ (e2 = e1)
% 140.72/20.47 (10) all_54_11 = all_52_14
% 140.72/20.47 (11) all_46_2 = all_10_2
% 140.72/20.47 (12) op(e2, e0) = e1
% 140.72/20.47 (13) ~ (all_52_13 = e3)
% 140.72/20.47 (14) ~ (all_52_9 = all_52_13)
% 140.72/20.47 (15) op(e0, e3) = all_52_3
% 140.72/20.48 (16) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.72/20.48 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.72/20.48 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.72/20.48 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.48 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.72/20.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.72/20.48 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.72/20.48 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.72/20.48 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.72/20.48 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.72/20.48 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.72/20.48 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 140.72/20.48 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 140.72/20.48 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.72/20.48 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.72/20.48 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 140.72/20.48 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.72/20.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 140.72/20.48 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.72/20.48 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 140.72/20.48 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 140.72/20.48 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 140.72/20.48 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.72/20.48 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.72/20.48 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 140.72/20.48 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.72/20.48 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.72/20.48 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 140.72/20.48 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 140.72/20.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.72/20.48 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.72/20.48 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.72/20.48 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 140.72/20.48 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 140.72/20.48 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.72/20.48 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 140.72/20.48 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 140.72/20.48 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 140.72/20.48 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 140.72/20.48 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 140.72/20.48 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 140.72/20.48 (17) ~ (all_10_2 = e1)
% 140.72/20.48 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 140.72/20.48 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 140.72/20.48 e1)
% 140.72/20.48 (19) ~ (all_52_9 = e2)
% 140.72/20.48 (20) ~ (all_52_9 = all_52_11)
% 140.72/20.48 (21) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 140.72/20.48 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 140.72/20.48 (22) ~ (all_52_1 = e0)
% 140.72/20.48 (23) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.72/20.48 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.72/20.48 (24) all_57_10 = e1
% 140.72/20.48 (25) op(e2, e3) = all_52_1
% 140.72/20.48 (26) ~ (all_52_6 = all_52_14)
% 140.72/20.48 (27) ~ (all_52_13 = all_52_14)
% 140.72/20.48 (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.72/20.48 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.72/20.48 (29) op(e0, e0) = all_10_2
% 140.72/20.48 (30) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 140.72/20.48 (31) ~ (e1 = e0)
% 140.72/20.48 (32) op(e1, e1) = e2
% 140.72/20.48 (33) op(e2, e2) = e2
% 140.72/20.48 (34) all_42_2 = all_10_2
% 140.72/20.48 (35) ~ (e2 = e0)
% 140.72/20.48 (36) ~ (e3 = e2)
% 140.72/20.48 (37) ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 &
% 140.72/20.48 op(e0, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 140.72/20.48 e1) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 140.72/20.48 (38) op(e0, e1) = all_52_11
% 140.72/20.48 (39) ~ (all_42_2 = e3) | ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 &
% 140.72/20.48 op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 140.72/20.48 e2) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 140.72/20.48 (40) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 140.72/20.48 (41) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 140.72/20.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 140.72/20.48 (42) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 140.72/20.48 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 140.72/20.48 (43) all_57_6 = e1
% 140.72/20.48 (44) all_54_15 = all_10_2
% 140.72/20.48 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.48 (46) ~ (all_52_14 = all_10_2)
% 140.72/20.48 (47) op(e3, e0) = e2
% 140.72/20.48 (48) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 140.72/20.48 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 140.72/20.48 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 140.72/20.48 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 140.72/20.48 (49) ~ (all_52_9 = e3)
% 140.72/20.48 (50) ~ (all_52_13 = e2)
% 140.72/20.48 (51) ~ (e3 = e1)
% 140.72/20.48 (52) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.48 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.48 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.72/20.48 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.48 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.48 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.72/20.48 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.72/20.48 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.72/20.48 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.72/20.48 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.72/20.48 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.48 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.48 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.72/20.48 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.72/20.48 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.48 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.48 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.48 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.48 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.48 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.48 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.48 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.48 $i(all_56_14))))
% 140.72/20.48 (53) op(e3, e3) = e0
% 140.72/20.48 (54) op(e1, e3) = e1
% 140.72/20.48 (55) ~ (all_52_2 = e3)
% 140.72/20.48 (56) op(e2, e1) = all_52_9
% 140.72/20.48 (57) all_57_2 = e3
% 140.72/20.48 (58) op(e2, e0) = all_52_13
% 140.72/20.48 (59) all_57_12 = e2
% 140.72/20.48 (60) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 140.72/20.48 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 140.72/20.48
% 140.72/20.48 Begin of proof
% 140.72/20.48 |
% 140.72/20.48 | BETA: splitting (60) gives:
% 140.72/20.48 |
% 140.72/20.48 | Case 1:
% 140.72/20.48 | |
% 140.72/20.48 | | (61) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 140.72/20.48 | | e0)
% 140.72/20.48 | |
% 140.72/20.48 | | REF_CLOSE: (22), (25), (33), (35), (45), (61) are inconsistent by sub-proof
% 140.72/20.48 | | #394.
% 140.72/20.48 | |
% 140.72/20.48 | Case 2:
% 140.72/20.48 | |
% 140.72/20.48 | | (62) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 140.72/20.48 | | e0)
% 140.72/20.48 | |
% 140.72/20.48 | | BETA: splitting (62) gives:
% 140.72/20.48 | |
% 140.72/20.48 | | Case 1:
% 140.72/20.48 | | |
% 140.72/20.48 | | | (63) all_57_5 = e0 & op(e2, e1) = e0
% 140.72/20.48 | | |
% 140.72/20.48 | | | ALPHA: (63) implies:
% 140.72/20.48 | | | (64) op(e2, e1) = e0
% 140.72/20.48 | | |
% 140.72/20.48 | | | BETA: splitting (16) gives:
% 140.72/20.48 | | |
% 140.72/20.48 | | | Case 1:
% 140.72/20.48 | | | |
% 140.72/20.48 | | | | (65) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 140.72/20.48 | | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 140.72/20.48 | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 140.72/20.48 | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.72/20.48 | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 140.72/20.48 | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.72/20.48 | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 140.72/20.48 | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 140.72/20.48 | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 140.72/20.48 | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 140.72/20.48 | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 140.72/20.48 | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.72/20.48 | | | | $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.72/20.48 | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.72/20.48 | | | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 140.72/20.48 | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 140.72/20.48 | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 140.72/20.48 | | | | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2)
% 140.72/20.48 | | | | = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.72/20.48 | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | (
% 140.72/20.48 | | | | ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)))
% 140.72/20.48 | | | | & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 140.72/20.48 | | | | op(e0, e2) = all_56_12 & $i(all_56_12))))
% 140.72/20.48 | | | |
% 140.72/20.48 | | | | REF_CLOSE: (7), (8), (32), (36), (45), (54), (65) are inconsistent by
% 140.72/20.48 | | | | sub-proof #29.
% 140.72/20.48 | | | |
% 140.72/20.48 | | | Case 2:
% 140.72/20.48 | | | |
% 140.72/20.48 | | | | (66) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 140.72/20.48 | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 140.72/20.48 | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) =
% 140.72/20.48 | | | | e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.72/20.48 | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.72/20.48 | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 140.72/20.48 | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 140.72/20.48 | | | | op(e2, e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0
% 140.72/20.48 | | | | & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.72/20.48 | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.72/20.48 | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.72/20.48 | | | | all_56_14 & $i(all_56_14)))) | (op(e0, e0) = all_56_15 &
% 140.72/20.48 | | | | $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.72/20.48 | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.72/20.48 | | | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 140.72/20.48 | | | | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 140.72/20.48 | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 140.72/20.48 | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3)
% 140.72/20.48 | | | | = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 140.72/20.48 | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 140.72/20.48 | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 140.72/20.48 | | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 140.72/20.48 | | | | op(e1, e0) = all_56_8 & $i(all_56_8))))
% 140.72/20.48 | | | |
% 140.72/20.48 | | | | BETA: splitting (66) gives:
% 140.72/20.48 | | | |
% 140.72/20.48 | | | | Case 1:
% 140.72/20.48 | | | | |
% 140.72/20.48 | | | | | (67) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 140.72/20.48 | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 140.72/20.48 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) =
% 140.72/20.48 | | | | | e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.72/20.48 | | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 140.72/20.48 | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 140.72/20.48 | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 140.72/20.48 | | | | | op(e2, e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0
% 140.72/20.48 | | | | | & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.72/20.48 | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.72/20.48 | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.72/20.48 | | | | | all_56_14 & $i(all_56_14)))
% 140.72/20.48 | | | | |
% 140.72/20.48 | | | | | ALPHA: (67) implies:
% 140.72/20.48 | | | | | (68) op(e1, e1) = all_56_13
% 140.72/20.48 | | | | | (69) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.72/20.48 | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.72/20.48 | | | | | (70) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) &
% 140.72/20.48 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 140.72/20.48 | | | | | (71) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 140.72/20.48 | | | | | op(e2, e1) = all_56_4 & $i(all_56_4))
% 140.72/20.48 | | | | | (72) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) &
% 140.72/20.48 | | | | | op(e2, e2) = all_56_11 & $i(all_56_11))
% 140.72/20.48 | | | | |
% 140.72/20.48 | | | | | BETA: splitting (71) gives:
% 140.72/20.48 | | | | |
% 140.72/20.48 | | | | | Case 1:
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | (73) all_56_11 = e1 & op(e2, e2) = e1
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | ALPHA: (73) implies:
% 140.72/20.48 | | | | | | (74) all_56_11 = e1
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | REF_CLOSE: (19), (45), (56), (72), (74) are inconsistent by
% 140.72/20.48 | | | | | | sub-proof #91.
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | Case 2:
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | (75) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | ALPHA: (75) implies:
% 140.72/20.48 | | | | | | (76) op(e2, e1) = all_56_4
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | BETA: splitting (69) gives:
% 140.72/20.48 | | | | | |
% 140.72/20.48 | | | | | | Case 1:
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | (77) all_56_15 = e1 & op(e0, e0) = e1
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | ALPHA: (77) implies:
% 140.72/20.48 | | | | | | | (78) op(e0, e0) = e1
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | REF_CLOSE: (17), (29), (45), (78) are inconsistent by sub-proof
% 140.72/20.48 | | | | | | | #237.
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | Case 2:
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | (79) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.72/20.48 | | | | | | | $i(all_56_14)
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | ALPHA: (79) implies:
% 140.72/20.48 | | | | | | | (80) ~ (all_56_14 = e0)
% 140.72/20.48 | | | | | | | (81) op(e0, e1) = all_56_14
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | BETA: splitting (72) gives:
% 140.72/20.48 | | | | | | |
% 140.72/20.48 | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | (82) all_56_4 = e2 & op(e2, e1) = e2
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | ALPHA: (82) implies:
% 140.72/20.48 | | | | | | | | (83) op(e2, e1) = e2
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | REF_CLOSE: (19), (45), (56), (83) are inconsistent by sub-proof
% 140.72/20.48 | | | | | | | | #890.
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | (84) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.72/20.48 | | | | | | | | $i(all_56_11)
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | ALPHA: (84) implies:
% 140.72/20.48 | | | | | | | | (85) op(e2, e2) = all_56_11
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | BETA: splitting (70) gives:
% 140.72/20.48 | | | | | | | |
% 140.72/20.48 | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | (86) all_56_14 = e0 & op(e0, e1) = e0
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | ALPHA: (86) implies:
% 140.72/20.48 | | | | | | | | | (87) op(e0, e1) = e0
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REF_CLOSE: (45), (80), (81), (87) are inconsistent by
% 140.72/20.48 | | | | | | | | | sub-proof #973.
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | (88) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.72/20.48 | | | | | | | | | $i(all_56_15)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | ALPHA: (88) implies:
% 140.72/20.48 | | | | | | | | | (89) op(e0, e0) = all_56_15
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with all_10_2, all_56_15, e0,
% 140.72/20.48 | | | | | | | | | e0, simplifying with (29), (89) gives:
% 140.72/20.48 | | | | | | | | | (90) all_56_15 = all_10_2
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with all_52_11, all_56_14, e1,
% 140.72/20.48 | | | | | | | | | e0, simplifying with (38), (81) gives:
% 140.72/20.48 | | | | | | | | | (91) all_56_14 = all_52_11
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with e2, all_56_13, e1, e1,
% 140.72/20.48 | | | | | | | | | simplifying with (32), (68) gives:
% 140.72/20.48 | | | | | | | | | (92) all_56_13 = e2
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with all_52_13, e1, e0, e2,
% 140.72/20.48 | | | | | | | | | simplifying with (12), (58) gives:
% 140.72/20.48 | | | | | | | | | (93) all_52_13 = e1
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with all_52_9, all_56_4, e1,
% 140.72/20.48 | | | | | | | | | e2, simplifying with (56), (76) gives:
% 140.72/20.48 | | | | | | | | | (94) all_56_4 = all_52_9
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with e0, all_56_4, e1, e2,
% 140.72/20.48 | | | | | | | | | simplifying with (64), (76) gives:
% 140.72/20.48 | | | | | | | | | (95) all_56_4 = e0
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | GROUND_INST: instantiating (45) with e2, all_56_11, e2, e2,
% 140.72/20.48 | | | | | | | | | simplifying with (33), (85) gives:
% 140.72/20.48 | | | | | | | | | (96) all_56_11 = e2
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | COMBINE_EQS: (94), (95) imply:
% 140.72/20.48 | | | | | | | | | (97) all_52_9 = e0
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (20), (97) imply:
% 140.72/20.48 | | | | | | | | | (98) ~ (all_52_11 = e0)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | SIMP: (98) implies:
% 140.72/20.48 | | | | | | | | | (99) ~ (all_52_11 = e0)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (14), (93), (97) imply:
% 140.72/20.48 | | | | | | | | | (100) ~ (e1 = e0)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (49), (97) imply:
% 140.72/20.48 | | | | | | | | | (101) ~ (e3 = e0)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | SIMP: (101) implies:
% 140.72/20.48 | | | | | | | | | (102) ~ (e3 = e0)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (19), (97) imply:
% 140.72/20.48 | | | | | | | | | (103) ~ (e2 = e0)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (27), (93) imply:
% 140.72/20.48 | | | | | | | | | (104) ~ (all_52_14 = e1)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | SIMP: (104) implies:
% 140.72/20.48 | | | | | | | | | (105) ~ (all_52_14 = e1)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (4), (93) imply:
% 140.72/20.48 | | | | | | | | | (106) ~ (all_10_2 = e1)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (13), (93) imply:
% 140.72/20.48 | | | | | | | | | (107) ~ (e3 = e1)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | REDUCE: (50), (93) imply:
% 140.72/20.48 | | | | | | | | | (108) ~ (e2 = e1)
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | BETA: splitting (39) gives:
% 140.72/20.48 | | | | | | | | |
% 140.72/20.48 | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | (109) ~ (all_42_2 = e3)
% 140.72/20.48 | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | REDUCE: (34), (109) imply:
% 140.72/20.48 | | | | | | | | | | (110) ~ (all_10_2 = e3)
% 140.72/20.48 | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | BETA: splitting (40) gives:
% 140.72/20.48 | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | (111) all_54_15 = e3
% 140.72/20.48 | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | REF_CLOSE: (44), (110), (111) are inconsistent by sub-proof
% 140.72/20.48 | | | | | | | | | | | #755.
% 140.72/20.48 | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | (112) ~ (all_54_15 = e3)
% 140.72/20.48 | | | | | | | | | | | (113) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 140.72/20.48 | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | BETA: splitting (113) gives:
% 140.72/20.48 | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | (114) all_54_15 = e2
% 140.72/20.48 | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | REF_CLOSE: (1), (44), (114) are inconsistent by sub-proof
% 140.72/20.48 | | | | | | | | | | | | #754.
% 140.72/20.48 | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | (115) ~ (all_54_15 = e2)
% 140.72/20.48 | | | | | | | | | | | | (116) all_54_15 = e1 | all_54_15 = e0
% 140.72/20.48 | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | BETA: splitting (52) gives:
% 140.72/20.48 | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | (117) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.72/20.48 | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.72/20.48 | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.48 | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.72/20.48 | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.72/20.48 | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.48 | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.72/20.48 | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.72/20.48 | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.72/20.48 | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.72/20.48 | | | | | | | | | | | | | $i(all_56_6))
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | BETA: splitting (117) gives:
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | (118) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.72/20.48 | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.72/20.48 | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.48 | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.72/20.48 | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.72/20.48 | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | BETA: splitting (118) gives:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | (119) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.72/20.48 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0 &
% 140.72/20.48 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_0)
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | ALPHA: (119) implies:
% 140.72/20.48 | | | | | | | | | | | | | | | (120) op(e3, e3) = e2
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | REF_CLOSE: (9), (23), (28), (31), (35), (45), (51), (57),
% 140.72/20.48 | | | | | | | | | | | | | | | (59), (102), (120) are inconsistent by sub-proof
% 140.72/20.48 | | | | | | | | | | | | | | | #53.
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | (121) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 =
% 140.72/20.48 | | | | | | | | | | | | | | | e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 &
% 140.72/20.48 | | | | | | | | | | | | | | | op(e2, e2) = e3 & $i(all_56_3)
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 140.72/20.48 | | | | | | | | | | | | | | | (122) op(e3, e3) = e2
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | REF_CLOSE: (9), (23), (28), (31), (35), (45), (51), (57),
% 140.72/20.48 | | | | | | | | | | | | | | | (59), (102), (122) are inconsistent by sub-proof
% 140.72/20.48 | | | | | | | | | | | | | | | #53.
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | End of split
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | (123) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 140.72/20.48 | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 140.72/20.48 | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.72/20.48 | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.72/20.48 | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | REF_CLOSE: (32), (36), (45), (123) are inconsistent by
% 140.72/20.48 | | | | | | | | | | | | | | sub-proof #76.
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | End of split
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | (124) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.72/20.48 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.72/20.48 | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.72/20.48 | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.72/20.48 | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.48 | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.72/20.48 | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.72/20.48 | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.72/20.48 | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.72/20.48 | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.72/20.48 | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.48 | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.72/20.48 | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.48 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.48 | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.72/20.48 | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.72/20.48 | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.48 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.48 | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.72/20.48 | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | BETA: splitting (124) gives:
% 140.72/20.48 | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | (125) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.72/20.48 | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.72/20.48 | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.72/20.48 | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.72/20.48 | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | BETA: splitting (125) gives:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | (126) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.72/20.48 | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.72/20.48 | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | ALPHA: (126) implies:
% 140.72/20.48 | | | | | | | | | | | | | | | (127) op(e0, e0) = e3
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | REF_CLOSE: (17), (29), (44), (45), (110), (116), (127) are
% 140.72/20.48 | | | | | | | | | | | | | | | inconsistent by sub-proof #750.
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | (128) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.72/20.48 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.72/20.48 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 140.72/20.48 | | | | | | | | | | | | | | | (129) op(e2, e2) = e1
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | REF_CLOSE: (19), (38), (45), (56), (69), (70), (71), (72),
% 140.72/20.48 | | | | | | | | | | | | | | | (99), (129) are inconsistent by sub-proof #63.
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | End of split
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | (130) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.72/20.48 | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.72/20.48 | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.72/20.48 | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.72/20.48 | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.72/20.48 | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.72/20.48 | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.48 | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.48 | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.48 | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.72/20.48 | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.72/20.48 | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.48 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.48 | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.72/20.48 | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | BETA: splitting (130) gives:
% 140.72/20.48 | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | (131) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.72/20.48 | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 140.72/20.48 | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 140.72/20.48 | | | | | | | | | | | | | | | (132) op(e2, e2) = e1
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | REF_CLOSE: (19), (38), (45), (56), (69), (70), (71), (72),
% 140.72/20.48 | | | | | | | | | | | | | | | (99), (132) are inconsistent by sub-proof #63.
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | Case 2:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | (133) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.72/20.48 | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 140.72/20.48 | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 140.72/20.48 | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.48 | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.48 | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.48 | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.72/20.48 | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.72/20.48 | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.48 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.48 | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.48 | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.48 | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.72/20.48 | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | BETA: splitting (133) gives:
% 140.72/20.48 | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | Case 1:
% 140.72/20.48 | | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | | (134) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 140.72/20.48 | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.72/20.48 | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 140.72/20.48 | | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | | ALPHA: (134) implies:
% 140.72/20.48 | | | | | | | | | | | | | | | | (135) op(e0, e0) = e2
% 140.72/20.48 | | | | | | | | | | | | | | | |
% 140.72/20.48 | | | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (18), (31), (35), (36), (45), (48),
% 140.72/20.48 | | | | | | | | | | | | | | | | (51), (59), (102), (135) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | sub-proof #28.
% 140.72/20.49 | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | (136) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.72/20.49 | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.72/20.49 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.72/20.49 | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.49 | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 140.72/20.49 | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 140.72/20.49 | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.72/20.49 | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.49 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.72/20.49 | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.72/20.49 | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 140.72/20.49 | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | (137) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.72/20.49 | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.72/20.49 | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.49 | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.49 | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.72/20.49 | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.72/20.49 | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.49 | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.72/20.49 | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | (138) all_54_15 = e1
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (138) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (139) all_10_2 = e1
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | SIMP: (139) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (140) all_10_2 = e1
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (140) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (141) all_56_15 = e1
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | REF_CLOSE: (38), (45), (70), (99), (141) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | sub-proof #432.
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | (142) all_54_15 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (142) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (143) all_10_2 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | SIMP: (143) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (144) all_10_2 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | COMBINE_EQS: (90), (144) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (145) all_56_15 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | REDUCE: (46), (144) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (146) ~ (all_52_14 = e0)
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | REDUCE: (29), (144) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | (147) op(e0, e0) = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | BETA: splitting (30) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | (148) all_54_11 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (10), (148) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | (149) all_52_14 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | SIMP: (149) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | (150) all_52_14 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | REDUCE: (26), (150) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | (151) ~ (all_52_6 = e3)
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | BETA: splitting (41) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | (152) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | (153) all_57_6 = e3 & op(e1, e3) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (45), (55), (153) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | sub-proof #95.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | (154) all_57_7 = e3 & op(e1, e2) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (45), (151), (154) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | sub-proof #27.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | (155) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | (156) all_57_8 = e3 & op(e1, e1) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (156) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | (157) op(e1, e1) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (36), (45), (157) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | sub-proof #77.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | (158) all_57_11 = e3 & op(e1, e0) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | (159) all_57_11 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | (160) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (160) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (161) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (162) all_56_15 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (145), (162) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (163) e3 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | SIMP: (163) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (164) e3 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (159), (164) imply:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (165) all_57_11 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | (166) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (166) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | (167) all_57_9 = e3 & op(e3, e0) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | (168) all_57_9 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | (169) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (169) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_57_9 = e2 & op(e3, e0) = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (168), (170) are inconsistent by sub-proof
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #598.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_57_10 = e2 & op(e2, e0) = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (24), (171) are inconsistent by sub-proof
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #593.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | (172) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (173) all_57_11 = e2 & op(e1, e0) = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (174) all_57_11 = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (165), (174) are inconsistent by sub-proof
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | #996.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_57_15 = e2 & op(e0, e0) = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (175) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | (176) op(e0, e0) = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (35), (45), (147), (176) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1094.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | (177) all_57_10 = e3 & op(e2, e0) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | (178) all_57_10 = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (51), (178) are inconsistent by sub-proof
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | #877.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | (179) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (179) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (102), (158), (165) are inconsistent by sub-proof
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | #957.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | (180) all_57_15 = e3 & op(e0, e0) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (180) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | (181) op(e0, e0) = e3
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (102), (147), (181) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #751.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (182) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | (183) op(e2, e2) = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (35), (45), (183) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | | sub-proof #1076.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | (184) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (35), (45), (184) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | | sub-proof #26.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | (185) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | BETA: splitting (185) gives:
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | (186) all_54_11 = e2
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (2), (10), (186) are inconsistent by sub-proof
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | #215.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | (187) all_54_11 = e1 | all_54_11 = e0
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (10), (105), (146), (187) are inconsistent by
% 140.72/20.49 | | | | | | | | | | | | | | | | | | | sub-proof #429.
% 140.72/20.49 | | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | (188) all_42_2 = e3
% 140.72/20.49 | | | | | | | | | | (189) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 &
% 140.72/20.49 | | | | | | | | | | op(e0, e3) = all_42_1 & $i(all_42_0) &
% 140.72/20.49 | | | | | | | | | | $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0, e3)
% 140.72/20.49 | | | | | | | | | | = all_42_1 & $i(all_42_1))
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | COMBINE_EQS: (34), (188) imply:
% 140.72/20.49 | | | | | | | | | | (190) all_10_2 = e3
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | SIMP: (190) implies:
% 140.72/20.49 | | | | | | | | | | (191) all_10_2 = e3
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | COMBINE_EQS: (11), (191) imply:
% 140.72/20.49 | | | | | | | | | | (192) all_46_2 = e3
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | | REF_CLOSE: (6), (12), (15), (37), (45), (58), (189), (192)
% 140.72/20.49 | | | | | | | | | | are inconsistent by sub-proof #269.
% 140.72/20.49 | | | | | | | | | |
% 140.72/20.49 | | | | | | | | | End of split
% 140.72/20.49 | | | | | | | | |
% 140.72/20.49 | | | | | | | | End of split
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | End of split
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | End of split
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | End of split
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | Case 2:
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | (193) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 140.72/20.49 | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 140.72/20.49 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 140.72/20.49 | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 140.72/20.49 | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 140.72/20.49 | | | | | ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.72/20.49 | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | (
% 140.72/20.49 | | | | | ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 140.72/20.49 | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | (
% 140.72/20.49 | | | | | ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.72/20.49 | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | (
% 140.72/20.49 | | | | | ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 140.72/20.49 | | | | | $i(all_56_8)))
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | ALPHA: (193) implies:
% 140.72/20.49 | | | | | (194) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) &
% 140.72/20.49 | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | REF_CLOSE: (36), (45), (47), (53), (194) are inconsistent by sub-proof
% 140.72/20.49 | | | | | #24.
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | End of split
% 140.72/20.49 | | | |
% 140.72/20.49 | | | End of split
% 140.72/20.49 | | |
% 140.72/20.49 | | Case 2:
% 140.72/20.49 | | |
% 140.72/20.49 | | | (195) all_57_10 = e0 & op(e2, e0) = e0
% 140.72/20.49 | | |
% 140.72/20.49 | | | ALPHA: (195) implies:
% 140.72/20.49 | | | (196) all_57_10 = e0
% 140.72/20.49 | | |
% 140.72/20.49 | | | COMBINE_EQS: (24), (196) imply:
% 140.72/20.49 | | | (197) e1 = e0
% 140.72/20.49 | | |
% 140.72/20.49 | | | SIMP: (197) implies:
% 140.72/20.49 | | | (198) e1 = e0
% 140.72/20.49 | | |
% 140.72/20.49 | | | COMBINE_EQS: (43), (198) imply:
% 140.72/20.49 | | | (199) all_57_6 = e0
% 140.72/20.49 | | |
% 140.72/20.49 | | | REF_CLOSE: (9), (28), (31), (45), (51), (53), (57), (59), (199) are
% 140.72/20.49 | | | inconsistent by sub-proof #773.
% 140.72/20.49 | | |
% 140.72/20.49 | | End of split
% 140.72/20.49 | |
% 140.72/20.49 | End of split
% 140.72/20.49 |
% 140.72/20.49 End of proof
% 140.72/20.49
% 140.72/20.49 Sub-proof #24 shows that the following formulas are inconsistent:
% 140.72/20.49 ----------------------------------------------------------------
% 140.72/20.49 (1) ~ (e3 = e2)
% 140.72/20.49 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.49 (3) op(e3, e0) = e2
% 140.72/20.49 (4) op(e3, e3) = e0
% 140.72/20.49 (5) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 140.72/20.49 all_56_9 & $i(all_56_9))
% 140.72/20.49
% 140.72/20.49 Begin of proof
% 140.72/20.49 |
% 140.72/20.49 | BETA: splitting (5) gives:
% 140.72/20.49 |
% 140.72/20.49 | Case 1:
% 140.72/20.49 | |
% 140.72/20.49 | | (6) all_56_2 = e3 & op(e3, e0) = e3
% 140.72/20.49 | |
% 140.72/20.49 | | ALPHA: (6) implies:
% 140.72/20.49 | | (7) op(e3, e0) = e3
% 140.72/20.49 | |
% 140.72/20.49 | | GROUND_INST: instantiating (2) with e2, e3, e0, e3, simplifying with (3),
% 140.72/20.49 | | (7) gives:
% 140.72/20.49 | | (8) e3 = e2
% 140.72/20.49 | |
% 140.72/20.49 | | REDUCE: (1), (8) imply:
% 140.72/20.49 | | (9) $false
% 140.72/20.49 | |
% 140.72/20.49 | | CLOSE: (9) is inconsistent.
% 140.72/20.49 | |
% 140.72/20.49 | Case 2:
% 140.72/20.49 | |
% 140.72/20.49 | | (10) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 140.72/20.49 | |
% 140.72/20.49 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #25.
% 140.72/20.49 | |
% 140.72/20.49 | End of split
% 140.72/20.49 |
% 140.72/20.49 End of proof
% 140.72/20.49
% 140.72/20.49 Sub-proof #25 shows that the following formulas are inconsistent:
% 140.72/20.49 ----------------------------------------------------------------
% 140.72/20.49 (1) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 140.72/20.49 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.49 (3) op(e3, e3) = e0
% 140.72/20.49
% 140.72/20.49 Begin of proof
% 140.72/20.49 |
% 140.72/20.49 | ALPHA: (1) implies:
% 140.72/20.49 | (4) ~ (all_56_9 = e0)
% 140.72/20.49 | (5) op(e3, e3) = all_56_9
% 140.72/20.49 |
% 140.72/20.49 | GROUND_INST: instantiating (2) with e0, all_56_9, e3, e3, simplifying with
% 140.72/20.49 | (3), (5) gives:
% 140.72/20.49 | (6) all_56_9 = e0
% 140.72/20.49 |
% 140.72/20.49 | REDUCE: (4), (6) imply:
% 140.72/20.49 | (7) $false
% 140.72/20.49 |
% 140.72/20.49 | CLOSE: (7) is inconsistent.
% 140.72/20.49 |
% 140.72/20.49 End of proof
% 140.72/20.49
% 140.72/20.49 Sub-proof #26 shows that the following formulas are inconsistent:
% 140.72/20.49 ----------------------------------------------------------------
% 140.72/20.49 (1) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.72/20.49 op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.49 e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.49 $i(all_56_14))
% 140.72/20.49 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.49 (3) op(e1, e1) = e2
% 140.72/20.49 (4) ~ (e2 = e0)
% 140.72/20.49
% 140.72/20.49 Begin of proof
% 140.72/20.49 |
% 140.72/20.49 | BETA: splitting (1) gives:
% 140.72/20.49 |
% 140.72/20.49 | Case 1:
% 140.72/20.49 | |
% 140.72/20.49 | | (5) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 140.72/20.49 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 140.72/20.49 | |
% 140.72/20.49 | | ALPHA: (5) implies:
% 140.72/20.49 | | (6) op(e1, e1) = e0
% 140.72/20.49 | |
% 140.72/20.49 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #61.
% 140.72/20.49 | |
% 140.72/20.49 | Case 2:
% 140.72/20.49 | |
% 140.72/20.49 | | (7) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 140.72/20.49 | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 140.72/20.49 | |
% 140.72/20.49 | | ALPHA: (7) implies:
% 140.72/20.49 | | (8) op(e1, e1) = e0
% 140.72/20.49 | |
% 140.72/20.49 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #61.
% 140.72/20.49 | |
% 140.72/20.49 | End of split
% 140.72/20.49 |
% 140.72/20.49 End of proof
% 140.72/20.49
% 140.72/20.49 Sub-proof #27 shows that the following formulas are inconsistent:
% 140.72/20.49 ----------------------------------------------------------------
% 140.72/20.49 (1) all_57_7 = e3 & op(e1, e2) = e3
% 140.72/20.49 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.49 (3) op(e1, e2) = all_52_6
% 140.72/20.49 (4) ~ (all_52_6 = e3)
% 140.72/20.49
% 140.72/20.49 Begin of proof
% 140.72/20.49 |
% 140.72/20.49 | ALPHA: (1) implies:
% 140.72/20.49 | (5) op(e1, e2) = e3
% 140.72/20.49 |
% 140.72/20.49 | GROUND_INST: instantiating (2) with all_52_6, e3, e2, e1, simplifying with
% 140.72/20.49 | (3), (5) gives:
% 140.72/20.49 | (6) all_52_6 = e3
% 140.72/20.49 |
% 140.72/20.49 | REDUCE: (4), (6) imply:
% 140.72/20.49 | (7) $false
% 140.72/20.49 |
% 140.72/20.49 | CLOSE: (7) is inconsistent.
% 140.72/20.49 |
% 140.72/20.49 End of proof
% 140.72/20.49
% 140.72/20.49 Sub-proof #28 shows that the following formulas are inconsistent:
% 140.72/20.49 ----------------------------------------------------------------
% 140.72/20.49 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 140.72/20.49 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 140.72/20.49 (2) ~ (e2 = e1)
% 140.72/20.49 (3) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 140.72/20.49 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 140.72/20.49 (4) ~ (e3 = e0)
% 140.72/20.49 (5) ~ (e1 = e0)
% 140.72/20.49 (6) ~ (e2 = e0)
% 140.72/20.49 (7) ~ (e3 = e2)
% 140.72/20.49 (8) op(e0, e0) = e2
% 140.72/20.49 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.49 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 140.72/20.49 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 140.72/20.49 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 140.72/20.49 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 140.72/20.49 (11) ~ (e3 = e1)
% 140.72/20.49 (12) all_57_12 = e2
% 140.72/20.49
% 140.72/20.49 Begin of proof
% 140.72/20.49 |
% 140.72/20.49 | BETA: splitting (1) gives:
% 140.72/20.49 |
% 140.72/20.49 | Case 1:
% 140.72/20.49 | |
% 140.72/20.49 | | (13) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 140.72/20.49 | | e3)
% 140.72/20.49 | |
% 140.72/20.49 | | BETA: splitting (13) gives:
% 140.72/20.49 | |
% 140.72/20.49 | | Case 1:
% 140.72/20.49 | | |
% 140.72/20.49 | | | (14) all_57_12 = e3 & op(e0, e3) = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | ALPHA: (14) implies:
% 140.72/20.49 | | | (15) all_57_12 = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | REF_CLOSE: (7), (12), (15) are inconsistent by sub-proof #772.
% 140.72/20.49 | | |
% 140.72/20.49 | | Case 2:
% 140.72/20.49 | | |
% 140.72/20.49 | | | (16) all_57_13 = e3 & op(e0, e2) = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | ALPHA: (16) implies:
% 140.72/20.49 | | | (17) all_57_13 = e3
% 140.72/20.49 | | | (18) op(e0, e2) = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (17), (18)
% 140.72/20.49 | | | are inconsistent by sub-proof #62.
% 140.72/20.49 | | |
% 140.72/20.49 | | End of split
% 140.72/20.49 | |
% 140.72/20.49 | Case 2:
% 140.72/20.49 | |
% 140.72/20.49 | | (19) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 140.72/20.49 | | e3)
% 140.72/20.49 | |
% 140.72/20.49 | | BETA: splitting (19) gives:
% 140.72/20.49 | |
% 140.72/20.49 | | Case 1:
% 140.72/20.49 | | |
% 140.72/20.49 | | | (20) all_57_14 = e3 & op(e0, e1) = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | ALPHA: (20) implies:
% 140.72/20.49 | | | (21) all_57_14 = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | BETA: splitting (10) gives:
% 140.72/20.49 | | |
% 140.72/20.49 | | | Case 1:
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | (22) all_57_15 = e0 & op(e0, e0) = e0
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | ALPHA: (22) implies:
% 140.72/20.49 | | | | (23) op(e0, e0) = e0
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | REF_CLOSE: (6), (8), (9), (23) are inconsistent by sub-proof #1094.
% 140.72/20.49 | | | |
% 140.72/20.49 | | | Case 2:
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | (24) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 140.72/20.49 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 140.72/20.49 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 140.72/20.49 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | ALPHA: (24) implies:
% 140.72/20.49 | | | | (25) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 140.72/20.49 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | BETA: splitting (3) gives:
% 140.72/20.49 | | | |
% 140.72/20.49 | | | | Case 1:
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | (26) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 140.72/20.49 | | | | | e2) = e1)
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | BETA: splitting (26) gives:
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | Case 1:
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | | (27) all_57_12 = e1 & op(e0, e3) = e1
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | | REF_CLOSE: (2), (12), (27) are inconsistent by sub-proof #848.
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | Case 2:
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | | (28) all_57_13 = e1 & op(e0, e2) = e1
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | | ALPHA: (28) implies:
% 140.72/20.49 | | | | | | (29) all_57_13 = e1
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | | BETA: splitting (25) gives:
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | | Case 1:
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | | (30) all_57_12 = e0 & op(e0, e3) = e0
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | | ALPHA: (30) implies:
% 140.72/20.49 | | | | | | | (31) all_57_12 = e0
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | | REF_CLOSE: (6), (12), (31) are inconsistent by sub-proof #1025.
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | Case 2:
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | | (32) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 140.72/20.49 | | | | | | | op(e0, e1) = e0)
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | | BETA: splitting (32) gives:
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | | Case 1:
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | | (33) all_57_13 = e0 & op(e0, e2) = e0
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | | ALPHA: (33) implies:
% 140.72/20.49 | | | | | | | | (34) all_57_13 = e0
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | | REF_CLOSE: (5), (29), (34) are inconsistent by sub-proof #721.
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | Case 2:
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | | (35) all_57_14 = e0 & op(e0, e1) = e0
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | | ALPHA: (35) implies:
% 140.72/20.49 | | | | | | | | (36) all_57_14 = e0
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | | REF_CLOSE: (4), (21), (36) are inconsistent by sub-proof #1067.
% 140.72/20.49 | | | | | | | |
% 140.72/20.49 | | | | | | | End of split
% 140.72/20.49 | | | | | | |
% 140.72/20.49 | | | | | | End of split
% 140.72/20.49 | | | | | |
% 140.72/20.49 | | | | | End of split
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | Case 2:
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | (37) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 140.72/20.49 | | | | | e0) = e1)
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | | REF_CLOSE: (2), (8), (9), (11), (21), (37) are inconsistent by
% 140.72/20.49 | | | | | sub-proof #251.
% 140.72/20.49 | | | | |
% 140.72/20.49 | | | | End of split
% 140.72/20.49 | | | |
% 140.72/20.49 | | | End of split
% 140.72/20.49 | | |
% 140.72/20.49 | | Case 2:
% 140.72/20.49 | | |
% 140.72/20.49 | | | (38) all_57_15 = e3 & op(e0, e0) = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | ALPHA: (38) implies:
% 140.72/20.49 | | | (39) op(e0, e0) = e3
% 140.72/20.49 | | |
% 140.72/20.49 | | | REF_CLOSE: (7), (8), (9), (39) are inconsistent by sub-proof #1066.
% 140.72/20.49 | | |
% 140.72/20.49 | | End of split
% 140.72/20.49 | |
% 140.72/20.49 | End of split
% 140.72/20.49 |
% 140.72/20.49 End of proof
% 140.72/20.49
% 140.72/20.49 Sub-proof #29 shows that the following formulas are inconsistent:
% 140.72/20.49 ----------------------------------------------------------------
% 140.72/20.49 (1) op(e1, e2) = all_52_6
% 140.72/20.49 (2) ~ (all_52_6 = e1)
% 140.72/20.49 (3) op(e1, e1) = e2
% 140.72/20.49 (4) ~ (e3 = e2)
% 140.72/20.49 (5) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.72/20.49 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.72/20.49 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.72/20.49 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.49 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 140.72/20.49 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 140.72/20.49 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 140.72/20.49 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 140.72/20.49 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 140.72/20.49 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 140.72/20.49 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 140.72/20.49 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.72/20.49 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.72/20.49 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 140.72/20.49 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.72/20.49 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 140.72/20.49 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.72/20.49 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 140.72/20.49 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 140.72/20.49 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12))))
% 140.72/20.49 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.49 (7) op(e1, e3) = e1
% 140.72/20.49
% 140.72/20.49 Begin of proof
% 140.72/20.49 |
% 140.72/20.49 | BETA: splitting (5) gives:
% 140.72/20.49 |
% 140.72/20.49 | Case 1:
% 140.72/20.49 | |
% 140.72/20.50 | | (8) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.72/20.50 | | e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.72/20.50 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.72/20.50 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.50 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.72/20.50 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.72/20.50 | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.72/20.50 | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.72/20.50 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.72/20.50 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.72/20.50 | | e3) = all_56_10 & $i(all_56_10)))
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (3), (4), (6), (7), (8) are inconsistent by sub-proof #71.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (9) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2)
% 140.72/20.50 | | = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.72/20.50 | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 140.72/20.50 | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.50 | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2)
% 140.72/20.50 | | = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0)
% 140.72/20.50 | | | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.72/20.50 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 140.72/20.50 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0)
% 140.72/20.50 | | = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 140.72/20.50 | | $i(all_56_12)))
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (9) implies:
% 140.72/20.50 | | (10) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.72/20.50 | | e1) = all_56_13 & $i(all_56_13))
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (1), (2), (3), (6), (10) are inconsistent by sub-proof #30.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #30 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) op(e1, e2) = all_52_6
% 140.72/20.50 (2) ~ (all_52_6 = e1)
% 140.72/20.50 (3) op(e1, e1) = e2
% 140.72/20.50 (4) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 140.72/20.50 all_56_13 & $i(all_56_13))
% 140.72/20.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (4) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (6) all_56_7 = e1 & op(e1, e2) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (6) implies:
% 140.72/20.50 | | (7) op(e1, e2) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #341.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (8) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #31.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #31 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 140.72/20.50 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (3) op(e1, e1) = e2
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | ALPHA: (1) implies:
% 140.72/20.50 | (4) ~ (all_56_13 = e2)
% 140.72/20.50 | (5) op(e1, e1) = all_56_13
% 140.72/20.50 |
% 140.72/20.50 | GROUND_INST: instantiating (2) with e2, all_56_13, e1, e1, simplifying with
% 140.72/20.50 | (3), (5) gives:
% 140.72/20.50 | (6) all_56_13 = e2
% 140.72/20.50 |
% 140.72/20.50 | REDUCE: (4), (6) imply:
% 140.72/20.50 | (7) $false
% 140.72/20.50 |
% 140.72/20.50 | CLOSE: (7) is inconsistent.
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #32 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) op(e1, e2) = all_52_6
% 140.72/20.50 (2) ~ (all_32_2 = e2) | ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 &
% 140.72/20.50 op(e1, e2) = all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 =
% 140.72/20.50 e3) & op(e1, e2) = all_32_1 & $i(all_32_1))
% 140.72/20.50 (3) op(e3, e1) = all_52_8
% 140.72/20.50 (4) op(e3, e1) = e0
% 140.72/20.50 (5) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.72/20.50 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.72/20.50 & $i(all_4_1))
% 140.72/20.50 (6) all_32_2 = e2
% 140.72/20.50 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (8) op(e1, e2) = e3
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | GROUND_INST: instantiating (7) with all_52_6, e3, e2, e1, simplifying with
% 140.72/20.50 | (1), (8) gives:
% 140.72/20.50 | (9) all_52_6 = e3
% 140.72/20.50 |
% 140.72/20.50 | GROUND_INST: instantiating (7) with all_52_8, e0, e1, e3, simplifying with
% 140.72/20.50 | (3), (4) gives:
% 140.72/20.50 | (10) all_52_8 = e0
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (2) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (11) ~ (all_32_2 = e2)
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (6), (11) imply:
% 140.72/20.50 | | (12) $false
% 140.72/20.50 | |
% 140.72/20.50 | | CLOSE: (12) is inconsistent.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (13) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 140.72/20.50 | | all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) &
% 140.72/20.50 | | op(e1, e2) = all_32_1 & $i(all_32_1))
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (4), (5), (7), (8), (13) are inconsistent by sub-proof #72.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #33 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) op(e0, e3) = e2
% 140.72/20.50 (2) ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 & op(e3, e1) = all_34_1
% 140.72/20.50 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e0) & op(e3, e1) =
% 140.72/20.50 all_34_1 & $i(all_34_1))
% 140.72/20.50 (3) op(e3, e1) = e0
% 140.72/20.50 (4) op(e3, e1) = all_22_1
% 140.72/20.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | GROUND_INST: instantiating (5) with e0, all_22_1, e1, e3, simplifying with
% 140.72/20.50 | (3), (4) gives:
% 140.72/20.50 | (6) all_22_1 = e0
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (2) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (7) ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 140.72/20.50 | | all_34_1 & $i(all_34_0) & $i(all_34_1)
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (7) implies:
% 140.72/20.50 | | (8) ~ (all_34_0 = e2)
% 140.72/20.50 | | (9) op(e3, e1) = all_34_1
% 140.72/20.50 | | (10) op(all_34_1, e3) = all_34_0
% 140.72/20.50 | |
% 140.72/20.50 | | GROUND_INST: instantiating (5) with e0, all_34_1, e1, e3, simplifying with
% 140.72/20.50 | | (3), (9) gives:
% 140.72/20.50 | | (11) all_34_1 = e0
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (10), (11) imply:
% 140.72/20.50 | | (12) op(e0, e3) = all_34_0
% 140.72/20.50 | |
% 140.72/20.50 | | GROUND_INST: instantiating (5) with e2, all_34_0, e3, e0, simplifying with
% 140.72/20.50 | | (1), (12) gives:
% 140.72/20.50 | | (13) all_34_0 = e2
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (8), (13) imply:
% 140.72/20.50 | | (14) $false
% 140.72/20.50 | |
% 140.72/20.50 | | CLOSE: (14) is inconsistent.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (15) ~ (all_34_1 = e0) & op(e3, e1) = all_34_1 & $i(all_34_1)
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (15) implies:
% 140.72/20.50 | | (16) ~ (all_34_1 = e0)
% 140.72/20.50 | | (17) op(e3, e1) = all_34_1
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (3), (5), (16), (17) are inconsistent by sub-proof #260.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #34 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) ~ (e3 = e0)
% 140.72/20.50 (2) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 140.72/20.50 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 140.72/20.50 (3) ~ (e1 = e0)
% 140.72/20.50 (4) op(e1, e1) = e2
% 140.72/20.50 (5) ~ (e2 = e0)
% 140.72/20.50 (6) all_57_6 = e2
% 140.72/20.50 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (8) all_57_11 = e1
% 140.72/20.50 (9) all_57_7 = e3
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (2) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (10) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 140.72/20.50 | | e0)
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (1), (5), (6), (9), (10) are inconsistent by sub-proof #247.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (11) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 140.72/20.50 | | e0)
% 140.72/20.50 | |
% 140.72/20.50 | | BETA: splitting (11) gives:
% 140.72/20.50 | |
% 140.72/20.50 | | Case 1:
% 140.72/20.50 | | |
% 140.72/20.50 | | | (12) all_57_8 = e0 & op(e1, e1) = e0
% 140.72/20.50 | | |
% 140.72/20.50 | | | ALPHA: (12) implies:
% 140.72/20.50 | | | (13) op(e1, e1) = e0
% 140.72/20.50 | | |
% 140.72/20.50 | | | REF_CLOSE: (4), (5), (7), (13) are inconsistent by sub-proof #61.
% 140.72/20.50 | | |
% 140.72/20.50 | | Case 2:
% 140.72/20.50 | | |
% 140.72/20.50 | | | (14) all_57_11 = e0 & op(e1, e0) = e0
% 140.72/20.50 | | |
% 140.72/20.50 | | | ALPHA: (14) implies:
% 140.72/20.50 | | | (15) all_57_11 = e0
% 140.72/20.50 | | |
% 140.72/20.50 | | | REF_CLOSE: (3), (8), (15) are inconsistent by sub-proof #690.
% 140.72/20.50 | | |
% 140.72/20.50 | | End of split
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #35 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) ~ (all_52_14 = e1)
% 140.72/20.50 (2) ~ (e2 = e1)
% 140.72/20.50 (3) op(e1, e1) = e2
% 140.72/20.50 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (5) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 140.72/20.50 (6) op(e1, e0) = all_52_14
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (5) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (7) implies:
% 140.72/20.50 | | (8) op(e1, e1) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1085.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (9) all_57_11 = e1 & op(e1, e0) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (9) implies:
% 140.72/20.50 | | (10) op(e1, e0) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #459.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #36 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) ~ (all_52_14 = e1)
% 140.72/20.50 (2) ~ (e2 = e1)
% 140.72/20.50 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 140.72/20.50 (4) op(e0, e0) = e2
% 140.72/20.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (6) op(e1, e0) = all_52_14
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (3) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (7) implies:
% 140.72/20.50 | | (8) op(e1, e0) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #459.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (9) all_57_15 = e1 & op(e0, e0) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (9) implies:
% 140.72/20.50 | | (10) op(e0, e0) = e1
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #1070.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #37 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) op(e3, e0) = e1
% 140.72/20.50 (2) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) = all_24_1
% 140.72/20.50 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2) =
% 140.72/20.50 all_24_1 & $i(all_24_1))
% 140.72/20.50 (3) op(e0, e2) = all_40_1
% 140.72/20.50 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (5) op(e0, e2) = e3
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (2) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (6) ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 140.72/20.50 | | all_24_1 & $i(all_24_0) & $i(all_24_1)
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (6) implies:
% 140.72/20.50 | | (7) ~ (all_24_0 = e1)
% 140.72/20.50 | | (8) op(e0, e2) = all_24_1
% 140.72/20.50 | | (9) op(all_24_1, e0) = all_24_0
% 140.72/20.50 | |
% 140.72/20.50 | | GROUND_INST: instantiating (4) with e3, all_40_1, e2, e0, simplifying with
% 140.72/20.50 | | (3), (5) gives:
% 140.72/20.50 | | (10) all_40_1 = e3
% 140.72/20.50 | |
% 140.72/20.50 | | GROUND_INST: instantiating (4) with all_24_1, all_40_1, e2, e0, simplifying
% 140.72/20.50 | | with (3), (8) gives:
% 140.72/20.50 | | (11) all_40_1 = all_24_1
% 140.72/20.50 | |
% 140.72/20.50 | | COMBINE_EQS: (10), (11) imply:
% 140.72/20.50 | | (12) all_24_1 = e3
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (9), (12) imply:
% 140.72/20.50 | | (13) op(e3, e0) = all_24_0
% 140.72/20.50 | |
% 140.72/20.50 | | GROUND_INST: instantiating (4) with e1, all_24_0, e0, e3, simplifying with
% 140.72/20.50 | | (1), (13) gives:
% 140.72/20.50 | | (14) all_24_0 = e1
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (7), (14) imply:
% 140.72/20.50 | | (15) $false
% 140.72/20.50 | |
% 140.72/20.50 | | CLOSE: (15) is inconsistent.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (16) ~ (all_24_1 = e3) & op(e0, e2) = all_24_1 & $i(all_24_1)
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (16) implies:
% 140.72/20.50 | | (17) ~ (all_24_1 = e3)
% 140.72/20.50 | | (18) op(e0, e2) = all_24_1
% 140.72/20.50 | |
% 140.72/20.50 | | GROUND_INST: instantiating (4) with e3, all_24_1, e2, e0, simplifying with
% 140.72/20.50 | | (5), (18) gives:
% 140.72/20.50 | | (19) all_24_1 = e3
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (17), (19) imply:
% 140.72/20.50 | | (20) $false
% 140.72/20.50 | |
% 140.72/20.50 | | CLOSE: (20) is inconsistent.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #38 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) op(e0, e1) = all_56_14
% 140.72/20.50 (2) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.72/20.50 all_56_11 & $i(all_56_11))
% 140.72/20.50 (3) op(e2, e2) = all_56_11
% 140.72/20.50 (4) ~ (all_10_2 = e1)
% 140.72/20.50 (5) op(e2, e2) = e1
% 140.72/20.50 (6) ~ (all_52_9 = e2)
% 140.72/20.50 (7) ~ (all_56_14 = e0)
% 140.72/20.50 (8) op(e0, e0) = all_10_2
% 140.72/20.50 (9) ~ (e1 = e0)
% 140.72/20.50 (10) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.72/20.50 all_56_14 & $i(all_56_14))
% 140.72/20.50 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (12) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 140.72/20.50 all_56_4 & $i(all_56_4))
% 140.72/20.50 (13) ~ (e3 = e1)
% 140.72/20.50 (14) op(e2, e2) = all_6_2
% 140.72/20.50 (15) op(e2, e1) = all_52_9
% 140.72/20.50 (16) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.72/20.50 all_56_15 & $i(all_56_15))
% 140.72/20.50 (17) op(e3, e3) = all_14_2
% 140.72/20.50 (18) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 140.72/20.50 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.72/20.50 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2,
% 140.72/20.50 e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.50 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.72/20.50 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.72/20.50 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.50 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.50 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.50 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.50 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.50 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.50 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.50 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.50 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.50 $i(all_56_14))))
% 140.72/20.50 (19) ~ (all_56_11 = e1)
% 140.72/20.50 (20) ~ (all_14_2 = e0)
% 140.72/20.50 (21) ~ (all_6_2 = e0)
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (18) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (22) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 140.72/20.50 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.72/20.50 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.72/20.50 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.50 | |
% 140.72/20.50 | | BETA: splitting (22) gives:
% 140.72/20.50 | |
% 140.72/20.50 | | Case 1:
% 140.72/20.50 | | |
% 140.72/20.50 | | | (23) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 140.72/20.50 | | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 140.72/20.50 | | |
% 140.72/20.50 | | | ALPHA: (23) implies:
% 140.72/20.50 | | | (24) op(e0, e0) = e3
% 140.72/20.50 | | |
% 140.72/20.50 | | | REF_CLOSE: (2), (3), (5), (10), (11), (12), (13), (16), (19), (24) are
% 140.72/20.50 | | | inconsistent by sub-proof #533.
% 140.72/20.50 | | |
% 140.72/20.50 | | Case 2:
% 140.72/20.50 | | |
% 140.72/20.50 | | | (25) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 140.72/20.50 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 140.72/20.50 | | |
% 140.72/20.50 | | | ALPHA: (25) implies:
% 140.72/20.50 | | | (26) ~ (all_56_4 = e2)
% 140.72/20.50 | | |
% 140.72/20.50 | | | REF_CLOSE: (1), (2), (3), (5), (7), (11), (16), (26) are inconsistent by
% 140.72/20.50 | | | sub-proof #534.
% 140.72/20.50 | | |
% 140.72/20.50 | | End of split
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (27) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 140.72/20.50 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.50 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.72/20.50 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.50 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.50 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.50 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.50 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.50 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.50 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.50 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.72/20.50 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.72/20.50 | | all_56_14 & $i(all_56_14))))
% 140.72/20.50 | |
% 140.72/20.50 | | BETA: splitting (27) gives:
% 140.72/20.50 | |
% 140.72/20.50 | | Case 1:
% 140.72/20.50 | | |
% 140.72/20.50 | | | (28) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.72/20.50 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 140.72/20.50 | | |
% 140.72/20.50 | | | ALPHA: (28) implies:
% 140.72/20.50 | | | (29) all_56_11 = e1
% 140.72/20.50 | | |
% 140.72/20.50 | | | REF_CLOSE: (2), (6), (11), (15), (29) are inconsistent by sub-proof #91.
% 140.72/20.50 | | |
% 140.72/20.50 | | Case 2:
% 140.72/20.50 | | |
% 140.72/20.50 | | | (30) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 140.72/20.50 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.50 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.50 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.50 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.50 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.50 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.50 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.72/20.50 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.50 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.50 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.50 | | |
% 140.72/20.50 | | | REF_CLOSE: (4), (5), (8), (9), (11), (14), (17), (20), (21), (30) are
% 140.72/20.50 | | | inconsistent by sub-proof #250.
% 140.72/20.50 | | |
% 140.72/20.50 | | End of split
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #39 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) ~ (all_10_2 = e1)
% 140.72/20.50 (2) op(e2, e2) = e1
% 140.72/20.50 (3) op(e0, e0) = all_10_2
% 140.72/20.50 (4) ~ (e1 = e0)
% 140.72/20.50 (5) ~ (all_56_13 = e2)
% 140.72/20.50 (6) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 140.72/20.50 op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.72/20.50 e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 140.72/20.50 = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 140.72/20.50 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.72/20.50 e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.50 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 140.72/20.50 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.50 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.50 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.50 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.50 $i(all_56_14))))
% 140.72/20.50 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50 (8) op(e2, e2) = all_6_2
% 140.72/20.50 (9) op(e3, e3) = all_14_2
% 140.72/20.50 (10) ~ (all_14_2 = e0)
% 140.72/20.50 (11) ~ (all_6_2 = e0)
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (6) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (12) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 140.72/20.50 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (12) implies:
% 140.72/20.50 | | (13) all_56_13 = e2
% 140.72/20.50 | |
% 140.72/20.50 | | REDUCE: (5), (13) imply:
% 140.72/20.50 | | (14) $false
% 140.72/20.50 | |
% 140.72/20.50 | | CLOSE: (14) is inconsistent.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.50 | | (15) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.72/20.50 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.50 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.50 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.50 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.50 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.50 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.50 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.72/20.50 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.72/20.50 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.72/20.50 | | all_56_14 & $i(all_56_14))))
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (15) are
% 140.72/20.50 | | inconsistent by sub-proof #250.
% 140.72/20.50 | |
% 140.72/20.50 | End of split
% 140.72/20.50 |
% 140.72/20.50 End of proof
% 140.72/20.50
% 140.72/20.50 Sub-proof #40 shows that the following formulas are inconsistent:
% 140.72/20.50 ----------------------------------------------------------------
% 140.72/20.50 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 140.72/20.50 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.72/20.50 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 140.72/20.50 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.50 (2) ~ (all_56_13 = e2)
% 140.72/20.50 (3) ~ (e3 = e2)
% 140.72/20.50 (4) op(e0, e0) = e2
% 140.72/20.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.50
% 140.72/20.50 Begin of proof
% 140.72/20.50 |
% 140.72/20.50 | BETA: splitting (1) gives:
% 140.72/20.50 |
% 140.72/20.50 | Case 1:
% 140.72/20.50 | |
% 140.72/20.50 | | (6) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 140.72/20.50 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 140.72/20.50 | |
% 140.72/20.50 | | ALPHA: (6) implies:
% 140.72/20.50 | | (7) op(e0, e0) = e3
% 140.72/20.50 | |
% 140.72/20.50 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1066.
% 140.72/20.50 | |
% 140.72/20.50 | Case 2:
% 140.72/20.50 | |
% 140.72/20.51 | | (8) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.72/20.51 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 140.72/20.51 | |
% 140.72/20.51 | | ALPHA: (8) implies:
% 140.72/20.51 | | (9) all_56_13 = e2
% 140.72/20.51 | |
% 140.72/20.51 | | REDUCE: (2), (9) imply:
% 140.72/20.51 | | (10) $false
% 140.72/20.51 | |
% 140.72/20.51 | | CLOSE: (10) is inconsistent.
% 140.72/20.51 | |
% 140.72/20.51 | End of split
% 140.72/20.51 |
% 140.72/20.51 End of proof
% 140.72/20.51
% 140.72/20.51 Sub-proof #41 shows that the following formulas are inconsistent:
% 140.72/20.51 ----------------------------------------------------------------
% 140.72/20.51 (1) ~ (all_56_9 = e2)
% 140.72/20.51 (2) op(e1, e1) = e2
% 140.72/20.51 (3) ~ (e3 = e2)
% 140.72/20.51 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.51 (5) op(e3, e3) = all_56_9
% 140.72/20.51 (6) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.51 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.51 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 140.72/20.51 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.51 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.51 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 140.72/20.51 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 140.72/20.51 op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.51
% 140.72/20.51 Begin of proof
% 140.72/20.51 |
% 140.72/20.51 | BETA: splitting (6) gives:
% 140.72/20.51 |
% 140.72/20.51 | Case 1:
% 140.72/20.51 | |
% 140.72/20.51 | | (7) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.72/20.51 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.72/20.51 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.72/20.51 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 140.72/20.51 | |
% 140.72/20.51 | | BETA: splitting (7) gives:
% 140.72/20.51 | |
% 140.72/20.51 | | Case 1:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (8) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.72/20.51 | | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 140.72/20.51 | | |
% 140.72/20.51 | | | ALPHA: (8) implies:
% 140.72/20.51 | | | (9) op(e3, e3) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #391.
% 140.72/20.51 | | |
% 140.72/20.51 | | Case 2:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (10) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.72/20.51 | | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 140.72/20.51 | | |
% 140.72/20.51 | | | ALPHA: (10) implies:
% 140.72/20.51 | | | (11) op(e3, e3) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #391.
% 140.72/20.51 | | |
% 140.72/20.51 | | End of split
% 140.72/20.51 | |
% 140.72/20.51 | Case 2:
% 140.72/20.51 | |
% 140.72/20.51 | | (12) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 140.72/20.51 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.51 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 140.72/20.51 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.51 | |
% 140.72/20.51 | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #76.
% 140.72/20.51 | |
% 140.72/20.51 | End of split
% 140.72/20.51 |
% 140.72/20.51 End of proof
% 140.72/20.51
% 140.72/20.51 Sub-proof #42 shows that the following formulas are inconsistent:
% 140.72/20.51 ----------------------------------------------------------------
% 140.72/20.51 (1) ~ (all_14_2 = e2)
% 140.72/20.51 (2) ~ (e2 = e1)
% 140.72/20.51 (3) all_54_0 = all_14_2
% 140.72/20.51 (4) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 140.72/20.51 (5) ~ (all_14_2 = e1)
% 140.72/20.51 (6) op(e1, e1) = e2
% 140.72/20.51 (7) op(e2, e2) = e3
% 140.72/20.51 (8) op(e0, e0) = e2
% 140.72/20.51 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.51 (10) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.51 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.51 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.72/20.51 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.51 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.51 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.72/20.51 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.72/20.51 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.72/20.51 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.72/20.51 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.72/20.51 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.51 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.51 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.72/20.51 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.72/20.51 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.51 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.51 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.51 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.51 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.51 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.51 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.51 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.51 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.51 $i(all_56_14))))
% 140.72/20.51 (11) op(e3, e3) = all_14_2
% 140.72/20.51 (12) ~ (all_14_2 = e0)
% 140.72/20.51
% 140.72/20.51 Begin of proof
% 140.72/20.51 |
% 140.72/20.51 | BETA: splitting (4) gives:
% 140.72/20.51 |
% 140.72/20.51 | Case 1:
% 140.72/20.51 | |
% 140.72/20.51 | | (13) all_54_0 = e3
% 140.72/20.51 | |
% 140.72/20.51 | | COMBINE_EQS: (3), (13) imply:
% 140.72/20.51 | | (14) all_14_2 = e3
% 140.72/20.51 | |
% 140.72/20.51 | | REDUCE: (1), (14) imply:
% 140.72/20.51 | | (15) ~ (e3 = e2)
% 140.72/20.51 | |
% 140.72/20.51 | | REDUCE: (5), (14) imply:
% 140.72/20.51 | | (16) ~ (e3 = e1)
% 140.72/20.51 | |
% 140.72/20.51 | | REDUCE: (12), (14) imply:
% 140.72/20.51 | | (17) ~ (e3 = e0)
% 140.72/20.51 | |
% 140.72/20.51 | | REDUCE: (11), (14) imply:
% 140.72/20.51 | | (18) op(e3, e3) = e3
% 140.72/20.51 | |
% 140.72/20.51 | | BETA: splitting (10) gives:
% 140.72/20.51 | |
% 140.72/20.51 | | Case 1:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (19) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 140.72/20.51 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.72/20.51 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 140.72/20.51 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 140.72/20.51 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.72/20.51 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.51 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 140.72/20.51 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.51 | | |
% 140.72/20.51 | | | BETA: splitting (19) gives:
% 140.72/20.51 | | |
% 140.72/20.51 | | | Case 1:
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | (20) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3,
% 140.72/20.51 | | | | e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 &
% 140.72/20.51 | | | | $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3
% 140.72/20.51 | | | | = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2, e2)
% 140.72/20.51 | | | | = e3 & $i(all_56_3))
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | REF_CLOSE: (9), (15), (18), (20) are inconsistent by sub-proof #125.
% 140.72/20.51 | | | |
% 140.72/20.51 | | | Case 2:
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | (21) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3,
% 140.72/20.51 | | | | e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.72/20.51 | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6
% 140.72/20.51 | | | | = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1, e1)
% 140.72/20.51 | | | | = e3 & $i(all_56_6))
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | REF_CLOSE: (6), (9), (15), (21) are inconsistent by sub-proof #76.
% 140.72/20.51 | | | |
% 140.72/20.51 | | | End of split
% 140.72/20.51 | | |
% 140.72/20.51 | | Case 2:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (22) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 140.72/20.51 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.72/20.51 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 140.72/20.51 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 140.72/20.51 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.72/20.51 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.51 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 140.72/20.51 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.51 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.51 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.51 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.51 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.51 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.51 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.72/20.51 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.51 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.51 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.51 | | |
% 140.72/20.51 | | | BETA: splitting (22) gives:
% 140.72/20.51 | | |
% 140.72/20.51 | | | Case 1:
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | (23) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 140.72/20.51 | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 140.72/20.51 | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 140.72/20.51 | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.72/20.51 | | | | op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | REF_CLOSE: (7), (8), (9), (15), (16), (23) are inconsistent by sub-proof
% 140.72/20.51 | | | | #43.
% 140.72/20.51 | | | |
% 140.72/20.51 | | | Case 2:
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | (24) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 140.72/20.51 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.72/20.51 | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.72/20.51 | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 140.72/20.51 | | | | op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.51 | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 140.72/20.51 | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.72/20.51 | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.72/20.51 | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 140.72/20.51 | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.51 | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 140.72/20.51 | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.51 | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.72/20.51 | | | | all_56_14 & $i(all_56_14))))
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | BETA: splitting (24) gives:
% 140.72/20.51 | | | |
% 140.72/20.51 | | | | Case 1:
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | | (25) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 140.72/20.51 | | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.72/20.51 | | | | | $i(all_56_7)
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | | ALPHA: (25) implies:
% 140.72/20.51 | | | | | (26) op(e2, e2) = e1
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | | REF_CLOSE: (7), (9), (16), (26) are inconsistent by sub-proof #69.
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | Case 2:
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | | (27) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 140.72/20.51 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 140.72/20.51 | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.72/20.51 | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.51 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.51 | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.72/20.51 | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 140.72/20.51 | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 140.72/20.51 | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.51 | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.72/20.51 | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.72/20.51 | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | | BETA: splitting (27) gives:
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | | Case 1:
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | | (28) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.72/20.51 | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 140.72/20.51 | | | | | | $i(all_56_5)
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | | ALPHA: (28) implies:
% 140.72/20.51 | | | | | | (29) op(e2, e2) = e0
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | | REF_CLOSE: (7), (9), (17), (29) are inconsistent by sub-proof #1119.
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | Case 2:
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | | (30) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.51 | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.72/20.51 | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 =
% 140.72/20.51 | | | | | | e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 140.72/20.51 | | | | | | e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.51 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 140.72/20.51 | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8))
% 140.72/20.51 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 140.72/20.51 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.51 | | | | | | $i(all_56_14)))
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | | ALPHA: (30) implies:
% 140.72/20.51 | | | | | | (31) op(e0, e0) = all_56_15
% 140.72/20.51 | | | | | | (32) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.51 | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 140.72/20.51 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 140.72/20.51 | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.72/20.51 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 140.72/20.51 | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.72/20.51 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 140.72/20.51 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | | REF_CLOSE: (2), (7), (8), (9), (11), (12), (17), (31), (32) are
% 140.72/20.51 | | | | | | inconsistent by sub-proof #123.
% 140.72/20.51 | | | | | |
% 140.72/20.51 | | | | | End of split
% 140.72/20.51 | | | | |
% 140.72/20.51 | | | | End of split
% 140.72/20.51 | | | |
% 140.72/20.51 | | | End of split
% 140.72/20.51 | | |
% 140.72/20.51 | | End of split
% 140.72/20.51 | |
% 140.72/20.51 | Case 2:
% 140.72/20.51 | |
% 140.72/20.51 | | (33) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 140.72/20.51 | |
% 140.72/20.51 | | REF_CLOSE: (1), (3), (5), (12), (33) are inconsistent by sub-proof #883.
% 140.72/20.51 | |
% 140.72/20.51 | End of split
% 140.72/20.51 |
% 140.72/20.51 End of proof
% 140.72/20.51
% 140.72/20.51 Sub-proof #43 shows that the following formulas are inconsistent:
% 140.72/20.51 ----------------------------------------------------------------
% 140.72/20.51 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 140.72/20.51 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.72/20.51 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 140.72/20.51 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.51 (2) ~ (e3 = e2)
% 140.72/20.51 (3) op(e2, e2) = e3
% 140.72/20.51 (4) op(e0, e0) = e2
% 140.72/20.51 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.51 (6) ~ (e3 = e1)
% 140.72/20.51
% 140.72/20.51 Begin of proof
% 140.72/20.51 |
% 140.72/20.51 | BETA: splitting (1) gives:
% 140.72/20.51 |
% 140.72/20.51 | Case 1:
% 140.72/20.51 | |
% 140.72/20.51 | | (7) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 140.72/20.51 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 140.72/20.51 | |
% 140.72/20.51 | | ALPHA: (7) implies:
% 140.72/20.51 | | (8) op(e0, e0) = e3
% 140.72/20.51 | |
% 140.72/20.51 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1066.
% 140.72/20.51 | |
% 140.72/20.51 | Case 2:
% 140.72/20.51 | |
% 140.72/20.51 | | (9) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.72/20.51 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 140.72/20.51 | |
% 140.72/20.51 | | ALPHA: (9) implies:
% 140.72/20.51 | | (10) op(e2, e2) = e1
% 140.72/20.51 | |
% 140.72/20.51 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #69.
% 140.72/20.51 | |
% 140.72/20.51 | End of split
% 140.72/20.51 |
% 140.72/20.51 End of proof
% 140.72/20.51
% 140.72/20.51 Sub-proof #44 shows that the following formulas are inconsistent:
% 140.72/20.51 ----------------------------------------------------------------
% 140.72/20.51 (1) ~ (all_52_4 = all_52_7)
% 140.72/20.51 (2) ~ (all_52_1 = e2)
% 140.72/20.51 (3) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 &
% 140.72/20.51 op(e3, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 140.72/20.51 e0) & op(e3, e2) = all_44_1 & $i(all_44_1))
% 140.72/20.51 (4) ~ (all_52_13 = all_10_2)
% 140.72/20.51 (5) all_57_13 = e2 & op(e0, e2) = e2
% 140.72/20.51 (6) op(e1, e3) = all_52_2
% 140.72/20.51 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 140.72/20.51 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 140.72/20.51 (8) op(e1, e2) = all_52_6
% 140.72/20.51 (9) ~ (all_52_6 = e1)
% 140.72/20.51 (10) ~ (e2 = e1)
% 140.72/20.51 (11) ~ (all_52_4 = all_52_8)
% 140.72/20.51 (12) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 140.72/20.51 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 140.72/20.51 (13) ~ (all_52_4 = e1)
% 140.72/20.51 (14) all_54_3 = all_52_12
% 140.72/20.51 (15) ~ (all_52_9 = all_52_13)
% 140.72/20.51 (16) all_44_2 = e2
% 140.72/20.51 (17) op(e0, e3) = all_52_3
% 140.72/20.51 (18) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.72/20.51 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.72/20.51 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.72/20.51 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.51 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.72/20.51 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.72/20.51 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.72/20.51 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.72/20.51 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.72/20.51 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.72/20.51 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.72/20.51 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 140.72/20.51 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 140.72/20.51 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.72/20.51 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.72/20.51 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 140.72/20.51 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.72/20.51 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 140.72/20.51 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.72/20.51 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 140.72/20.51 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 140.72/20.51 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 140.72/20.51 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.72/20.51 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.72/20.51 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 140.72/20.51 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.72/20.51 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.72/20.51 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 140.72/20.51 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 140.72/20.51 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.72/20.51 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.72/20.51 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.72/20.51 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 140.72/20.51 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 140.72/20.51 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.72/20.51 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 140.72/20.51 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 140.72/20.51 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 140.72/20.51 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 140.72/20.51 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 140.72/20.51 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 140.72/20.51 (19) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 140.72/20.51 all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3,
% 140.72/20.51 e2) = all_36_1 & $i(all_36_1))
% 140.72/20.51 (20) ~ (all_10_2 = e1)
% 140.72/20.51 (21) op(e2, e2) = e1
% 140.72/20.51 (22) ~ (all_52_9 = e2)
% 140.72/20.51 (23) all_54_1 = all_52_4
% 140.72/20.51 (24) ~ (all_14_2 = e1)
% 140.72/20.51 (25) ~ (all_52_1 = e1)
% 140.72/20.51 (26) op(e3, e3) = e2
% 140.72/20.51 (27) ~ (e3 = e0)
% 140.72/20.51 (28) op(e3, e1) = all_52_8
% 140.72/20.51 (29) ~ (all_52_12 = all_52_14)
% 140.72/20.51 (30) ~ (all_52_1 = all_52_13)
% 140.72/20.51 (31) op(e2, e3) = all_52_1
% 140.72/20.51 (32) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 140.72/20.51 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 140.72/20.51 (33) ~ (all_52_13 = all_52_14)
% 140.72/20.51 (34) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.72/20.51 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.72/20.51 (35) op(e0, e0) = all_10_2
% 140.72/20.51 (36) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.72/20.51 (37) ~ (all_52_8 = all_52_12)
% 140.72/20.51 (38) ~ (e1 = e0)
% 140.72/20.51 (39) op(e1, e1) = e2
% 140.72/20.51 (40) op(e3, e2) = all_52_4
% 140.72/20.51 (41) ~ (e2 = e0)
% 140.72/20.51 (42) ~ (e3 = e2)
% 140.72/20.51 (43) op(e3, e0) = all_52_12
% 140.72/20.51 (44) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 140.72/20.51 (45) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 140.72/20.51 (46) all_54_15 = all_10_2
% 140.72/20.51 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.51 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.51 (48) ~ (all_52_14 = all_10_2)
% 140.72/20.51 (49) ~ (all_52_12 = all_52_13)
% 140.72/20.51 (50) ~ (e3 = e1)
% 140.72/20.51 (51) op(e0, e2) = all_52_7
% 140.72/20.51 (52) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.51 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.51 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.72/20.51 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.51 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.51 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.72/20.51 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.72/20.51 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.72/20.51 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.72/20.51 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.72/20.51 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.51 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.51 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.72/20.51 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.72/20.51 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.51 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.51 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.51 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.51 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.51 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.51 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.72/20.51 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.72/20.51 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.51 $i(all_56_14))))
% 140.72/20.51 (53) op(e2, e2) = all_6_2
% 140.72/20.51 (54) op(e2, e1) = all_52_9
% 140.72/20.51 (55) op(e3, e3) = all_14_2
% 140.72/20.51 (56) ~ (all_52_13 = e1)
% 140.72/20.51 (57) ~ (all_52_4 = all_52_12)
% 140.72/20.51 (58) op(e2, e0) = all_52_13
% 140.72/20.51 (59) ~ (all_52_12 = all_10_2)
% 140.72/20.51 (60) ~ (all_14_2 = e0)
% 140.72/20.51 (61) ~ (all_6_2 = e0)
% 140.72/20.51 (62) op(e1, e0) = all_52_14
% 140.72/20.51
% 140.72/20.51 Begin of proof
% 140.72/20.51 |
% 140.72/20.51 | ALPHA: (5) implies:
% 140.72/20.51 | (63) op(e0, e2) = e2
% 140.72/20.51 |
% 140.72/20.51 | BETA: splitting (7) gives:
% 140.72/20.51 |
% 140.72/20.51 | Case 1:
% 140.72/20.51 | |
% 140.72/20.51 | | (64) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 140.72/20.51 | | e2)
% 140.72/20.51 | |
% 140.72/20.51 | | BETA: splitting (64) gives:
% 140.72/20.51 | |
% 140.72/20.51 | | Case 1:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (65) all_57_2 = e2 & op(e2, e3) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | ALPHA: (65) implies:
% 140.72/20.51 | | | (66) op(e2, e3) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | REF_CLOSE: (2), (31), (47), (66) are inconsistent by sub-proof #882.
% 140.72/20.51 | | |
% 140.72/20.51 | | Case 2:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (67) all_57_3 = e2 & op(e2, e2) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | ALPHA: (67) implies:
% 140.72/20.51 | | | (68) op(e2, e2) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | REF_CLOSE: (10), (20), (24), (35), (41), (42), (47), (52), (53), (55),
% 140.72/20.51 | | | (60), (61), (68) are inconsistent by sub-proof #314.
% 140.72/20.51 | | |
% 140.72/20.51 | | End of split
% 140.72/20.51 | |
% 140.72/20.51 | Case 2:
% 140.72/20.51 | |
% 140.72/20.51 | | (69) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 140.72/20.51 | | e2)
% 140.72/20.51 | |
% 140.72/20.51 | | BETA: splitting (69) gives:
% 140.72/20.51 | |
% 140.72/20.51 | | Case 1:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (70) all_57_5 = e2 & op(e2, e1) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | ALPHA: (70) implies:
% 140.72/20.51 | | | (71) op(e2, e1) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | REF_CLOSE: (22), (47), (54), (71) are inconsistent by sub-proof #890.
% 140.72/20.51 | | |
% 140.72/20.51 | | Case 2:
% 140.72/20.51 | | |
% 140.72/20.51 | | | (72) all_57_10 = e2 & op(e2, e0) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | ALPHA: (72) implies:
% 140.72/20.51 | | | (73) op(e2, e0) = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | GROUND_INST: instantiating (47) with all_52_7, e2, e2, e0, simplifying
% 140.72/20.51 | | | with (51), (63) gives:
% 140.72/20.51 | | | (74) all_52_7 = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | GROUND_INST: instantiating (47) with all_52_13, e2, e0, e2, simplifying
% 140.72/20.51 | | | with (58), (73) gives:
% 140.72/20.51 | | | (75) all_52_13 = e2
% 140.72/20.51 | | |
% 140.72/20.51 | | | REDUCE: (1), (74) imply:
% 140.72/20.51 | | | (76) ~ (all_52_4 = e2)
% 140.72/20.51 | | |
% 140.72/20.51 | | | REDUCE: (49), (75) imply:
% 140.72/20.51 | | | (77) ~ (all_52_12 = e2)
% 140.72/20.51 | | |
% 140.72/20.51 | | | REDUCE: (33), (75) imply:
% 140.72/20.51 | | | (78) ~ (all_52_14 = e2)
% 140.72/20.51 | | |
% 140.72/20.51 | | | SIMP: (78) implies:
% 140.72/20.51 | | | (79) ~ (all_52_14 = e2)
% 140.72/20.51 | | |
% 140.72/20.51 | | | REDUCE: (4), (75) imply:
% 140.72/20.51 | | | (80) ~ (all_10_2 = e2)
% 140.72/20.51 | | |
% 140.72/20.51 | | | SIMP: (80) implies:
% 140.72/20.51 | | | (81) ~ (all_10_2 = e2)
% 140.72/20.52 | | |
% 140.72/20.52 | | | BETA: splitting (18) gives:
% 140.72/20.52 | | |
% 140.72/20.52 | | | Case 1:
% 140.72/20.52 | | | |
% 140.72/20.52 | | | | (82) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 140.72/20.52 | | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 140.72/20.52 | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 140.72/20.52 | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.72/20.52 | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 140.72/20.52 | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 140.72/20.52 | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 140.72/20.52 | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 140.72/20.52 | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 140.72/20.52 | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 140.72/20.52 | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.72/20.52 | | | | $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.72/20.52 | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.72/20.52 | | | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 140.72/20.52 | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 140.72/20.52 | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 140.72/20.52 | | | | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2)
% 140.72/20.52 | | | | = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | (
% 140.72/20.52 | | | | ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)))
% 140.72/20.52 | | | | & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 140.72/20.52 | | | | op(e0, e2) = all_56_12 & $i(all_56_12))))
% 140.72/20.52 | | | |
% 140.72/20.52 | | | | BETA: splitting (82) gives:
% 140.72/20.52 | | | |
% 140.72/20.52 | | | | Case 1:
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | (83) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 140.72/20.52 | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 140.72/20.52 | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 140.72/20.52 | | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.72/20.52 | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 140.72/20.52 | | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 140.72/20.52 | | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 140.72/20.52 | | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 140.72/20.52 | | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 140.72/20.52 | | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 140.72/20.52 | | | | | all_56_10 & $i(all_56_10)))
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | ALPHA: (83) implies:
% 140.72/20.52 | | | | | (84) op(e3, e3) = all_56_9
% 140.72/20.52 | | | | | (85) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 140.72/20.52 | | | | | op(e0, e3) = all_56_10 & $i(all_56_10))
% 140.72/20.52 | | | | | (86) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 140.72/20.52 | | | | | op(e1, e3) = all_56_6 & $i(all_56_6))
% 140.72/20.52 | | | | | (87) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) &
% 140.72/20.52 | | | | | op(e2, e3) = all_56_3 & $i(all_56_3))
% 140.72/20.52 | | | | | (88) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 140.72/20.52 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 140.72/20.52 | | | | | (89) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) &
% 140.72/20.52 | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))
% 140.72/20.52 | | | | | (90) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3) &
% 140.72/20.52 | | | | | op(e2, e2) = all_56_11 & $i(all_56_11))
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | BETA: splitting (87) gives:
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | Case 1:
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | (91) all_56_11 = e3 & op(e2, e2) = e3
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | ALPHA: (91) implies:
% 140.72/20.52 | | | | | | (92) op(e2, e2) = e3
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | REF_CLOSE: (2), (31), (47), (90), (92) are inconsistent by sub-proof
% 140.72/20.52 | | | | | | #178.
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | Case 2:
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | (93) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | ALPHA: (93) implies:
% 140.72/20.52 | | | | | | (94) op(e2, e3) = all_56_3
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | BETA: splitting (86) gives:
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | Case 1:
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | (95) all_56_13 = e3 & op(e1, e1) = e3
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | ALPHA: (95) implies:
% 140.72/20.52 | | | | | | | (96) op(e1, e1) = e3
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | REF_CLOSE: (39), (42), (47), (96) are inconsistent by sub-proof
% 140.72/20.52 | | | | | | | #77.
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | Case 2:
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | (97) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6)
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | ALPHA: (97) implies:
% 140.72/20.52 | | | | | | | (98) ~ (all_56_6 = e1)
% 140.72/20.52 | | | | | | | (99) op(e1, e3) = all_56_6
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | BETA: splitting (89) gives:
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | (100) all_56_6 = e1 & op(e1, e3) = e1
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | ALPHA: (100) implies:
% 140.72/20.52 | | | | | | | | (101) op(e1, e3) = e1
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | REF_CLOSE: (47), (98), (99), (101) are inconsistent by sub-proof
% 140.72/20.52 | | | | | | | | #435.
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | (102) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.72/20.52 | | | | | | | | $i(all_56_13)
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | ALPHA: (102) implies:
% 140.72/20.52 | | | | | | | | (103) op(e1, e1) = all_56_13
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | GROUND_INST: instantiating (47) with e2, all_56_13, e1, e1,
% 140.72/20.52 | | | | | | | | simplifying with (39), (103) gives:
% 140.72/20.52 | | | | | | | | (104) all_56_13 = e2
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | GROUND_INST: instantiating (47) with all_52_2, all_56_6, e3, e1,
% 140.72/20.52 | | | | | | | | simplifying with (6), (99) gives:
% 140.72/20.52 | | | | | | | | (105) all_56_6 = all_52_2
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | GROUND_INST: instantiating (47) with all_52_1, all_56_3, e3, e2,
% 140.72/20.52 | | | | | | | | simplifying with (31), (94) gives:
% 140.72/20.52 | | | | | | | | (106) all_56_3 = all_52_1
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | GROUND_INST: instantiating (47) with e2, all_56_9, e3, e3,
% 140.72/20.52 | | | | | | | | simplifying with (26), (84) gives:
% 140.72/20.52 | | | | | | | | (107) all_56_9 = e2
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | REDUCE: (98), (105) imply:
% 140.72/20.52 | | | | | | | | (108) ~ (all_52_2 = e1)
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | BETA: splitting (34) gives:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | (109) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 140.72/20.52 | | | | | | | | | op(e2, e3) = e1)
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | BETA: splitting (109) gives:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | (110) all_57_0 = e1 & op(e3, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | ALPHA: (110) implies:
% 140.72/20.52 | | | | | | | | | | (111) op(e3, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | REF_CLOSE: (10), (26), (47), (111) are inconsistent by
% 140.72/20.52 | | | | | | | | | | sub-proof #818.
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | (112) all_57_2 = e1 & op(e2, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | REF_CLOSE: (25), (31), (47), (112) are inconsistent by
% 140.72/20.52 | | | | | | | | | | sub-proof #846.
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | (113) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 &
% 140.72/20.52 | | | | | | | | | op(e0, e3) = e1)
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | BETA: splitting (113) gives:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | (114) all_57_6 = e1 & op(e1, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | ALPHA: (114) implies:
% 140.72/20.52 | | | | | | | | | | (115) op(e1, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | REF_CLOSE: (6), (47), (108), (115) are inconsistent by
% 140.72/20.52 | | | | | | | | | | sub-proof #332.
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | (116) all_57_12 = e1 & op(e0, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | ALPHA: (116) implies:
% 140.72/20.52 | | | | | | | | | | (117) op(e0, e3) = e1
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | BETA: splitting (12) gives:
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | (118) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 140.72/20.52 | | | | | | | | | | | & op(e1, e2) = e1)
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | REF_CLOSE: (6), (8), (9), (47), (108), (118) are inconsistent
% 140.72/20.52 | | | | | | | | | | | by sub-proof #85.
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | (119) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 140.72/20.52 | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | BETA: splitting (119) gives:
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | (120) all_57_8 = e1 & op(e1, e1) = e1
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | ALPHA: (120) implies:
% 140.72/20.52 | | | | | | | | | | | | (121) op(e1, e1) = e1
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | REF_CLOSE: (10), (39), (47), (121) are inconsistent by
% 140.72/20.52 | | | | | | | | | | | | sub-proof #1085.
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | (122) all_57_11 = e1 & op(e1, e0) = e1
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | ALPHA: (122) implies:
% 140.72/20.52 | | | | | | | | | | | | (123) op(e1, e0) = e1
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_52_3, e1, e3, e0,
% 140.72/20.52 | | | | | | | | | | | | simplifying with (17), (117) gives:
% 140.72/20.52 | | | | | | | | | | | | (124) all_52_3 = e1
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_52_14, e1, e0, e1,
% 140.72/20.52 | | | | | | | | | | | | simplifying with (62), (123) gives:
% 140.72/20.52 | | | | | | | | | | | | (125) all_52_14 = e1
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | REDUCE: (29), (125) imply:
% 140.72/20.52 | | | | | | | | | | | | (126) ~ (all_52_12 = e1)
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | REDUCE: (48), (125) imply:
% 140.72/20.52 | | | | | | | | | | | | (127) ~ (all_10_2 = e1)
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | REDUCE: (79), (125) imply:
% 140.72/20.52 | | | | | | | | | | | | (128) ~ (e2 = e1)
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | BETA: splitting (88) gives:
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | (129) all_56_10 = e0 & op(e0, e3) = e0
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | ALPHA: (129) implies:
% 140.72/20.52 | | | | | | | | | | | | | (130) op(e0, e3) = e0
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e1, e0, e3, e0,
% 140.72/20.52 | | | | | | | | | | | | | simplifying with (117), (130) gives:
% 140.72/20.52 | | | | | | | | | | | | | (131) e1 = e0
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | REDUCE: (38), (131) imply:
% 140.72/20.52 | | | | | | | | | | | | | (132) $false
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | CLOSE: (132) is inconsistent.
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | (133) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | | | | | | | | | | $i(all_56_15)
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | ALPHA: (133) implies:
% 140.72/20.52 | | | | | | | | | | | | | (134) ~ (all_56_15 = e3)
% 140.72/20.52 | | | | | | | | | | | | | (135) op(e0, e0) = all_56_15
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | BETA: splitting (85) gives:
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | (136) all_56_15 = e3 & op(e0, e0) = e3
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | ALPHA: (136) implies:
% 140.72/20.52 | | | | | | | | | | | | | | (137) op(e0, e0) = e3
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | REF_CLOSE: (47), (134), (135), (137) are inconsistent by
% 140.72/20.52 | | | | | | | | | | | | | | sub-proof #740.
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | (138) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 &
% 140.72/20.52 | | | | | | | | | | | | | | $i(all_56_10)
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | ALPHA: (138) implies:
% 140.72/20.52 | | | | | | | | | | | | | | (139) op(e0, e3) = all_56_10
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | BETA: splitting (32) gives:
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | (140) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | (141) all_57_0 = e1 & op(e3, e3) = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 140.72/20.52 | | | | | | | | | | | | | | | | (142) op(e3, e3) = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | REF_CLOSE: (10), (26), (47), (142) are inconsistent by
% 140.72/20.52 | | | | | | | | | | | | | | | | sub-proof #818.
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | (143) all_57_1 = e1 & op(e3, e2) = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | REF_CLOSE: (13), (40), (47), (143) are inconsistent by
% 140.72/20.52 | | | | | | | | | | | | | | | | sub-proof #844.
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | (144) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | (145) all_57_4 = e1 & op(e3, e1) = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 140.72/20.52 | | | | | | | | | | | | | | | | (146) op(e3, e1) = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_10_2, all_56_15, e0,
% 140.72/20.52 | | | | | | | | | | | | | | | | e0, simplifying with (35), (135) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | (147) all_56_15 = all_10_2
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with e1, all_56_10, e3, e0,
% 140.72/20.52 | | | | | | | | | | | | | | | | simplifying with (117), (139) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | (148) all_56_10 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (47) with all_52_8, e1, e1, e3,
% 140.72/20.52 | | | | | | | | | | | | | | | | simplifying with (28), (146) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | (149) all_52_8 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | REDUCE: (134), (147) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | (150) ~ (all_10_2 = e3)
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | REDUCE: (37), (149) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | (151) ~ (all_52_12 = e1)
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | (152) all_54_15 = e3
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (150), (152) are inconsistent by sub-proof
% 140.72/20.52 | | | | | | | | | | | | | | | | | #755.
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | (153) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | (154) all_54_15 = e2
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (81), (154) are inconsistent by sub-proof
% 140.72/20.52 | | | | | | | | | | | | | | | | | | #754.
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | (155) all_54_15 = e1 | all_54_15 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | BETA: splitting (155) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | (156) all_54_15 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (46), (156) are inconsistent by sub-proof
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | #748.
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | (157) all_54_15 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (46), (157) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | (158) all_10_2 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | SIMP: (158) implies:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | (159) all_10_2 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | REDUCE: (59), (159) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | (160) ~ (all_52_12 = e0)
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | (161) all_54_3 = e3
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (14), (161) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | (162) all_52_12 = e3
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | SIMP: (162) implies:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | (163) all_52_12 = e3
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | REDUCE: (57), (163) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | (164) ~ (all_52_4 = e3)
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | (165) all_54_1 = e3
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (165) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | (166) all_52_4 = e3
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | REDUCE: (164), (166) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | (167) $false
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | (168) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (168) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | (169) all_54_1 = e2
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (169) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | (170) all_52_4 = e2
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (76), (170) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | (171) $false
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (171) is inconsistent.
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | (172) all_54_1 = e1 | all_54_1 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (172) gives:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | (173) all_54_1 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (173) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | (174) all_52_4 = e1
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (13), (174) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | (175) $false
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (175) is inconsistent.
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | (176) all_54_1 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (23), (176) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | (177) all_52_4 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (40), (177) imply:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | (178) op(e3, e2) = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (16), (19), (47), (117), (178) are
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #48.
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | (179) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (77), (126), (160), (179) are inconsistent
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | | by sub-proof #157.
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | (180) all_57_9 = e1 & op(e3, e0) = e1
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | | REF_CLOSE: (43), (47), (126), (180) are inconsistent by
% 140.72/20.52 | | | | | | | | | | | | | | | | sub-proof #461.
% 140.72/20.52 | | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | | |
% 140.72/20.52 | | | | | | | | | End of split
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | End of split
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | End of split
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | End of split
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | End of split
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | Case 2:
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | (181) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 140.72/20.52 | | | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 140.72/20.52 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 140.72/20.52 | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.72/20.52 | | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | (
% 140.72/20.52 | | | | | ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 140.72/20.52 | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | (
% 140.72/20.52 | | | | | ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | (
% 140.72/20.52 | | | | | ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.72/20.52 | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | (
% 140.72/20.52 | | | | | ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 140.72/20.52 | | | | | $i(all_56_12)))
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | ALPHA: (181) implies:
% 140.72/20.52 | | | | | (182) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 140.72/20.52 | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | BETA: splitting (182) gives:
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | Case 1:
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | (183) all_56_7 = e1 & op(e1, e2) = e1
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | ALPHA: (183) implies:
% 140.72/20.52 | | | | | | (184) op(e1, e2) = e1
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | REF_CLOSE: (8), (9), (47), (184) are inconsistent by sub-proof #341.
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | Case 2:
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | (185) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.72/20.52 | | | | | | $i(all_56_13)
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | ALPHA: (185) implies:
% 140.72/20.52 | | | | | | (186) ~ (all_56_13 = e2)
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | BETA: splitting (52) gives:
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | | Case 1:
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | (187) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 140.72/20.52 | | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) =
% 140.72/20.52 | | | | | | | e3 & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 &
% 140.72/20.52 | | | | | | | ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) =
% 140.72/20.52 | | | | | | | all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9
% 140.72/20.52 | | | | | | | = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.72/20.52 | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.72/20.52 | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 & ~
% 140.72/20.52 | | | | | | | (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.72/20.52 | | | | | | | all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | REF_CLOSE: (21), (39), (42), (47), (50), (187) are inconsistent by
% 140.72/20.52 | | | | | | | sub-proof #47.
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | Case 2:
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | (188) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 140.72/20.52 | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) =
% 140.72/20.52 | | | | | | | e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 &
% 140.72/20.52 | | | | | | | ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.52 | | | | | | | all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11
% 140.72/20.52 | | | | | | | = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.72/20.52 | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.72/20.52 | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.72/20.52 | | | | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.52 | | | | | | | all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0,
% 140.72/20.52 | | | | | | | e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.52 | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.72/20.52 | | | | | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.52 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.72/20.52 | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.72/20.52 | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 140.72/20.52 | | | | | | | ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 140.72/20.52 | | | | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.52 | | | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 140.72/20.52 | | | | | | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | BETA: splitting (188) gives:
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | (189) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 140.72/20.52 | | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 140.72/20.52 | | | | | | | | = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 =
% 140.72/20.52 | | | | | | | | e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2,
% 140.72/20.52 | | | | | | | | e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | BETA: splitting (189) gives:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | (190) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 140.72/20.52 | | | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 140.72/20.52 | | | | | | | | | = e3 & $i(all_56_2)
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | ALPHA: (190) implies:
% 140.72/20.52 | | | | | | | | | (191) op(e3, e3) = e0
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | REF_CLOSE: (26), (41), (47), (191) are inconsistent by
% 140.72/20.52 | | | | | | | | | sub-proof #880.
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | (192) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2)
% 140.72/20.52 | | | | | | | | | & op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.72/20.52 | | | | | | | | | e1) = e2 & $i(all_56_4)
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | ALPHA: (192) implies:
% 140.72/20.52 | | | | | | | | | (193) all_56_13 = e2
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | REDUCE: (186), (193) imply:
% 140.72/20.52 | | | | | | | | | (194) $false
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | CLOSE: (194) is inconsistent.
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | End of split
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | (195) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 140.72/20.52 | | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1)
% 140.72/20.52 | | | | | | | | = e2 & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 =
% 140.72/20.52 | | | | | | | | e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.72/20.52 | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.72/20.52 | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 140.72/20.52 | | | | | | | | e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.72/20.52 | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.52 | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2
% 140.72/20.52 | | | | | | | | & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.72/20.52 | | | | | | | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 =
% 140.72/20.52 | | | | | | | | e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 140.72/20.52 | | | | | | | | e1) = e0 & op(e1, e0) = all_56_8 &
% 140.72/20.52 | | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1
% 140.72/20.52 | | | | | | | | & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.72/20.52 | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | BETA: splitting (195) gives:
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | | Case 1:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | (196) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1)
% 140.72/20.52 | | | | | | | | | & op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1,
% 140.72/20.52 | | | | | | | | | e1) = e2 & $i(all_56_7)
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | ALPHA: (196) implies:
% 140.72/20.52 | | | | | | | | | (197) all_56_13 = e2
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | REDUCE: (186), (197) imply:
% 140.72/20.52 | | | | | | | | | (198) $false
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | CLOSE: (198) is inconsistent.
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | Case 2:
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | (199) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2)
% 140.72/20.52 | | | | | | | | | & op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.72/20.52 | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.72/20.52 | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.52 | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 140.72/20.52 | | | | | | | | | e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.52 | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 140.72/20.52 | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.72/20.52 | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.52 | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.72/20.52 | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.72/20.52 | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.52 | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.72/20.52 | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | | REF_CLOSE: (20), (35), (47), (53), (55), (60), (61), (73),
% 140.72/20.52 | | | | | | | | | (199) are inconsistent by sub-proof #46.
% 140.72/20.52 | | | | | | | | |
% 140.72/20.52 | | | | | | | | End of split
% 140.72/20.52 | | | | | | | |
% 140.72/20.52 | | | | | | | End of split
% 140.72/20.52 | | | | | | |
% 140.72/20.52 | | | | | | End of split
% 140.72/20.52 | | | | | |
% 140.72/20.52 | | | | | End of split
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | End of split
% 140.72/20.52 | | | |
% 140.72/20.52 | | | Case 2:
% 140.72/20.52 | | | |
% 140.72/20.52 | | | | (200) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 140.72/20.52 | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 140.72/20.52 | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 140.72/20.52 | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.72/20.52 | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 140.72/20.52 | | | | ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.72/20.52 | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | (
% 140.72/20.52 | | | | ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.72/20.52 | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | (
% 140.72/20.52 | | | | ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) | (
% 140.72/20.52 | | | | ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.72/20.52 | | | | $i(all_56_14)))) | (op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 140.72/20.52 | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.72/20.52 | | | | & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 140.72/20.52 | | | | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 =
% 140.72/20.52 | | | | e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 140.72/20.52 | | | | = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 140.72/20.52 | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2
% 140.72/20.52 | | | | & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) |
% 140.72/20.52 | | | | ( ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.72/20.52 | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | (
% 140.72/20.52 | | | | ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 140.72/20.52 | | | | $i(all_56_8))))
% 140.72/20.52 | | | |
% 140.72/20.52 | | | | BETA: splitting (200) gives:
% 140.72/20.52 | | | |
% 140.72/20.52 | | | | Case 1:
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | (201) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 140.72/20.52 | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 140.72/20.52 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 140.72/20.52 | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 140.72/20.52 | | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 140.72/20.52 | | | | | ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.72/20.52 | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | (
% 140.72/20.52 | | | | | ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 140.72/20.52 | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | (
% 140.72/20.52 | | | | | ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 140.72/20.52 | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) | (
% 140.72/20.52 | | | | | ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.72/20.52 | | | | | $i(all_56_14)))
% 140.72/20.52 | | | | |
% 140.72/20.52 | | | | | ALPHA: (201) implies:
% 140.72/20.52 | | | | | (202) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 140.72/20.52 | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 140.72/20.52 | | | | | (203) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) &
% 140.72/20.52 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 140.72/20.52 | | | | | (204) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 140.72/20.52 | | | | | op(e2, e1) = all_56_4 & $i(all_56_4))
% 140.72/20.53 | | | | | (205) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) &
% 140.72/20.53 | | | | | op(e2, e2) = all_56_11 & $i(all_56_11))
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | BETA: splitting (52) gives:
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | Case 1:
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | | (206) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 140.72/20.53 | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3
% 140.72/20.53 | | | | | | & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~
% 140.72/20.53 | | | | | | (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3
% 140.72/20.53 | | | | | | & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.53 | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 &
% 140.72/20.53 | | | | | | op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.53 | | | | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 140.72/20.53 | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3
% 140.72/20.53 | | | | | | & $i(all_56_6))
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | | REF_CLOSE: (21), (39), (42), (47), (50), (206) are inconsistent by
% 140.72/20.53 | | | | | | sub-proof #47.
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | Case 2:
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | | (207) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 140.72/20.53 | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3
% 140.72/20.53 | | | | | | & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 140.72/20.53 | | | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4
% 140.72/20.53 | | | | | | & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.72/20.53 | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 140.72/20.53 | | | | | | op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.72/20.53 | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.72/20.53 | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2
% 140.72/20.53 | | | | | | & $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15)
% 140.72/20.53 | | | | | | & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.72/20.53 | | | | | | & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.53 | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 140.72/20.53 | | | | | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 140.72/20.53 | | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.72/20.53 | | | | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0
% 140.72/20.53 | | | | | | & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 140.72/20.53 | | | | | | = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 140.72/20.53 | | | | | | e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.53 | | | | | | $i(all_56_14))))
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | | BETA: splitting (207) gives:
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | | Case 1:
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | | (208) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 140.72/20.53 | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) =
% 140.72/20.53 | | | | | | | e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 &
% 140.72/20.53 | | | | | | | ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.72/20.53 | | | | | | | all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | | BETA: splitting (208) gives:
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | | Case 1:
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | (209) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 140.72/20.53 | | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) =
% 140.72/20.53 | | | | | | | | e3 & $i(all_56_2)
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | ALPHA: (209) implies:
% 140.72/20.53 | | | | | | | | (210) op(e0, e0) = e3
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | REF_CLOSE: (21), (22), (47), (50), (54), (202), (203), (204),
% 140.72/20.53 | | | | | | | | (205), (210) are inconsistent by sub-proof #45.
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | Case 2:
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | (211) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.72/20.53 | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) =
% 140.72/20.53 | | | | | | | | e2 & $i(all_56_4)
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | ALPHA: (211) implies:
% 140.72/20.53 | | | | | | | | (212) all_56_11 = e1
% 140.72/20.53 | | | | | | | | (213) ~ (all_56_4 = e2)
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | REF_CLOSE: (205), (212), (213) are inconsistent by sub-proof
% 140.72/20.53 | | | | | | | | #646.
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | End of split
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | Case 2:
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | | (214) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 140.72/20.53 | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) =
% 140.72/20.53 | | | | | | | e2 & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 &
% 140.72/20.53 | | | | | | | ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.72/20.53 | | | | | | | all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0,
% 140.72/20.53 | | | | | | | e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.72/20.53 | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.72/20.53 | | | | | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.72/20.53 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.72/20.53 | | | | | | | e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.72/20.53 | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 140.72/20.53 | | | | | | | ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 140.72/20.53 | | | | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.53 | | | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 140.72/20.53 | | | | | | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | | BETA: splitting (214) gives:
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | | Case 1:
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | (215) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 140.72/20.53 | | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) =
% 140.72/20.53 | | | | | | | | e2 & $i(all_56_7)
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | ALPHA: (215) implies:
% 140.72/20.53 | | | | | | | | (216) all_56_11 = e1
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | REF_CLOSE: (22), (47), (54), (205), (216) are inconsistent by
% 140.72/20.53 | | | | | | | | sub-proof #91.
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | Case 2:
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | (217) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.72/20.53 | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0)
% 140.72/20.53 | | | | | | | | = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.72/20.53 | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 140.72/20.53 | | | | | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.72/20.53 | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.53 | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.72/20.53 | | | | | | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.53 | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 140.72/20.53 | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 140.72/20.53 | | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1
% 140.72/20.53 | | | | | | | | & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.72/20.53 | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | | REF_CLOSE: (20), (35), (47), (53), (55), (60), (61), (73), (217)
% 140.72/20.53 | | | | | | | | are inconsistent by sub-proof #46.
% 140.72/20.53 | | | | | | | |
% 140.72/20.53 | | | | | | | End of split
% 140.72/20.53 | | | | | | |
% 140.72/20.53 | | | | | | End of split
% 140.72/20.53 | | | | | |
% 140.72/20.53 | | | | | End of split
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | Case 2:
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | (218) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 140.72/20.53 | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 140.72/20.53 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 140.72/20.53 | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 140.72/20.53 | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 140.72/20.53 | | | | | ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 140.72/20.53 | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | (
% 140.72/20.53 | | | | | ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 140.72/20.53 | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | (
% 140.72/20.53 | | | | | ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 140.72/20.53 | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | (
% 140.72/20.53 | | | | | ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 140.72/20.53 | | | | | $i(all_56_8)))
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | REF_CLOSE: (20), (24), (27), (35), (38), (47), (52), (55), (60), (73),
% 140.72/20.53 | | | | | (81), (218) are inconsistent by sub-proof #151.
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | End of split
% 140.72/20.53 | | | |
% 140.72/20.53 | | | End of split
% 140.72/20.53 | | |
% 140.72/20.53 | | End of split
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #45 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) op(e0, e0) = e3
% 140.72/20.53 (2) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.72/20.53 all_56_11 & $i(all_56_11))
% 140.72/20.53 (3) op(e2, e2) = e1
% 140.72/20.53 (4) ~ (all_52_9 = e2)
% 140.72/20.53 (5) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.72/20.53 all_56_14 & $i(all_56_14))
% 140.72/20.53 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (7) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 140.72/20.53 all_56_4 & $i(all_56_4))
% 140.72/20.53 (8) ~ (e3 = e1)
% 140.72/20.53 (9) op(e2, e1) = all_52_9
% 140.72/20.53 (10) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.72/20.53 all_56_15 & $i(all_56_15))
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (2) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (11) all_56_4 = e2 & op(e2, e1) = e2
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (11) implies:
% 140.72/20.53 | | (12) op(e2, e1) = e2
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (4), (6), (9), (12) are inconsistent by sub-proof #890.
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (13) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (13) implies:
% 140.72/20.53 | | (14) ~ (all_56_11 = e1)
% 140.72/20.53 | | (15) op(e2, e2) = all_56_11
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (14), (15) are
% 140.72/20.53 | | inconsistent by sub-proof #533.
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #46 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 140.72/20.53 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.72/20.53 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 140.72/20.53 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.72/20.53 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 140.72/20.53 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.72/20.53 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 140.72/20.53 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.72/20.53 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 140.72/20.53 = all_56_14 & $i(all_56_14))))
% 140.72/20.53 (2) ~ (all_10_2 = e1)
% 140.72/20.53 (3) op(e0, e0) = all_10_2
% 140.72/20.53 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (5) op(e2, e2) = all_6_2
% 140.72/20.53 (6) op(e3, e3) = all_14_2
% 140.72/20.53 (7) op(e2, e0) = e2
% 140.72/20.53 (8) ~ (all_14_2 = e0)
% 140.72/20.53 (9) ~ (all_6_2 = e0)
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (1) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (10) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.72/20.53 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (10) implies:
% 140.72/20.53 | | (11) ~ (all_56_5 = e2)
% 140.72/20.53 | | (12) op(e2, e0) = all_56_5
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (4), (7), (11), (12) are inconsistent by sub-proof #152.
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (13) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 140.72/20.53 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 140.72/20.53 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 140.72/20.53 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 140.72/20.53 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 140.72/20.53 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 140.72/20.53 | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.72/20.53 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.53 | | $i(all_56_14)))
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (13) implies:
% 140.72/20.53 | | (14) op(e0, e0) = all_56_15
% 140.72/20.53 | | (15) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 140.72/20.53 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.72/20.53 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.72/20.53 | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 140.72/20.53 | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 140.72/20.53 | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 140.72/20.53 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.72/20.53 | | $i(all_56_14))
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (14), (15) are inconsistent by
% 140.72/20.53 | | sub-proof #1120.
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #47 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) op(e2, e2) = e1
% 140.72/20.53 (2) op(e1, e1) = e2
% 140.72/20.53 (3) ~ (e3 = e2)
% 140.72/20.53 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (5) ~ (e3 = e1)
% 140.72/20.53 (6) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.72/20.53 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.72/20.53 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 140.72/20.53 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.72/20.53 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.72/20.53 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 140.72/20.53 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 140.72/20.53 op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (6) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (7) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.72/20.53 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.72/20.53 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.72/20.53 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 140.72/20.53 | |
% 140.72/20.53 | | BETA: splitting (7) gives:
% 140.72/20.53 | |
% 140.72/20.53 | | Case 1:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (8) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.72/20.53 | | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 140.72/20.53 | | |
% 140.72/20.53 | | | ALPHA: (8) implies:
% 140.72/20.53 | | | (9) op(e2, e2) = e3
% 140.72/20.53 | | |
% 140.72/20.53 | | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #69.
% 140.72/20.53 | | |
% 140.72/20.53 | | Case 2:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (10) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.72/20.53 | | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 140.72/20.53 | | |
% 140.72/20.53 | | | ALPHA: (10) implies:
% 140.72/20.53 | | | (11) op(e2, e2) = e3
% 140.72/20.53 | | |
% 140.72/20.53 | | | REF_CLOSE: (1), (4), (5), (11) are inconsistent by sub-proof #69.
% 140.72/20.53 | | |
% 140.72/20.53 | | End of split
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (12) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 140.72/20.53 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.72/20.53 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 140.72/20.53 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (2), (3), (4), (12) are inconsistent by sub-proof #76.
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #48 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 &
% 140.72/20.53 op(e3, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 140.72/20.53 e0) & op(e3, e2) = all_44_1 & $i(all_44_1))
% 140.72/20.53 (2) all_44_2 = e2
% 140.72/20.53 (3) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) = all_36_1
% 140.72/20.53 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2) =
% 140.72/20.53 all_36_1 & $i(all_36_1))
% 140.72/20.53 (4) op(e0, e3) = e1
% 140.72/20.53 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (6) op(e3, e2) = e0
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (1) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (7) ~ (all_44_2 = e2)
% 140.72/20.53 | |
% 140.72/20.53 | | REDUCE: (2), (7) imply:
% 140.72/20.53 | | (8) $false
% 140.72/20.53 | |
% 140.72/20.53 | | CLOSE: (8) is inconsistent.
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (9) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 140.72/20.53 | | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) &
% 140.72/20.53 | | op(e3, e2) = all_44_1 & $i(all_44_1))
% 140.72/20.53 | |
% 140.72/20.53 | | BETA: splitting (3) gives:
% 140.72/20.53 | |
% 140.72/20.53 | | Case 1:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (10) ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 140.72/20.53 | | | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 140.72/20.53 | | |
% 140.72/20.53 | | | ALPHA: (10) implies:
% 140.72/20.53 | | | (11) op(e3, e2) = all_36_1
% 140.72/20.53 | | |
% 140.72/20.53 | | | REF_CLOSE: (4), (5), (6), (9), (11) are inconsistent by sub-proof #49.
% 140.72/20.53 | | |
% 140.72/20.53 | | Case 2:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (12) ~ (all_36_1 = e1) & op(e3, e2) = all_36_1 & $i(all_36_1)
% 140.72/20.53 | | |
% 140.72/20.53 | | | ALPHA: (12) implies:
% 140.72/20.53 | | | (13) op(e3, e2) = all_36_1
% 140.72/20.53 | | |
% 140.72/20.53 | | | REF_CLOSE: (4), (5), (6), (9), (13) are inconsistent by sub-proof #49.
% 140.72/20.53 | | |
% 140.72/20.53 | | End of split
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #49 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) op(e0, e3) = e1
% 140.72/20.53 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (3) op(e3, e2) = all_36_1
% 140.72/20.53 (4) op(e3, e2) = e0
% 140.72/20.53 (5) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) = all_44_1
% 140.72/20.53 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3, e2) =
% 140.72/20.53 all_44_1 & $i(all_44_1))
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | GROUND_INST: instantiating (2) with e0, all_36_1, e2, e3, simplifying with
% 140.72/20.53 | (3), (4) gives:
% 140.72/20.53 | (6) all_36_1 = e0
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (5) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (7) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 140.72/20.53 | | all_44_1 & $i(all_44_0) & $i(all_44_1)
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (7) implies:
% 140.72/20.53 | | (8) ~ (all_44_0 = e1)
% 140.72/20.53 | | (9) op(e3, e2) = all_44_1
% 140.72/20.53 | | (10) op(all_44_1, e3) = all_44_0
% 140.72/20.53 | |
% 140.72/20.53 | | GROUND_INST: instantiating (2) with e0, all_44_1, e2, e3, simplifying with
% 140.72/20.53 | | (4), (9) gives:
% 140.72/20.53 | | (11) all_44_1 = e0
% 140.72/20.53 | |
% 140.72/20.53 | | REDUCE: (10), (11) imply:
% 140.72/20.53 | | (12) op(e0, e3) = all_44_0
% 140.72/20.53 | |
% 140.72/20.53 | | GROUND_INST: instantiating (2) with e1, all_44_0, e3, e0, simplifying with
% 140.72/20.53 | | (1), (12) gives:
% 140.72/20.53 | | (13) all_44_0 = e1
% 140.72/20.53 | |
% 140.72/20.53 | | REDUCE: (8), (13) imply:
% 140.72/20.53 | | (14) $false
% 140.72/20.53 | |
% 140.72/20.53 | | CLOSE: (14) is inconsistent.
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (15) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (2), (3), (4), (15) are inconsistent by sub-proof #147.
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #50 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) ~ (e2 = e1)
% 140.72/20.53 (2) op(e3, e3) = e2
% 140.72/20.53 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.72/20.53 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.72/20.53 (4) ~ (e3 = e0)
% 140.72/20.53 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 140.72/20.53 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 140.72/20.53 (6) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.72/20.53 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.72/20.53 (7) ~ (e1 = e0)
% 140.72/20.53 (8) ~ (e2 = e0)
% 140.72/20.53 (9) ~ (e3 = e2)
% 140.72/20.53 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (11) ~ (e3 = e1)
% 140.72/20.53 (12) all_57_12 = e2
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (5) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 140.72/20.53 | | e3)
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13)
% 140.72/20.53 | | are inconsistent by sub-proof #52.
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 140.72/20.53 | | e3)
% 140.72/20.53 | |
% 140.72/20.53 | | BETA: splitting (14) gives:
% 140.72/20.53 | |
% 140.72/20.53 | | Case 1:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (15) all_57_6 = e3 & op(e1, e3) = e3
% 140.72/20.53 | | |
% 140.72/20.53 | | | ALPHA: (15) implies:
% 140.72/20.53 | | | (16) all_57_6 = e3
% 140.72/20.53 | | |
% 140.72/20.53 | | | BETA: splitting (6) gives:
% 140.72/20.53 | | |
% 140.72/20.53 | | | Case 1:
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | (17) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 140.72/20.53 | | | | = e1)
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (10), (12), (16), (17) are
% 140.72/20.53 | | | | inconsistent by sub-proof #51.
% 140.72/20.53 | | | |
% 140.72/20.53 | | | Case 2:
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | (18) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 140.72/20.53 | | | | = e1)
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | BETA: splitting (18) gives:
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | Case 1:
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | (19) all_57_6 = e1 & op(e1, e3) = e1
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | REF_CLOSE: (11), (16), (19) are inconsistent by sub-proof #865.
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | Case 2:
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | (20) all_57_12 = e1 & op(e0, e3) = e1
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | | REF_CLOSE: (1), (12), (20) are inconsistent by sub-proof #848.
% 140.72/20.53 | | | | |
% 140.72/20.53 | | | | End of split
% 140.72/20.53 | | | |
% 140.72/20.53 | | | End of split
% 140.72/20.53 | | |
% 140.72/20.53 | | Case 2:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (21) all_57_12 = e3 & op(e0, e3) = e3
% 140.72/20.53 | | |
% 140.72/20.53 | | | ALPHA: (21) implies:
% 140.72/20.53 | | | (22) all_57_12 = e3
% 140.72/20.53 | | |
% 140.72/20.53 | | | REF_CLOSE: (9), (12), (22) are inconsistent by sub-proof #772.
% 140.72/20.53 | | |
% 140.72/20.53 | | End of split
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #51 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) all_57_6 = e3
% 140.72/20.53 (2) ~ (e2 = e1)
% 140.72/20.53 (3) op(e3, e3) = e2
% 140.72/20.53 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.72/20.53 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.72/20.53 (5) ~ (e3 = e0)
% 140.72/20.53 (6) ~ (e1 = e0)
% 140.72/20.53 (7) ~ (e2 = e0)
% 140.72/20.53 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 140.72/20.53 (10) all_57_12 = e2
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (9) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (11) all_57_0 = e1 & op(e3, e3) = e1
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (11) implies:
% 140.72/20.53 | | (12) op(e3, e3) = e1
% 140.72/20.53 | |
% 140.72/20.53 | | REF_CLOSE: (2), (3), (8), (12) are inconsistent by sub-proof #818.
% 140.72/20.53 | |
% 140.72/20.53 | Case 2:
% 140.72/20.53 | |
% 140.72/20.53 | | (13) all_57_2 = e1 & op(e2, e3) = e1
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (13) implies:
% 140.72/20.53 | | (14) all_57_2 = e1
% 140.72/20.53 | |
% 140.72/20.53 | | BETA: splitting (4) gives:
% 140.72/20.53 | |
% 140.72/20.53 | | Case 1:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (15) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 140.72/20.53 | | | e0)
% 140.72/20.53 | | |
% 140.72/20.53 | | | REF_CLOSE: (3), (6), (7), (8), (14), (15) are inconsistent by sub-proof
% 140.72/20.53 | | | #405.
% 140.72/20.53 | | |
% 140.72/20.53 | | Case 2:
% 140.72/20.53 | | |
% 140.72/20.53 | | | (16) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 140.72/20.53 | | | e0)
% 140.72/20.53 | | |
% 140.72/20.53 | | | BETA: splitting (16) gives:
% 140.72/20.53 | | |
% 140.72/20.53 | | | Case 1:
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | (17) all_57_6 = e0 & op(e1, e3) = e0
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | REF_CLOSE: (1), (5), (17) are inconsistent by sub-proof #603.
% 140.72/20.53 | | | |
% 140.72/20.53 | | | Case 2:
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | (18) all_57_12 = e0 & op(e0, e3) = e0
% 140.72/20.53 | | | |
% 140.72/20.53 | | | | REF_CLOSE: (7), (10), (18) are inconsistent by sub-proof #958.
% 140.72/20.53 | | | |
% 140.72/20.53 | | | End of split
% 140.72/20.53 | | |
% 140.72/20.53 | | End of split
% 140.72/20.53 | |
% 140.72/20.53 | End of split
% 140.72/20.53 |
% 140.72/20.53 End of proof
% 140.72/20.53
% 140.72/20.53 Sub-proof #52 shows that the following formulas are inconsistent:
% 140.72/20.53 ----------------------------------------------------------------
% 140.72/20.53 (1) ~ (e2 = e1)
% 140.72/20.53 (2) op(e3, e3) = e2
% 140.72/20.53 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.72/20.53 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.72/20.53 (4) ~ (e3 = e0)
% 140.72/20.53 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.72/20.53 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.72/20.53 (6) ~ (e1 = e0)
% 140.72/20.53 (7) ~ (e2 = e0)
% 140.72/20.53 (8) ~ (e3 = e2)
% 140.72/20.53 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.53 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.53 (10) ~ (e3 = e1)
% 140.72/20.53 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 140.72/20.53 (12) all_57_12 = e2
% 140.72/20.53
% 140.72/20.53 Begin of proof
% 140.72/20.53 |
% 140.72/20.53 | BETA: splitting (11) gives:
% 140.72/20.53 |
% 140.72/20.53 | Case 1:
% 140.72/20.53 | |
% 140.72/20.53 | | (13) all_57_0 = e3 & op(e3, e3) = e3
% 140.72/20.53 | |
% 140.72/20.53 | | ALPHA: (13) implies:
% 140.72/20.54 | | (14) op(e3, e3) = e3
% 140.72/20.54 | |
% 140.72/20.54 | | REF_CLOSE: (2), (8), (9), (14) are inconsistent by sub-proof #450.
% 140.72/20.54 | |
% 140.72/20.54 | Case 2:
% 140.72/20.54 | |
% 140.72/20.54 | | (15) all_57_2 = e3 & op(e2, e3) = e3
% 140.72/20.54 | |
% 140.72/20.54 | | ALPHA: (15) implies:
% 140.72/20.54 | | (16) all_57_2 = e3
% 140.72/20.54 | |
% 140.72/20.54 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (12), (16) are
% 140.72/20.54 | | inconsistent by sub-proof #53.
% 140.72/20.54 | |
% 140.72/20.54 | End of split
% 140.72/20.54 |
% 140.72/20.54 End of proof
% 140.72/20.54
% 140.72/20.54 Sub-proof #53 shows that the following formulas are inconsistent:
% 140.72/20.54 ----------------------------------------------------------------
% 140.72/20.54 (1) ~ (e2 = e1)
% 140.72/20.54 (2) op(e3, e3) = e2
% 140.72/20.54 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.72/20.54 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.72/20.54 (4) ~ (e3 = e0)
% 140.72/20.54 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.72/20.54 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.72/20.54 (6) ~ (e1 = e0)
% 140.72/20.54 (7) ~ (e2 = e0)
% 140.72/20.54 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.54 (9) ~ (e3 = e1)
% 140.72/20.54 (10) all_57_2 = e3
% 140.72/20.54 (11) all_57_12 = e2
% 140.72/20.54
% 140.72/20.54 Begin of proof
% 140.72/20.54 |
% 140.72/20.54 | BETA: splitting (3) gives:
% 140.72/20.54 |
% 140.72/20.54 | Case 1:
% 140.72/20.54 | |
% 140.72/20.54 | | (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 140.72/20.54 | | e0)
% 140.72/20.54 | |
% 140.72/20.54 | | REF_CLOSE: (2), (4), (7), (8), (10), (12) are inconsistent by sub-proof
% 140.72/20.54 | | #132.
% 140.72/20.54 | |
% 140.72/20.54 | Case 2:
% 140.72/20.54 | |
% 140.72/20.54 | | (13) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 140.72/20.54 | | e0)
% 140.72/20.54 | |
% 140.72/20.54 | | BETA: splitting (13) gives:
% 140.72/20.54 | |
% 140.72/20.54 | | Case 1:
% 140.72/20.54 | | |
% 140.72/20.54 | | | (14) all_57_6 = e0 & op(e1, e3) = e0
% 140.72/20.54 | | |
% 140.72/20.54 | | | ALPHA: (14) implies:
% 140.72/20.54 | | | (15) all_57_6 = e0
% 140.72/20.54 | | |
% 140.72/20.54 | | | REF_CLOSE: (1), (2), (5), (6), (8), (9), (10), (11), (15) are inconsistent
% 140.72/20.54 | | | by sub-proof #281.
% 140.72/20.54 | | |
% 140.72/20.54 | | Case 2:
% 140.72/20.54 | | |
% 140.72/20.54 | | | (16) all_57_12 = e0 & op(e0, e3) = e0
% 140.72/20.54 | | |
% 140.72/20.54 | | | REF_CLOSE: (7), (11), (16) are inconsistent by sub-proof #958.
% 140.72/20.54 | | |
% 140.72/20.54 | | End of split
% 140.72/20.54 | |
% 140.72/20.54 | End of split
% 140.72/20.54 |
% 140.72/20.54 End of proof
% 140.72/20.54
% 140.72/20.54 Sub-proof #54 shows that the following formulas are inconsistent:
% 140.72/20.54 ----------------------------------------------------------------
% 140.72/20.54 (1) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 140.72/20.54 all_56_8 & $i(all_56_8))
% 140.72/20.54 (2) op(e1, e1) = e2
% 140.72/20.54 (3) ~ (e2 = e0)
% 140.72/20.54 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.54 (5) op(e1, e0) = e1
% 140.72/20.54
% 140.72/20.54 Begin of proof
% 140.72/20.54 |
% 140.72/20.54 | BETA: splitting (1) gives:
% 140.72/20.54 |
% 140.72/20.54 | Case 1:
% 140.72/20.54 | |
% 140.72/20.54 | | (6) all_56_13 = e0 & op(e1, e1) = e0
% 140.72/20.54 | |
% 140.72/20.54 | | ALPHA: (6) implies:
% 140.72/20.54 | | (7) op(e1, e1) = e0
% 140.72/20.54 | |
% 140.72/20.54 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #61.
% 140.72/20.54 | |
% 140.72/20.54 | Case 2:
% 140.72/20.54 | |
% 140.72/20.54 | | (8) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8)
% 140.72/20.54 | |
% 140.72/20.54 | | ALPHA: (8) implies:
% 140.72/20.54 | | (9) ~ (all_56_8 = e1)
% 140.72/20.54 | | (10) op(e1, e0) = all_56_8
% 140.72/20.54 | |
% 140.72/20.54 | | REF_CLOSE: (4), (5), (9), (10) are inconsistent by sub-proof #294.
% 140.72/20.54 | |
% 140.72/20.54 | End of split
% 140.72/20.54 |
% 140.72/20.54 End of proof
% 140.72/20.54
% 140.72/20.54 Sub-proof #55 shows that the following formulas are inconsistent:
% 140.72/20.54 ----------------------------------------------------------------
% 140.72/20.54 (1) ~ (all_10_2 = e2)
% 140.72/20.54 (2) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 140.72/20.54 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 140.72/20.54 (3) ~ (all_52_13 = e0)
% 140.72/20.54 (4) op(e1, e2) = all_52_6
% 140.72/20.54 (5) ~ (all_52_6 = e1)
% 140.72/20.54 (6) ~ (e2 = e1)
% 140.72/20.54 (7) op(e2, e3) = e2
% 140.72/20.54 (8) op(e3, e3) = e3
% 140.72/20.54 (9) all_54_7 = all_52_13
% 140.72/20.54 (10) ~ (all_52_7 = e0)
% 140.72/20.54 (11) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 140.72/20.54 all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1,
% 140.72/20.54 e2) = all_32_1 & $i(all_32_1))
% 140.72/20.54 (12) op(e0, e1) = e3
% 140.72/20.54 (13) op(e0, e3) = all_52_3
% 140.72/20.54 (14) ~ (all_10_2 = e1)
% 140.72/20.54 (15) ~ (all_14_2 = e1)
% 140.72/20.54 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 140.72/20.54 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 140.72/20.54 (17) ~ (e3 = e0)
% 140.72/20.54 (18) ~ (all_52_4 = e3)
% 140.72/20.54 (19) ~ (all_52_13 = all_52_14)
% 140.72/20.54 (20) op(e0, e0) = all_10_2
% 140.72/20.54 (21) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 140.72/20.54 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 140.72/20.54 (22) ~ (e1 = e0)
% 140.72/20.54 (23) ~ (all_52_11 = e0)
% 140.72/20.54 (24) op(e1, e1) = e2
% 140.72/20.54 (25) op(e3, e2) = all_52_4
% 140.72/20.54 (26) ~ (e2 = e0)
% 140.72/20.54 (27) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.72/20.54 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.72/20.54 & $i(all_4_1))
% 140.72/20.54 (28) ~ (e3 = e2)
% 140.72/20.54 (29) op(e0, e1) = all_52_11
% 140.72/20.54 (30) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 140.72/20.54 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 140.72/20.54 (31) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.72/20.54 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.72/20.54 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.72/20.54 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.72/20.54 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.72/20.54 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.72/20.54 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.72/20.54 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.72/20.54 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.72/20.54 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.72/20.54 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.72/20.54 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 140.72/20.54 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 140.72/20.54 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.72/20.54 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.72/20.54 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 140.72/20.54 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.72/20.54 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 140.72/20.54 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.72/20.54 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 140.72/20.54 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12))))
% 140.72/20.54 (32) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.72/20.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.72/20.54 (33) ~ (all_52_3 = e0)
% 140.72/20.54 (34) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 140.72/20.54 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 140.72/20.54 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 140.72/20.54 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 140.72/20.54 (35) all_57_4 = e1
% 140.72/20.54 (36) ~ (all_52_13 = e2)
% 140.72/20.54 (37) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 140.72/20.54 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 140.72/20.54 (38) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 140.72/20.54 (39) ~ (e3 = e1)
% 140.72/20.54 (40) op(e0, e2) = all_52_7
% 140.93/20.54 (41) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.93/20.54 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.93/20.54 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.93/20.54 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.93/20.54 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.93/20.54 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.93/20.54 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.93/20.54 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.93/20.54 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.93/20.54 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.93/20.54 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.93/20.54 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.93/20.54 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.93/20.54 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.93/20.54 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.93/20.54 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.93/20.54 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.93/20.54 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.93/20.54 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.93/20.54 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.54 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.93/20.54 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.54 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.93/20.54 $i(all_56_14))))
% 140.93/20.54 (42) op(e2, e2) = all_6_2
% 140.93/20.54 (43) op(e3, e3) = all_14_2
% 140.93/20.54 (44) ~ (all_52_13 = e1)
% 140.93/20.54 (45) ~ (all_14_2 = e0)
% 140.93/20.54 (46) ~ (all_6_2 = e0)
% 140.93/20.54 (47) op(e1, e0) = all_52_14
% 140.93/20.54
% 140.93/20.54 Begin of proof
% 140.93/20.54 |
% 140.93/20.54 | BETA: splitting (31) gives:
% 140.93/20.54 |
% 140.93/20.54 | Case 1:
% 140.93/20.54 | |
% 140.93/20.54 | | (48) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 140.93/20.54 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.93/20.54 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.93/20.54 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.93/20.54 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.93/20.54 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.93/20.54 | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.93/20.54 | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.93/20.54 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.93/20.54 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.93/20.54 | | e3) = all_56_10 & $i(all_56_10)))
% 140.93/20.54 | |
% 140.93/20.54 | | ALPHA: (48) implies:
% 140.93/20.54 | | (49) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 140.93/20.54 | | e3) = all_56_3 & $i(all_56_3))
% 140.93/20.54 | |
% 140.93/20.54 | | BETA: splitting (49) gives:
% 140.93/20.54 | |
% 140.93/20.54 | | Case 1:
% 140.93/20.54 | | |
% 140.93/20.54 | | | (50) all_56_11 = e3 & op(e2, e2) = e3
% 140.93/20.54 | | |
% 140.93/20.54 | | | ALPHA: (50) implies:
% 140.93/20.54 | | | (51) op(e2, e2) = e3
% 140.93/20.54 | | |
% 140.93/20.54 | | | REF_CLOSE: (1), (8), (14), (20), (24), (28), (32), (39), (41), (43), (45),
% 140.93/20.54 | | | (51) are inconsistent by sub-proof #68.
% 140.93/20.54 | | |
% 140.93/20.54 | | Case 2:
% 140.93/20.54 | | |
% 140.93/20.54 | | | (52) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)
% 140.93/20.54 | | |
% 140.93/20.54 | | | ALPHA: (52) implies:
% 140.93/20.54 | | | (53) ~ (all_56_3 = e2)
% 140.93/20.54 | | | (54) op(e2, e3) = all_56_3
% 140.93/20.54 | | |
% 140.93/20.54 | | | REF_CLOSE: (7), (32), (53), (54) are inconsistent by sub-proof #979.
% 140.93/20.54 | | |
% 140.93/20.54 | | End of split
% 140.93/20.54 | |
% 140.93/20.54 | Case 2:
% 140.93/20.54 | |
% 140.93/20.54 | | (55) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 140.93/20.54 | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.93/20.54 | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 140.93/20.54 | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.93/20.54 | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 140.93/20.54 | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 140.93/20.54 | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.93/20.54 | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 140.93/20.54 | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 140.93/20.54 | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.93/20.54 | | e2) = all_56_12 & $i(all_56_12)))
% 140.93/20.54 | |
% 140.93/20.54 | | ALPHA: (55) implies:
% 140.93/20.54 | | (56) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 140.93/20.54 | | e2) = all_56_12 & $i(all_56_12))
% 140.93/20.54 | | (57) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.93/20.54 | | e0) = all_56_15 & $i(all_56_15))
% 140.93/20.54 | | (58) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2)
% 140.93/20.54 | | = all_56_0 & $i(all_56_0))
% 140.93/20.54 | | (59) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 140.93/20.54 | | e1) = all_56_13 & $i(all_56_13))
% 140.93/20.54 | | (60) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3)
% 140.93/20.54 | | = all_56_9 & $i(all_56_9))
% 140.93/20.54 | |
% 140.93/20.54 | | BETA: splitting (58) gives:
% 140.93/20.54 | |
% 140.93/20.54 | | Case 1:
% 140.93/20.54 | | |
% 140.93/20.54 | | | (61) all_56_9 = e2 & op(e3, e3) = e2
% 140.93/20.54 | | |
% 140.93/20.54 | | | ALPHA: (61) implies:
% 140.93/20.54 | | | (62) all_56_9 = e2
% 140.93/20.54 | | |
% 140.93/20.54 | | | REF_CLOSE: (18), (25), (32), (60), (62) are inconsistent by sub-proof
% 140.93/20.54 | | | #345.
% 140.93/20.54 | | |
% 140.93/20.54 | | Case 2:
% 140.93/20.54 | | |
% 140.93/20.54 | | | (63) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0)
% 140.93/20.54 | | |
% 140.93/20.54 | | | ALPHA: (63) implies:
% 140.93/20.54 | | | (64) ~ (all_56_0 = e3)
% 140.93/20.54 | | | (65) op(e3, e2) = all_56_0
% 140.93/20.54 | | |
% 140.93/20.54 | | | BETA: splitting (21) gives:
% 140.93/20.54 | | |
% 140.93/20.54 | | | Case 1:
% 140.93/20.54 | | | |
% 140.93/20.54 | | | | (66) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 140.93/20.54 | | | | = e0)
% 140.93/20.54 | | | |
% 140.93/20.54 | | | | BETA: splitting (66) gives:
% 140.93/20.54 | | | |
% 140.93/20.54 | | | | Case 1:
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | (67) all_57_1 = e0 & op(e3, e2) = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | ALPHA: (67) implies:
% 140.93/20.54 | | | | | (68) all_57_1 = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | BETA: splitting (38) gives:
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | Case 1:
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | (69) all_54_7 = e3
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | COMBINE_EQS: (9), (69) imply:
% 140.93/20.54 | | | | | | (70) all_52_13 = e3
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | SIMP: (70) implies:
% 140.93/20.54 | | | | | | (71) all_52_13 = e3
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | REDUCE: (19), (71) imply:
% 140.93/20.54 | | | | | | (72) ~ (all_52_14 = e3)
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | SIMP: (72) implies:
% 140.93/20.54 | | | | | | (73) ~ (all_52_14 = e3)
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | BETA: splitting (59) gives:
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | Case 1:
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | (74) all_56_7 = e1 & op(e1, e2) = e1
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | ALPHA: (74) implies:
% 140.93/20.54 | | | | | | | (75) op(e1, e2) = e1
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | REF_CLOSE: (4), (5), (32), (75) are inconsistent by sub-proof
% 140.93/20.54 | | | | | | | #341.
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | Case 2:
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | (76) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.93/20.54 | | | | | | | $i(all_56_13)
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | ALPHA: (76) implies:
% 140.93/20.54 | | | | | | | (77) ~ (all_56_13 = e2)
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | BETA: splitting (60) gives:
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | (78) all_56_0 = e3 & op(e3, e2) = e3
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | ALPHA: (78) implies:
% 140.93/20.54 | | | | | | | | (79) op(e3, e2) = e3
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | REF_CLOSE: (32), (64), (65), (79) are inconsistent by sub-proof
% 140.93/20.54 | | | | | | | | #670.
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | (80) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 140.93/20.54 | | | | | | | | $i(all_56_9)
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | ALPHA: (80) implies:
% 140.93/20.54 | | | | | | | | (81) ~ (all_56_9 = e2)
% 140.93/20.54 | | | | | | | | (82) op(e3, e3) = all_56_9
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | BETA: splitting (30) gives:
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | | (83) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 140.93/20.54 | | | | | | | | | op(e2, e0) = e3)
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | | BETA: splitting (83) gives:
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | (84) all_57_9 = e3 & op(e3, e0) = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | ALPHA: (84) implies:
% 140.93/20.54 | | | | | | | | | | (85) all_57_9 = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | REF_CLOSE: (2), (6), (26), (28), (32), (35), (68), (81),
% 140.93/20.54 | | | | | | | | | | (82), (85) are inconsistent by sub-proof #352.
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | (86) all_57_10 = e3 & op(e2, e0) = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | ALPHA: (86) implies:
% 140.93/20.54 | | | | | | | | | | (87) all_57_10 = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | BETA: splitting (41) gives:
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | (88) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 140.93/20.54 | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 140.93/20.54 | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.93/20.54 | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 140.93/20.54 | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 140.93/20.54 | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.93/20.54 | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.93/20.54 | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 140.93/20.54 | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 140.93/20.54 | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 140.93/20.54 | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 140.93/20.54 | | | | | | | | | | | $i(all_56_6))
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | REF_CLOSE: (18), (24), (25), (28), (32), (60), (88) are
% 140.93/20.54 | | | | | | | | | | | inconsistent by sub-proof #70.
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | (89) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.93/20.54 | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.93/20.54 | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.93/20.54 | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.93/20.54 | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.93/20.54 | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.93/20.54 | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.93/20.54 | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.93/20.54 | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 140.93/20.54 | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 140.93/20.54 | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 140.93/20.54 | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.93/20.54 | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 140.93/20.54 | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.93/20.54 | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.93/20.54 | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 140.93/20.54 | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 140.93/20.54 | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 140.93/20.54 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.54 | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.93/20.54 | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.93/20.54 | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.54 | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.93/20.54 | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | BETA: splitting (89) gives:
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | (90) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.93/20.54 | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 140.93/20.54 | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 140.93/20.54 | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 140.93/20.54 | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 140.93/20.54 | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | BETA: splitting (90) gives:
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | (91) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 140.93/20.54 | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 140.93/20.54 | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | ALPHA: (91) implies:
% 140.93/20.54 | | | | | | | | | | | | | (92) op(e0, e0) = e3
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | REF_CLOSE: (6), (16), (17), (22), (26), (28), (32), (34),
% 140.93/20.54 | | | | | | | | | | | | | (37), (39), (87), (92) are inconsistent by
% 140.93/20.54 | | | | | | | | | | | | | sub-proof #650.
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | (93) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 140.93/20.54 | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 140.93/20.54 | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | ALPHA: (93) implies:
% 140.93/20.54 | | | | | | | | | | | | | (94) all_56_13 = e2
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | REDUCE: (77), (94) imply:
% 140.93/20.54 | | | | | | | | | | | | | (95) $false
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | | CLOSE: (95) is inconsistent.
% 140.93/20.54 | | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | End of split
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | (96) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 140.93/20.54 | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 140.93/20.54 | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.93/20.54 | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 140.93/20.54 | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 140.93/20.54 | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 140.93/20.54 | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.93/20.54 | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.93/20.54 | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 140.93/20.54 | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 140.93/20.54 | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 140.93/20.54 | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 140.93/20.54 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.54 | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.93/20.54 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 140.93/20.54 | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.54 | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 140.93/20.54 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | | REF_CLOSE: (10), (14), (20), (32), (40), (42), (43), (45),
% 140.93/20.54 | | | | | | | | | | | | (46), (57), (77), (96) are inconsistent by
% 140.93/20.54 | | | | | | | | | | | | sub-proof #64.
% 140.93/20.54 | | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | | End of split
% 140.93/20.54 | | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | End of split
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | End of split
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | | (97) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 140.93/20.54 | | | | | | | | | op(e0, e0) = e3)
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | | BETA: splitting (97) gives:
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | | Case 1:
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | (98) all_57_11 = e3 & op(e1, e0) = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | REF_CLOSE: (32), (47), (73), (98) are inconsistent by
% 140.93/20.54 | | | | | | | | | | sub-proof #160.
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | Case 2:
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | (99) all_57_15 = e3 & op(e0, e0) = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | ALPHA: (99) implies:
% 140.93/20.54 | | | | | | | | | | (100) op(e0, e0) = e3
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | | REF_CLOSE: (13), (17), (23), (28), (29), (32), (33), (34),
% 140.93/20.54 | | | | | | | | | | (56), (100) are inconsistent by sub-proof #735.
% 140.93/20.54 | | | | | | | | | |
% 140.93/20.54 | | | | | | | | | End of split
% 140.93/20.54 | | | | | | | | |
% 140.93/20.54 | | | | | | | | End of split
% 140.93/20.54 | | | | | | | |
% 140.93/20.54 | | | | | | | End of split
% 140.93/20.54 | | | | | | |
% 140.93/20.54 | | | | | | End of split
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | Case 2:
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | (101) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | | REF_CLOSE: (3), (9), (36), (44), (101) are inconsistent by sub-proof
% 140.93/20.54 | | | | | | #59.
% 140.93/20.54 | | | | | |
% 140.93/20.54 | | | | | End of split
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | Case 2:
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | (102) all_57_3 = e0 & op(e2, e2) = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | ALPHA: (102) implies:
% 140.93/20.54 | | | | | (103) op(e2, e2) = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | REF_CLOSE: (1), (14), (15), (17), (20), (22), (32), (41), (43), (45),
% 140.93/20.54 | | | | | (103) are inconsistent by sub-proof #235.
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | End of split
% 140.93/20.54 | | | |
% 140.93/20.54 | | | Case 2:
% 140.93/20.54 | | | |
% 140.93/20.54 | | | | (104) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 140.93/20.54 | | | | e2) = e0)
% 140.93/20.54 | | | |
% 140.93/20.54 | | | | BETA: splitting (104) gives:
% 140.93/20.54 | | | |
% 140.93/20.54 | | | | Case 1:
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | (105) all_57_7 = e0 & op(e1, e2) = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | REF_CLOSE: (11), (12), (27), (32), (105) are inconsistent by sub-proof
% 140.93/20.54 | | | | | #56.
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | Case 2:
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | (106) all_57_13 = e0 & op(e0, e2) = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | ALPHA: (106) implies:
% 140.93/20.54 | | | | | (107) op(e0, e2) = e0
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | | REF_CLOSE: (10), (32), (40), (107) are inconsistent by sub-proof #977.
% 140.93/20.54 | | | | |
% 140.93/20.54 | | | | End of split
% 140.93/20.54 | | | |
% 140.93/20.54 | | | End of split
% 140.93/20.54 | | |
% 140.93/20.54 | | End of split
% 140.93/20.54 | |
% 140.93/20.54 | End of split
% 140.93/20.54 |
% 140.93/20.54 End of proof
% 140.93/20.54
% 140.93/20.54 Sub-proof #56 shows that the following formulas are inconsistent:
% 140.93/20.54 ----------------------------------------------------------------
% 140.93/20.54 (1) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) = all_32_1
% 140.93/20.54 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2) =
% 140.93/20.54 all_32_1 & $i(all_32_1))
% 140.93/20.54 (2) op(e0, e1) = e3
% 140.93/20.54 (3) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.93/20.54 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.93/20.54 & $i(all_4_1))
% 140.93/20.54 (4) all_57_7 = e0 & op(e1, e2) = e0
% 140.93/20.54 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.54
% 140.93/20.54 Begin of proof
% 140.93/20.54 |
% 140.93/20.54 | ALPHA: (4) implies:
% 140.93/20.54 | (6) op(e1, e2) = e0
% 140.93/20.54 |
% 140.93/20.54 | BETA: splitting (1) gives:
% 140.93/20.54 |
% 140.93/20.54 | Case 1:
% 140.93/20.54 | |
% 140.93/20.54 | | (7) ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 140.93/20.54 | | all_32_1 & $i(all_32_0) & $i(all_32_1)
% 140.93/20.54 | |
% 140.93/20.54 | | ALPHA: (7) implies:
% 140.93/20.54 | | (8) op(e1, e2) = all_32_1
% 140.93/20.54 | |
% 140.93/20.54 | | REF_CLOSE: (2), (3), (5), (6), (8) are inconsistent by sub-proof #57.
% 140.93/20.54 | |
% 140.93/20.54 | Case 2:
% 140.93/20.54 | |
% 140.93/20.54 | | (9) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1)
% 140.93/20.54 | |
% 140.93/20.54 | | ALPHA: (9) implies:
% 140.93/20.54 | | (10) op(e1, e2) = all_32_1
% 140.93/20.54 | |
% 140.93/20.54 | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #57.
% 140.93/20.54 | |
% 140.93/20.54 | End of split
% 140.93/20.54 |
% 140.93/20.54 End of proof
% 140.93/20.54
% 140.93/20.54 Sub-proof #57 shows that the following formulas are inconsistent:
% 140.93/20.54 ----------------------------------------------------------------
% 140.93/20.54 (1) op(e0, e1) = e3
% 140.93/20.54 (2) op(e1, e2) = e0
% 140.93/20.54 (3) op(e1, e2) = all_32_1
% 140.93/20.54 (4) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.93/20.54 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.93/20.54 & $i(all_4_1))
% 140.93/20.54 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.54 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.54
% 140.93/20.54 Begin of proof
% 140.93/20.54 |
% 140.93/20.54 | BETA: splitting (4) gives:
% 140.93/20.54 |
% 140.93/20.54 | Case 1:
% 140.93/20.54 | |
% 140.93/20.54 | | (6) ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1
% 140.93/20.54 | | & $i(all_4_0) & $i(all_4_1)
% 140.93/20.54 | |
% 140.93/20.54 | | ALPHA: (6) implies:
% 140.93/20.55 | | (7) ~ (all_4_0 = e3)
% 140.93/20.55 | | (8) op(e1, e2) = all_4_1
% 140.93/20.55 | | (9) op(all_4_1, e1) = all_4_0
% 140.93/20.55 | |
% 140.93/20.55 | | GROUND_INST: instantiating (5) with e0, all_32_1, e2, e1, simplifying with
% 140.93/20.55 | | (2), (3) gives:
% 140.93/20.55 | | (10) all_32_1 = e0
% 140.93/20.55 | |
% 140.93/20.55 | | GROUND_INST: instantiating (5) with all_4_1, all_32_1, e2, e1, simplifying
% 140.93/20.55 | | with (3), (8) gives:
% 140.93/20.55 | | (11) all_32_1 = all_4_1
% 140.93/20.55 | |
% 140.93/20.55 | | COMBINE_EQS: (10), (11) imply:
% 140.93/20.55 | | (12) all_4_1 = e0
% 140.93/20.55 | |
% 140.93/20.55 | | REDUCE: (9), (12) imply:
% 140.93/20.55 | | (13) op(e0, e1) = all_4_0
% 140.93/20.55 | |
% 140.93/20.55 | | GROUND_INST: instantiating (5) with e3, all_4_0, e1, e0, simplifying with
% 140.93/20.55 | | (1), (13) gives:
% 140.93/20.55 | | (14) all_4_0 = e3
% 140.93/20.55 | |
% 140.93/20.55 | | REDUCE: (7), (14) imply:
% 140.93/20.55 | | (15) $false
% 140.93/20.55 | |
% 140.93/20.55 | | CLOSE: (15) is inconsistent.
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (16) ~ (all_4_1 = e0) & op(e1, e2) = all_4_1 & $i(all_4_1)
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (16) implies:
% 140.93/20.55 | | (17) ~ (all_4_1 = e0)
% 140.93/20.55 | | (18) op(e1, e2) = all_4_1
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (2), (3), (5), (17), (18) are inconsistent by sub-proof #58.
% 140.93/20.55 | |
% 140.93/20.55 | End of split
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #58 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) op(e1, e2) = all_4_1
% 140.93/20.55 (2) op(e1, e2) = e0
% 140.93/20.55 (3) ~ (all_4_1 = e0)
% 140.93/20.55 (4) op(e1, e2) = all_32_1
% 140.93/20.55 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | GROUND_INST: instantiating (5) with e0, all_32_1, e2, e1, simplifying with
% 140.93/20.55 | (2), (4) gives:
% 140.93/20.55 | (6) all_32_1 = e0
% 140.93/20.55 |
% 140.93/20.55 | GROUND_INST: instantiating (5) with all_4_1, all_32_1, e2, e1, simplifying
% 140.93/20.55 | with (1), (4) gives:
% 140.93/20.55 | (7) all_32_1 = all_4_1
% 140.93/20.55 |
% 140.93/20.55 | COMBINE_EQS: (6), (7) imply:
% 140.93/20.55 | (8) all_4_1 = e0
% 140.93/20.55 |
% 140.93/20.55 | REDUCE: (3), (8) imply:
% 140.93/20.55 | (9) $false
% 140.93/20.55 |
% 140.93/20.55 | CLOSE: (9) is inconsistent.
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #59 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) ~ (all_52_13 = e0)
% 140.93/20.55 (2) all_54_7 = all_52_13
% 140.93/20.55 (3) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 140.93/20.55 (4) ~ (all_52_13 = e2)
% 140.93/20.55 (5) ~ (all_52_13 = e1)
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | BETA: splitting (3) gives:
% 140.93/20.55 |
% 140.93/20.55 | Case 1:
% 140.93/20.55 | |
% 140.93/20.55 | | (6) all_54_7 = e2
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #1006.
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (7) all_54_7 = e1 | all_54_7 = e0
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #101.
% 140.93/20.55 | |
% 140.93/20.55 | End of split
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #60 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) ~ (all_52_11 = e0)
% 140.93/20.55 (2) op(e1, e1) = e2
% 140.93/20.55 (3) ~ (e2 = e0)
% 140.93/20.55 (4) op(e0, e1) = all_52_11
% 140.93/20.55 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55 (6) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | BETA: splitting (6) gives:
% 140.93/20.55 |
% 140.93/20.55 | Case 1:
% 140.93/20.55 | |
% 140.93/20.55 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (7) implies:
% 140.93/20.55 | | (8) op(e1, e1) = e0
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #61.
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (9) all_57_14 = e0 & op(e0, e1) = e0
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (9) implies:
% 140.93/20.55 | | (10) op(e0, e1) = e0
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #886.
% 140.93/20.55 | |
% 140.93/20.55 | End of split
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #61 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55 (2) op(e1, e1) = e2
% 140.93/20.55 (3) op(e1, e1) = e0
% 140.93/20.55 (4) ~ (e2 = e0)
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | GROUND_INST: instantiating (1) with e2, e0, e1, e1, simplifying with (2), (3)
% 140.93/20.55 | gives:
% 140.93/20.55 | (5) e2 = e0
% 140.93/20.55 |
% 140.93/20.55 | REDUCE: (4), (5) imply:
% 140.93/20.55 | (6) $false
% 140.93/20.55 |
% 140.93/20.55 | CLOSE: (6) is inconsistent.
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #62 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) ~ (e2 = e1)
% 140.93/20.55 (2) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 140.93/20.55 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 140.93/20.55 (3) ~ (e3 = e0)
% 140.93/20.55 (4) ~ (e1 = e0)
% 140.93/20.55 (5) ~ (e2 = e0)
% 140.93/20.55 (6) op(e0, e0) = e2
% 140.93/20.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55 (8) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 140.93/20.55 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 140.93/20.55 e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 140.93/20.55 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 140.93/20.55 (9) ~ (e3 = e1)
% 140.93/20.55 (10) all_57_13 = e3
% 140.93/20.55 (11) op(e0, e2) = e3
% 140.93/20.55 (12) all_57_12 = e2
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | BETA: splitting (8) gives:
% 140.93/20.55 |
% 140.93/20.55 | Case 1:
% 140.93/20.55 | |
% 140.93/20.55 | | (13) all_57_15 = e0 & op(e0, e0) = e0
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (13) implies:
% 140.93/20.55 | | (14) op(e0, e0) = e0
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (5), (6), (7), (14) are inconsistent by sub-proof #1094.
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (15) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 140.93/20.55 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 140.93/20.55 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 140.93/20.55 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (15) implies:
% 140.93/20.55 | | (16) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 140.93/20.55 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 140.93/20.55 | |
% 140.93/20.55 | | BETA: splitting (16) gives:
% 140.93/20.55 | |
% 140.93/20.55 | | Case 1:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (17) all_57_12 = e0 & op(e0, e3) = e0
% 140.93/20.55 | | |
% 140.93/20.55 | | | REF_CLOSE: (5), (12), (17) are inconsistent by sub-proof #958.
% 140.93/20.55 | | |
% 140.93/20.55 | | Case 2:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (18) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 140.93/20.55 | | | = e0)
% 140.93/20.55 | | |
% 140.93/20.55 | | | BETA: splitting (18) gives:
% 140.93/20.55 | | |
% 140.93/20.55 | | | Case 1:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | (19) all_57_13 = e0 & op(e0, e2) = e0
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | ALPHA: (19) implies:
% 140.93/20.55 | | | | (20) op(e0, e2) = e0
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | REF_CLOSE: (3), (7), (11), (20) are inconsistent by sub-proof #243.
% 140.93/20.55 | | | |
% 140.93/20.55 | | | Case 2:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | (21) all_57_14 = e0 & op(e0, e1) = e0
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | ALPHA: (21) implies:
% 140.93/20.55 | | | | (22) all_57_14 = e0
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | BETA: splitting (2) gives:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | Case 1:
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | (23) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 140.93/20.55 | | | | | e2) = e1)
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | BETA: splitting (23) gives:
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | Case 1:
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | (24) all_57_12 = e1 & op(e0, e3) = e1
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | ALPHA: (24) implies:
% 140.93/20.55 | | | | | | (25) all_57_12 = e1
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | REF_CLOSE: (1), (12), (25) are inconsistent by sub-proof #970.
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | Case 2:
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | (26) all_57_13 = e1 & op(e0, e2) = e1
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | ALPHA: (26) implies:
% 140.93/20.55 | | | | | | (27) all_57_13 = e1
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | REF_CLOSE: (9), (10), (27) are inconsistent by sub-proof #1001.
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | End of split
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | Case 2:
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | (28) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 140.93/20.55 | | | | | e0) = e1)
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | REF_CLOSE: (1), (4), (6), (7), (22), (28) are inconsistent by
% 140.93/20.55 | | | | | sub-proof #470.
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | End of split
% 140.93/20.55 | | | |
% 140.93/20.55 | | | End of split
% 140.93/20.55 | | |
% 140.93/20.55 | | End of split
% 140.93/20.55 | |
% 140.93/20.55 | End of split
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #63 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 140.93/20.55 all_56_11 & $i(all_56_11))
% 140.93/20.55 (2) op(e2, e2) = e1
% 140.93/20.55 (3) ~ (all_52_9 = e2)
% 140.93/20.55 (4) ~ (all_52_11 = e0)
% 140.93/20.55 (5) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 140.93/20.55 all_56_14 & $i(all_56_14))
% 140.93/20.55 (6) op(e0, e1) = all_52_11
% 140.93/20.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55 (8) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 140.93/20.55 all_56_4 & $i(all_56_4))
% 140.93/20.55 (9) op(e2, e1) = all_52_9
% 140.93/20.55 (10) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 140.93/20.55 all_56_15 & $i(all_56_15))
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | BETA: splitting (1) gives:
% 140.93/20.55 |
% 140.93/20.55 | Case 1:
% 140.93/20.55 | |
% 140.93/20.55 | | (11) all_56_4 = e2 & op(e2, e1) = e2
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (11) implies:
% 140.93/20.55 | | (12) op(e2, e1) = e2
% 140.93/20.55 | |
% 140.93/20.55 | | REF_CLOSE: (3), (7), (9), (12) are inconsistent by sub-proof #890.
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (13) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (13) implies:
% 140.93/20.55 | | (14) op(e2, e2) = all_56_11
% 140.93/20.55 | |
% 140.93/20.55 | | BETA: splitting (8) gives:
% 140.93/20.55 | |
% 140.93/20.55 | | Case 1:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (15) all_56_11 = e1 & op(e2, e2) = e1
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (15) implies:
% 140.93/20.55 | | | (16) all_56_11 = e1
% 140.93/20.55 | | |
% 140.93/20.55 | | | REF_CLOSE: (1), (3), (7), (9), (16) are inconsistent by sub-proof #91.
% 140.93/20.55 | | |
% 140.93/20.55 | | Case 2:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (17) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (17) implies:
% 140.93/20.55 | | | (18) ~ (all_56_4 = e2)
% 140.93/20.55 | | |
% 140.93/20.55 | | | BETA: splitting (5) gives:
% 140.93/20.55 | | |
% 140.93/20.55 | | | Case 1:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | (19) all_56_15 = e1 & op(e0, e0) = e1
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | ALPHA: (19) implies:
% 140.93/20.55 | | | | (20) all_56_15 = e1
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | REF_CLOSE: (4), (6), (7), (10), (20) are inconsistent by sub-proof #432.
% 140.93/20.55 | | | |
% 140.93/20.55 | | | Case 2:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | (21) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | ALPHA: (21) implies:
% 140.93/20.55 | | | | (22) ~ (all_56_14 = e0)
% 140.93/20.55 | | | | (23) op(e0, e1) = all_56_14
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | REF_CLOSE: (1), (2), (7), (10), (14), (18), (22), (23) are inconsistent
% 140.93/20.55 | | | | by sub-proof #534.
% 140.93/20.55 | | | |
% 140.93/20.55 | | | End of split
% 140.93/20.55 | | |
% 140.93/20.55 | | End of split
% 140.93/20.55 | |
% 140.93/20.55 | End of split
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #64 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) ~ (all_52_7 = e0)
% 140.93/20.55 (2) ~ (all_10_2 = e1)
% 140.93/20.55 (3) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 140.93/20.55 all_56_15 & $i(all_56_15))
% 140.93/20.55 (4) op(e0, e0) = all_10_2
% 140.93/20.55 (5) ~ (all_56_13 = e2)
% 140.93/20.55 (6) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 140.93/20.55 op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 140.93/20.55 e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 140.93/20.55 = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 140.93/20.55 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 140.93/20.55 e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.93/20.55 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 140.93/20.55 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.55 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.93/20.55 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.55 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.93/20.55 $i(all_56_14))))
% 140.93/20.55 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55 (8) op(e0, e2) = all_52_7
% 140.93/20.55 (9) op(e2, e2) = all_6_2
% 140.93/20.55 (10) op(e3, e3) = all_14_2
% 140.93/20.55 (11) ~ (all_14_2 = e0)
% 140.93/20.55 (12) ~ (all_6_2 = e0)
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | BETA: splitting (6) gives:
% 140.93/20.55 |
% 140.93/20.55 | Case 1:
% 140.93/20.55 | |
% 140.93/20.55 | | (13) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 140.93/20.55 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 140.93/20.55 | |
% 140.93/20.55 | | ALPHA: (13) implies:
% 140.93/20.55 | | (14) all_56_13 = e2
% 140.93/20.55 | |
% 140.93/20.55 | | REDUCE: (5), (14) imply:
% 140.93/20.55 | | (15) $false
% 140.93/20.55 | |
% 140.93/20.55 | | CLOSE: (15) is inconsistent.
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (16) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.93/20.55 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.93/20.55 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.93/20.55 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.93/20.55 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.93/20.55 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.93/20.55 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.55 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.93/20.55 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.93/20.55 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.93/20.55 | | all_56_14 & $i(all_56_14))))
% 140.93/20.55 | |
% 140.93/20.55 | | BETA: splitting (16) gives:
% 140.93/20.55 | |
% 140.93/20.55 | | Case 1:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (17) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 140.93/20.55 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (17) implies:
% 140.93/20.55 | | | (18) all_56_15 = e2
% 140.93/20.55 | | |
% 140.93/20.55 | | | REF_CLOSE: (1), (3), (7), (8), (18) are inconsistent by sub-proof #976.
% 140.93/20.55 | | |
% 140.93/20.55 | | Case 2:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (19) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.93/20.55 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.93/20.55 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.93/20.55 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.93/20.55 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.55 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.93/20.55 | | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.93/20.55 | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.93/20.55 | | | all_56_14 & $i(all_56_14)))
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (19) implies:
% 140.93/20.55 | | | (20) op(e0, e0) = all_56_15
% 140.93/20.55 | | | (21) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 140.93/20.55 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0
% 140.93/20.55 | | | & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.93/20.55 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.55 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.93/20.55 | | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 140.93/20.55 | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.93/20.55 | | | all_56_14 & $i(all_56_14))
% 140.93/20.55 | | |
% 140.93/20.55 | | | REF_CLOSE: (2), (4), (7), (9), (10), (11), (12), (20), (21) are
% 140.93/20.55 | | | inconsistent by sub-proof #1120.
% 140.93/20.55 | | |
% 140.93/20.55 | | End of split
% 140.93/20.55 | |
% 140.93/20.55 | End of split
% 140.93/20.55 |
% 140.93/20.55 End of proof
% 140.93/20.55
% 140.93/20.55 Sub-proof #65 shows that the following formulas are inconsistent:
% 140.93/20.55 ----------------------------------------------------------------
% 140.93/20.55 (1) ~ (all_10_2 = e2)
% 140.93/20.55 (2) ~ (all_52_4 = all_52_7)
% 140.93/20.55 (3) ~ (all_52_8 = all_52_11)
% 140.93/20.55 (4) ~ (all_52_8 = all_52_9)
% 140.93/20.55 (5) ~ (all_52_7 = e1)
% 140.93/20.55 (6) op(e1, e2) = all_52_6
% 140.93/20.55 (7) op(e2, e1) = e3
% 140.93/20.55 (8) ~ (e2 = e1)
% 140.93/20.55 (9) op(e3, e3) = e3
% 140.93/20.55 (10) op(e0, e0) = e3
% 140.93/20.55 (11) ~ (all_52_4 = e1)
% 140.93/20.55 (12) all_54_13 = all_52_7
% 140.93/20.55 (13) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 140.93/20.55 all_32_1 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1,
% 140.93/20.55 e2) = all_32_1 & $i(all_32_1))
% 140.93/20.55 (14) ~ (all_10_2 = e1)
% 140.93/20.55 (15) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 140.93/20.55 (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 140.93/20.55 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 140.93/20.55 e1)
% 140.93/20.55 (17) ~ (all_52_4 = all_52_6)
% 140.93/20.55 (18) ~ (all_52_11 = e2)
% 140.93/20.55 (19) all_54_1 = all_52_4
% 140.93/20.55 (20) ~ (all_52_9 = all_52_11)
% 140.93/20.55 (21) all_54_2 = all_52_8
% 140.93/20.55 (22) ~ (e3 = e0)
% 140.93/20.55 (23) ~ (all_52_4 = e3)
% 140.93/20.55 (24) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 140.93/20.55 all_20_1 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2,
% 140.93/20.55 e1) = all_20_1 & $i(all_20_1))
% 140.93/20.55 (25) op(e3, e1) = all_52_8
% 140.93/20.55 (26) ~ (all_52_6 = all_52_7)
% 140.93/20.55 (27) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 140.93/20.55 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 140.93/20.55 e2)
% 140.93/20.55 (28) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 140.93/20.55 (29) ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 140.93/20.55 all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) & op(e2,
% 140.93/20.55 e1) = all_38_1 & $i(all_38_1))
% 140.93/20.55 (30) op(e0, e0) = all_10_2
% 140.93/20.55 (31) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.93/20.55 (32) ~ (e1 = e0)
% 140.93/20.55 (33) op(e1, e1) = e2
% 140.93/20.55 (34) op(e3, e2) = all_52_4
% 140.93/20.55 (35) ~ (all_52_7 = all_52_11)
% 140.93/20.55 (36) ~ (e2 = e0)
% 140.93/20.55 (37) ~ (e3 = e2)
% 140.93/20.55 (38) all_54_14 = all_52_11
% 140.93/20.55 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.55 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.55 (40) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 140.93/20.55 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 140.93/20.55 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 140.93/20.55 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 140.93/20.55 (41) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.93/20.55 (42) ~ (e3 = e1)
% 140.93/20.55 (43) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.93/20.55 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.93/20.55 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.93/20.55 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.93/20.55 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.93/20.55 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.93/20.55 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.93/20.55 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.93/20.55 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.93/20.55 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.93/20.55 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.93/20.55 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.93/20.55 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.93/20.55 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.93/20.55 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.93/20.55 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.93/20.55 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.93/20.55 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.93/20.55 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.93/20.55 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.55 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.93/20.55 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.55 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.93/20.55 $i(all_56_14))))
% 140.93/20.55 (44) op(e2, e1) = all_52_9
% 140.93/20.55 (45) op(e3, e3) = all_14_2
% 140.93/20.55 (46) ~ (all_52_8 = e2)
% 140.93/20.55 (47) ~ (all_14_2 = e0)
% 140.93/20.55 (48) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 140.93/20.55 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 140.93/20.55
% 140.93/20.55 Begin of proof
% 140.93/20.55 |
% 140.93/20.55 | BETA: splitting (48) gives:
% 140.93/20.55 |
% 140.93/20.55 | Case 1:
% 140.93/20.55 | |
% 140.93/20.55 | | (49) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 140.93/20.55 | | e3)
% 140.93/20.55 | |
% 140.93/20.55 | | BETA: splitting (49) gives:
% 140.93/20.55 | |
% 140.93/20.55 | | Case 1:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (50) all_57_1 = e3 & op(e3, e2) = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (50) implies:
% 140.93/20.55 | | | (51) op(e3, e2) = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | REF_CLOSE: (23), (34), (39), (51) are inconsistent by sub-proof #1107.
% 140.93/20.55 | | |
% 140.93/20.55 | | Case 2:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (52) all_57_3 = e3 & op(e2, e2) = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (52) implies:
% 140.93/20.55 | | | (53) op(e2, e2) = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | REF_CLOSE: (1), (9), (14), (30), (33), (37), (39), (42), (43), (45), (47),
% 140.93/20.55 | | | (53) are inconsistent by sub-proof #68.
% 140.93/20.55 | | |
% 140.93/20.55 | | End of split
% 140.93/20.55 | |
% 140.93/20.55 | Case 2:
% 140.93/20.55 | |
% 140.93/20.55 | | (54) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 140.93/20.55 | | e3)
% 140.93/20.55 | |
% 140.93/20.55 | | BETA: splitting (54) gives:
% 140.93/20.55 | |
% 140.93/20.55 | | Case 1:
% 140.93/20.55 | | |
% 140.93/20.55 | | | (55) all_57_7 = e3 & op(e1, e2) = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | ALPHA: (55) implies:
% 140.93/20.55 | | | (56) op(e1, e2) = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | GROUND_INST: instantiating (39) with all_52_6, e3, e2, e1, simplifying
% 140.93/20.55 | | | with (6), (56) gives:
% 140.93/20.55 | | | (57) all_52_6 = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | GROUND_INST: instantiating (39) with all_52_9, e3, e1, e2, simplifying
% 140.93/20.55 | | | with (7), (44) gives:
% 140.93/20.55 | | | (58) all_52_9 = e3
% 140.93/20.55 | | |
% 140.93/20.55 | | | REDUCE: (26), (57) imply:
% 140.93/20.55 | | | (59) ~ (all_52_7 = e3)
% 140.93/20.55 | | |
% 140.93/20.55 | | | SIMP: (59) implies:
% 140.93/20.55 | | | (60) ~ (all_52_7 = e3)
% 140.93/20.55 | | |
% 140.93/20.55 | | | REDUCE: (4), (58) imply:
% 140.93/20.55 | | | (61) ~ (all_52_8 = e3)
% 140.93/20.55 | | |
% 140.93/20.55 | | | REDUCE: (20), (58) imply:
% 140.93/20.55 | | | (62) ~ (all_52_11 = e3)
% 140.93/20.55 | | |
% 140.93/20.55 | | | SIMP: (62) implies:
% 140.93/20.55 | | | (63) ~ (all_52_11 = e3)
% 140.93/20.55 | | |
% 140.93/20.55 | | | BETA: splitting (13) gives:
% 140.93/20.55 | | |
% 140.93/20.55 | | | Case 1:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | (64) ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 140.93/20.55 | | | | all_32_1 & $i(all_32_0) & $i(all_32_1)
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | ALPHA: (64) implies:
% 140.93/20.55 | | | | (65) ~ (all_32_0 = e0)
% 140.93/20.55 | | | | (66) op(e1, e2) = all_32_1
% 140.93/20.55 | | | | (67) op(all_32_1, e1) = all_32_0
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | BETA: splitting (24) gives:
% 140.93/20.55 | | | |
% 140.93/20.55 | | | | Case 1:
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | (68) ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1)
% 140.93/20.55 | | | | | = all_20_1 & $i(all_20_0) & $i(all_20_1)
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | ALPHA: (68) implies:
% 140.93/20.55 | | | | | (69) op(e2, e1) = all_20_1
% 140.93/20.55 | | | | | (70) op(all_20_1, e2) = all_20_0
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | BETA: splitting (29) gives:
% 140.93/20.55 | | | | |
% 140.93/20.55 | | | | | Case 1:
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | (71) ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2,
% 140.93/20.55 | | | | | | e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 140.93/20.55 | | | | | |
% 140.93/20.55 | | | | | | ALPHA: (71) implies:
% 140.93/20.55 | | | | | | (72) ~ (all_38_0 = e0)
% 140.93/20.56 | | | | | | (73) op(e2, e1) = all_38_1
% 140.93/20.56 | | | | | | (74) op(all_38_1, e2) = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with e3, all_32_1, e2, e1,
% 140.93/20.56 | | | | | | simplifying with (56), (66) gives:
% 140.93/20.56 | | | | | | (75) all_32_1 = e3
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with e3, all_38_1, e1, e2,
% 140.93/20.56 | | | | | | simplifying with (7), (73) gives:
% 140.93/20.56 | | | | | | (76) all_38_1 = e3
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_20_1, all_38_1, e1, e2,
% 140.93/20.56 | | | | | | simplifying with (69), (73) gives:
% 140.93/20.56 | | | | | | (77) all_38_1 = all_20_1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (76), (77) imply:
% 140.93/20.56 | | | | | | (78) all_20_1 = e3
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (74), (76) imply:
% 140.93/20.56 | | | | | | (79) op(e3, e2) = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (67), (75) imply:
% 140.93/20.56 | | | | | | (80) op(e3, e1) = all_32_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (70), (78) imply:
% 140.93/20.56 | | | | | | (81) op(e3, e2) = all_20_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_52_8, all_32_0, e1, e3,
% 140.93/20.56 | | | | | | simplifying with (25), (80) gives:
% 140.93/20.56 | | | | | | (82) all_52_8 = all_32_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_52_4, all_20_0, e2, e3,
% 140.93/20.56 | | | | | | simplifying with (34), (81) gives:
% 140.93/20.56 | | | | | | (83) all_52_4 = all_20_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_52_4, all_38_0, e2, e3,
% 140.93/20.56 | | | | | | simplifying with (34), (79) gives:
% 140.93/20.56 | | | | | | (84) all_52_4 = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (83), (84) imply:
% 140.93/20.56 | | | | | | (85) all_38_0 = all_20_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (21), (82) imply:
% 140.93/20.56 | | | | | | (86) all_54_2 = all_32_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (19), (83) imply:
% 140.93/20.56 | | | | | | (87) all_54_1 = all_20_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (2), (83) imply:
% 140.93/20.56 | | | | | | (88) ~ (all_52_7 = all_20_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | SIMP: (88) implies:
% 140.93/20.56 | | | | | | (89) ~ (all_52_7 = all_20_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (23), (83) imply:
% 140.93/20.56 | | | | | | (90) ~ (all_20_0 = e3)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (11), (83) imply:
% 140.93/20.56 | | | | | | (91) ~ (all_20_0 = e1)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (3), (82) imply:
% 140.93/20.56 | | | | | | (92) ~ (all_52_11 = all_32_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | SIMP: (92) implies:
% 140.93/20.56 | | | | | | (93) ~ (all_52_11 = all_32_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (61), (82) imply:
% 140.93/20.56 | | | | | | (94) ~ (all_32_0 = e3)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (46), (82) imply:
% 140.93/20.56 | | | | | | (95) ~ (all_32_0 = e2)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (72), (85) imply:
% 140.93/20.56 | | | | | | (96) ~ (all_20_0 = e0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | BETA: splitting (15) gives:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | Case 1:
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | (97) all_54_2 = e3
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | COMBINE_EQS: (86), (97) imply:
% 140.93/20.56 | | | | | | | (98) all_32_0 = e3
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | REDUCE: (94), (98) imply:
% 140.93/20.56 | | | | | | | (99) $false
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | CLOSE: (99) is inconsistent.
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | Case 2:
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | (100) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | BETA: splitting (100) gives:
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | (101) all_54_2 = e2
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | COMBINE_EQS: (86), (101) imply:
% 140.93/20.56 | | | | | | | | (102) all_32_0 = e2
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | REDUCE: (95), (102) imply:
% 140.93/20.56 | | | | | | | | (103) $false
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | CLOSE: (103) is inconsistent.
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | (104) all_54_2 = e1 | all_54_2 = e0
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | BETA: splitting (31) gives:
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | (105) all_54_1 = e3
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | COMBINE_EQS: (87), (105) imply:
% 140.93/20.56 | | | | | | | | | (106) all_20_0 = e3
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | REDUCE: (90), (106) imply:
% 140.93/20.56 | | | | | | | | | (107) $false
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | CLOSE: (107) is inconsistent.
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | (108) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | BETA: splitting (108) gives:
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | (109) all_54_1 = e2
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | COMBINE_EQS: (87), (109) imply:
% 140.93/20.56 | | | | | | | | | | (110) all_20_0 = e2
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | REDUCE: (89), (110) imply:
% 140.93/20.56 | | | | | | | | | | (111) ~ (all_52_7 = e2)
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | REF_CLOSE: (5), (12), (18), (28), (35), (38), (41), (60),
% 140.93/20.56 | | | | | | | | | | (63), (65), (86), (93), (104), (111) are
% 140.93/20.56 | | | | | | | | | | inconsistent by sub-proof #66.
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | (112) all_54_1 = e1 | all_54_1 = e0
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | BETA: splitting (112) gives:
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | (113) all_54_1 = e1
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | COMBINE_EQS: (87), (113) imply:
% 140.93/20.56 | | | | | | | | | | | (114) all_20_0 = e1
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | REDUCE: (91), (114) imply:
% 140.93/20.56 | | | | | | | | | | | (115) $false
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | CLOSE: (115) is inconsistent.
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | (116) all_54_1 = e0
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | COMBINE_EQS: (87), (116) imply:
% 140.93/20.56 | | | | | | | | | | | (117) all_20_0 = e0
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | REDUCE: (96), (117) imply:
% 140.93/20.56 | | | | | | | | | | | (118) $false
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | CLOSE: (118) is inconsistent.
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | End of split
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | End of split
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | End of split
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | End of split
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | End of split
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | Case 2:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | (119) ~ (all_38_1 = e3) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | ALPHA: (119) implies:
% 140.93/20.56 | | | | | | (120) ~ (all_38_1 = e3)
% 140.93/20.56 | | | | | | (121) op(e2, e1) = all_38_1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REF_CLOSE: (7), (24), (39), (120), (121) are inconsistent by
% 140.93/20.56 | | | | | | sub-proof #359.
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | End of split
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | Case 2:
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | (122) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | ALPHA: (122) implies:
% 140.93/20.56 | | | | | (123) op(e2, e1) = all_20_1
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | BETA: splitting (29) gives:
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | Case 1:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | (124) ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2,
% 140.93/20.56 | | | | | | e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | ALPHA: (124) implies:
% 140.93/20.56 | | | | | | (125) ~ (all_38_0 = e0)
% 140.93/20.56 | | | | | | (126) op(e2, e1) = all_38_1
% 140.93/20.56 | | | | | | (127) op(all_38_1, e2) = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with e3, all_32_1, e2, e1,
% 140.93/20.56 | | | | | | simplifying with (56), (66) gives:
% 140.93/20.56 | | | | | | (128) all_32_1 = e3
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with e3, all_38_1, e1, e2,
% 140.93/20.56 | | | | | | simplifying with (7), (126) gives:
% 140.93/20.56 | | | | | | (129) all_38_1 = e3
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_20_1, all_38_1, e1, e2,
% 140.93/20.56 | | | | | | simplifying with (123), (126) gives:
% 140.93/20.56 | | | | | | (130) all_38_1 = all_20_1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (129), (130) imply:
% 140.93/20.56 | | | | | | (131) all_20_1 = e3
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (127), (129) imply:
% 140.93/20.56 | | | | | | (132) op(e3, e2) = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (67), (128) imply:
% 140.93/20.56 | | | | | | (133) op(e3, e1) = all_32_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_52_8, all_32_0, e1, e3,
% 140.93/20.56 | | | | | | simplifying with (25), (133) gives:
% 140.93/20.56 | | | | | | (134) all_52_8 = all_32_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | GROUND_INST: instantiating (39) with all_52_4, all_38_0, e2, e3,
% 140.93/20.56 | | | | | | simplifying with (34), (132) gives:
% 140.93/20.56 | | | | | | (135) all_52_4 = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (21), (134) imply:
% 140.93/20.56 | | | | | | (136) all_54_2 = all_32_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (19), (135) imply:
% 140.93/20.56 | | | | | | (137) all_54_1 = all_38_0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (2), (135) imply:
% 140.93/20.56 | | | | | | (138) ~ (all_52_7 = all_38_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | SIMP: (138) implies:
% 140.93/20.56 | | | | | | (139) ~ (all_52_7 = all_38_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (23), (135) imply:
% 140.93/20.56 | | | | | | (140) ~ (all_38_0 = e3)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (11), (135) imply:
% 140.93/20.56 | | | | | | (141) ~ (all_38_0 = e1)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (3), (134) imply:
% 140.93/20.56 | | | | | | (142) ~ (all_52_11 = all_32_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | SIMP: (142) implies:
% 140.93/20.56 | | | | | | (143) ~ (all_52_11 = all_32_0)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (61), (134) imply:
% 140.93/20.56 | | | | | | (144) ~ (all_32_0 = e3)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (46), (134) imply:
% 140.93/20.56 | | | | | | (145) ~ (all_32_0 = e2)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | BETA: splitting (15) gives:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | Case 1:
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | (146) all_54_2 = e3
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | COMBINE_EQS: (136), (146) imply:
% 140.93/20.56 | | | | | | | (147) all_32_0 = e3
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | REDUCE: (144), (147) imply:
% 140.93/20.56 | | | | | | | (148) $false
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | CLOSE: (148) is inconsistent.
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | Case 2:
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | (149) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | BETA: splitting (149) gives:
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | (150) all_54_2 = e2
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | COMBINE_EQS: (136), (150) imply:
% 140.93/20.56 | | | | | | | | (151) all_32_0 = e2
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | REDUCE: (145), (151) imply:
% 140.93/20.56 | | | | | | | | (152) $false
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | CLOSE: (152) is inconsistent.
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | (153) all_54_2 = e1 | all_54_2 = e0
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | BETA: splitting (31) gives:
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | (154) all_54_1 = e3
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | COMBINE_EQS: (137), (154) imply:
% 140.93/20.56 | | | | | | | | | (155) all_38_0 = e3
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | REDUCE: (140), (155) imply:
% 140.93/20.56 | | | | | | | | | (156) $false
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | CLOSE: (156) is inconsistent.
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | (157) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | BETA: splitting (157) gives:
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | (158) all_54_1 = e2
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | COMBINE_EQS: (137), (158) imply:
% 140.93/20.56 | | | | | | | | | | (159) all_38_0 = e2
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | REDUCE: (139), (159) imply:
% 140.93/20.56 | | | | | | | | | | (160) ~ (all_52_7 = e2)
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | REF_CLOSE: (5), (12), (18), (28), (35), (38), (41), (60),
% 140.93/20.56 | | | | | | | | | | (63), (65), (136), (143), (153), (160) are
% 140.93/20.56 | | | | | | | | | | inconsistent by sub-proof #66.
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | (161) all_54_1 = e1 | all_54_1 = e0
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | BETA: splitting (161) gives:
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | Case 1:
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | (162) all_54_1 = e1
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | COMBINE_EQS: (137), (162) imply:
% 140.93/20.56 | | | | | | | | | | | (163) all_38_0 = e1
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | REDUCE: (141), (163) imply:
% 140.93/20.56 | | | | | | | | | | | (164) $false
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | CLOSE: (164) is inconsistent.
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | Case 2:
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | (165) all_54_1 = e0
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | COMBINE_EQS: (137), (165) imply:
% 140.93/20.56 | | | | | | | | | | | (166) all_38_0 = e0
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | REDUCE: (125), (166) imply:
% 140.93/20.56 | | | | | | | | | | | (167) $false
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | | CLOSE: (167) is inconsistent.
% 140.93/20.56 | | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | | End of split
% 140.93/20.56 | | | | | | | | | |
% 140.93/20.56 | | | | | | | | | End of split
% 140.93/20.56 | | | | | | | | |
% 140.93/20.56 | | | | | | | | End of split
% 140.93/20.56 | | | | | | | |
% 140.93/20.56 | | | | | | | End of split
% 140.93/20.56 | | | | | | |
% 140.93/20.56 | | | | | | End of split
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | Case 2:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | (168) ~ (all_38_1 = e3) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | ALPHA: (168) implies:
% 140.93/20.56 | | | | | | (169) ~ (all_38_1 = e3)
% 140.93/20.56 | | | | | | (170) op(e2, e1) = all_38_1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REF_CLOSE: (7), (24), (39), (169), (170) are inconsistent by
% 140.93/20.56 | | | | | | sub-proof #359.
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | End of split
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | End of split
% 140.93/20.56 | | | |
% 140.93/20.56 | | | Case 2:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (171) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1)
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | ALPHA: (171) implies:
% 140.93/20.56 | | | | (172) ~ (all_32_1 = e3)
% 140.93/20.56 | | | | (173) op(e1, e2) = all_32_1
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | GROUND_INST: instantiating (39) with e3, all_32_1, e2, e1, simplifying
% 140.93/20.56 | | | | with (56), (173) gives:
% 140.93/20.56 | | | | (174) all_32_1 = e3
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REDUCE: (172), (174) imply:
% 140.93/20.56 | | | | (175) $false
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | CLOSE: (175) is inconsistent.
% 140.93/20.56 | | | |
% 140.93/20.56 | | | End of split
% 140.93/20.56 | | |
% 140.93/20.56 | | Case 2:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (176) all_57_13 = e3 & op(e0, e2) = e3
% 140.93/20.56 | | |
% 140.93/20.56 | | | ALPHA: (176) implies:
% 140.93/20.56 | | | (177) all_57_13 = e3
% 140.93/20.56 | | |
% 140.93/20.56 | | | REF_CLOSE: (8), (10), (16), (22), (27), (32), (36), (37), (39), (40),
% 140.93/20.56 | | | (42), (177) are inconsistent by sub-proof #252.
% 140.93/20.56 | | |
% 140.93/20.56 | | End of split
% 140.93/20.56 | |
% 140.93/20.56 | End of split
% 140.93/20.56 |
% 140.93/20.56 End of proof
% 140.93/20.56
% 140.93/20.56 Sub-proof #66 shows that the following formulas are inconsistent:
% 140.93/20.56 ----------------------------------------------------------------
% 140.93/20.56 (1) all_54_2 = all_32_0
% 140.93/20.56 (2) ~ (all_52_11 = all_32_0)
% 140.93/20.56 (3) ~ (all_52_7 = e1)
% 140.93/20.56 (4) all_54_13 = all_52_7
% 140.93/20.56 (5) ~ (all_52_11 = e3)
% 140.93/20.56 (6) ~ (all_52_7 = e3)
% 140.93/20.56 (7) ~ (all_52_11 = e2)
% 140.93/20.56 (8) ~ (all_32_0 = e0)
% 140.93/20.56 (9) ~ (all_52_7 = e2)
% 140.93/20.56 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 140.93/20.56 (11) ~ (all_52_7 = all_52_11)
% 140.93/20.56 (12) all_54_14 = all_52_11
% 140.93/20.56 (13) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.93/20.56 (14) all_54_2 = e1 | all_54_2 = e0
% 140.93/20.56
% 140.93/20.56 Begin of proof
% 140.93/20.56 |
% 140.93/20.56 | BETA: splitting (13) gives:
% 140.93/20.56 |
% 140.93/20.56 | Case 1:
% 140.93/20.56 | |
% 140.93/20.56 | | (15) all_54_13 = e3
% 140.93/20.56 | |
% 140.93/20.56 | | REF_CLOSE: (4), (6), (15) are inconsistent by sub-proof #364.
% 140.93/20.56 | |
% 140.93/20.56 | Case 2:
% 140.93/20.56 | |
% 140.93/20.56 | | (16) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 140.93/20.56 | |
% 140.93/20.56 | | BETA: splitting (16) gives:
% 140.93/20.56 | |
% 140.93/20.56 | | Case 1:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (17) all_54_13 = e2
% 140.93/20.56 | | |
% 140.93/20.56 | | | REF_CLOSE: (4), (9), (17) are inconsistent by sub-proof #67.
% 140.93/20.56 | | |
% 140.93/20.56 | | Case 2:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (18) all_54_13 = e1 | all_54_13 = e0
% 140.93/20.56 | | |
% 140.93/20.56 | | | BETA: splitting (18) gives:
% 140.93/20.56 | | |
% 140.93/20.56 | | | Case 1:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (19) all_54_13 = e1
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REF_CLOSE: (3), (4), (19) are inconsistent by sub-proof #363.
% 140.93/20.56 | | | |
% 140.93/20.56 | | | Case 2:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (20) all_54_13 = e0
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | COMBINE_EQS: (4), (20) imply:
% 140.93/20.56 | | | | (21) all_52_7 = e0
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | SIMP: (21) implies:
% 140.93/20.56 | | | | (22) all_52_7 = e0
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REDUCE: (11), (22) imply:
% 140.93/20.56 | | | | (23) ~ (all_52_11 = e0)
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | SIMP: (23) implies:
% 140.93/20.56 | | | | (24) ~ (all_52_11 = e0)
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | BETA: splitting (10) gives:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | Case 1:
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | (25) all_54_14 = e3
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | REF_CLOSE: (5), (12), (25) are inconsistent by sub-proof #764.
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | Case 2:
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | (26) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | BETA: splitting (14) gives:
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | | Case 1:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | (27) all_54_2 = e1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (1), (27) imply:
% 140.93/20.56 | | | | | | (28) all_32_0 = e1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | SIMP: (28) implies:
% 140.93/20.56 | | | | | | (29) all_32_0 = e1
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (2), (29) imply:
% 140.93/20.56 | | | | | | (30) ~ (all_52_11 = e1)
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REF_CLOSE: (7), (12), (24), (26), (30) are inconsistent by sub-proof
% 140.93/20.56 | | | | | | #760.
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | Case 2:
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | (31) all_54_2 = e0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | COMBINE_EQS: (1), (31) imply:
% 140.93/20.56 | | | | | | (32) all_32_0 = e0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | SIMP: (32) implies:
% 140.93/20.56 | | | | | | (33) all_32_0 = e0
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | REDUCE: (8), (33) imply:
% 140.93/20.56 | | | | | | (34) $false
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | | CLOSE: (34) is inconsistent.
% 140.93/20.56 | | | | | |
% 140.93/20.56 | | | | | End of split
% 140.93/20.56 | | | | |
% 140.93/20.56 | | | | End of split
% 140.93/20.56 | | | |
% 140.93/20.56 | | | End of split
% 140.93/20.56 | | |
% 140.93/20.56 | | End of split
% 140.93/20.56 | |
% 140.93/20.56 | End of split
% 140.93/20.56 |
% 140.93/20.56 End of proof
% 140.93/20.56
% 140.93/20.56 Sub-proof #67 shows that the following formulas are inconsistent:
% 140.93/20.56 ----------------------------------------------------------------
% 140.93/20.56 (1) all_54_13 = all_52_7
% 140.93/20.56 (2) all_54_13 = e2
% 140.93/20.56 (3) ~ (all_52_7 = e2)
% 140.93/20.56
% 140.93/20.56 Begin of proof
% 140.93/20.56 |
% 140.93/20.56 | COMBINE_EQS: (1), (2) imply:
% 140.93/20.56 | (4) all_52_7 = e2
% 140.93/20.56 |
% 140.93/20.56 | SIMP: (4) implies:
% 140.93/20.56 | (5) all_52_7 = e2
% 140.93/20.56 |
% 140.93/20.56 | REDUCE: (3), (5) imply:
% 140.93/20.56 | (6) $false
% 140.93/20.56 |
% 140.93/20.56 | CLOSE: (6) is inconsistent.
% 140.93/20.56 |
% 140.93/20.56 End of proof
% 140.93/20.56
% 140.93/20.56 Sub-proof #68 shows that the following formulas are inconsistent:
% 140.93/20.56 ----------------------------------------------------------------
% 140.93/20.56 (1) ~ (all_10_2 = e2)
% 140.93/20.56 (2) op(e3, e3) = e3
% 140.93/20.56 (3) ~ (all_10_2 = e1)
% 140.93/20.56 (4) op(e0, e0) = all_10_2
% 140.93/20.56 (5) op(e1, e1) = e2
% 140.93/20.56 (6) ~ (e3 = e2)
% 140.93/20.56 (7) op(e2, e2) = e3
% 140.93/20.56 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.56 (9) ~ (e3 = e1)
% 140.93/20.56 (10) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.93/20.56 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.93/20.56 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 140.93/20.56 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.93/20.56 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.93/20.56 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 140.93/20.56 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 140.93/20.56 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 140.93/20.56 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 140.93/20.56 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 140.93/20.56 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 140.93/20.56 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 140.93/20.56 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 140.93/20.56 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 140.93/20.56 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 140.93/20.56 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 140.93/20.56 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 140.93/20.56 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 140.93/20.56 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 140.93/20.56 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.56 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 140.93/20.56 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 140.93/20.56 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.93/20.56 $i(all_56_14))))
% 140.93/20.56 (11) op(e3, e3) = all_14_2
% 140.93/20.56 (12) ~ (all_14_2 = e0)
% 140.93/20.56
% 140.93/20.56 Begin of proof
% 140.93/20.56 |
% 140.93/20.56 | BETA: splitting (10) gives:
% 140.93/20.56 |
% 140.93/20.56 | Case 1:
% 140.93/20.56 | |
% 140.93/20.56 | | (13) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.93/20.56 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.93/20.56 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.93/20.56 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 140.93/20.56 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 140.93/20.56 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.93/20.56 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 140.93/20.56 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.93/20.56 | |
% 140.93/20.56 | | BETA: splitting (13) gives:
% 140.93/20.56 | |
% 140.93/20.56 | | Case 1:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (14) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 140.93/20.56 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.93/20.56 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 140.93/20.56 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 140.93/20.56 | | |
% 140.93/20.56 | | | REF_CLOSE: (2), (6), (8), (14) are inconsistent by sub-proof #125.
% 140.93/20.56 | | |
% 140.93/20.56 | | Case 2:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (15) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 140.93/20.56 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.93/20.56 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 140.93/20.56 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.93/20.56 | | |
% 140.93/20.56 | | | REF_CLOSE: (5), (6), (8), (15) are inconsistent by sub-proof #76.
% 140.93/20.56 | | |
% 140.93/20.56 | | End of split
% 140.93/20.56 | |
% 140.93/20.56 | Case 2:
% 140.93/20.56 | |
% 140.93/20.56 | | (16) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 140.93/20.56 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.93/20.56 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 140.93/20.56 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 140.93/20.56 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 140.93/20.56 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.93/20.56 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 140.93/20.56 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.93/20.56 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.93/20.56 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.93/20.56 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.93/20.56 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.93/20.56 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.56 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 140.93/20.56 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 140.93/20.56 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 140.93/20.56 | | all_56_14 & $i(all_56_14))))
% 140.93/20.56 | |
% 140.93/20.56 | | BETA: splitting (16) gives:
% 140.93/20.56 | |
% 140.93/20.56 | | Case 1:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (17) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 140.93/20.56 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 140.93/20.56 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 140.93/20.56 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 140.93/20.56 | | |
% 140.93/20.56 | | | BETA: splitting (17) gives:
% 140.93/20.56 | | |
% 140.93/20.56 | | | Case 1:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (18) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 140.93/20.56 | | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | ALPHA: (18) implies:
% 140.93/20.56 | | | | (19) op(e3, e3) = e0
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REF_CLOSE: (8), (11), (12), (19) are inconsistent by sub-proof #1125.
% 140.93/20.56 | | | |
% 140.93/20.56 | | | Case 2:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (20) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2,
% 140.93/20.56 | | | | e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 140.93/20.56 | | | | $i(all_56_4)
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | ALPHA: (20) implies:
% 140.93/20.56 | | | | (21) op(e2, e2) = e1
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REF_CLOSE: (7), (8), (9), (21) are inconsistent by sub-proof #69.
% 140.93/20.56 | | | |
% 140.93/20.56 | | | End of split
% 140.93/20.56 | | |
% 140.93/20.56 | | Case 2:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (22) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 140.93/20.56 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 140.93/20.56 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 140.93/20.56 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 140.93/20.56 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 140.93/20.56 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 140.93/20.56 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 140.93/20.56 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 140.93/20.56 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 140.93/20.56 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 140.93/20.56 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 140.93/20.56 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 140.93/20.56 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 140.93/20.56 | | |
% 140.93/20.56 | | | BETA: splitting (22) gives:
% 140.93/20.56 | | |
% 140.93/20.56 | | | Case 1:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (23) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 140.93/20.56 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 140.93/20.56 | | | | $i(all_56_7)
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | ALPHA: (23) implies:
% 140.93/20.56 | | | | (24) op(e2, e2) = e1
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REF_CLOSE: (7), (8), (9), (24) are inconsistent by sub-proof #69.
% 140.93/20.56 | | | |
% 140.93/20.56 | | | Case 2:
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | (25) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 140.93/20.56 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 140.93/20.56 | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.93/20.56 | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 140.93/20.56 | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 140.93/20.56 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 140.93/20.56 | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.93/20.56 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 140.93/20.56 | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 140.93/20.56 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 140.93/20.56 | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 140.93/20.56 | | | | $i(all_56_14))))
% 140.93/20.56 | | | |
% 140.93/20.56 | | | | REF_CLOSE: (1), (3), (4), (8), (11), (12), (25) are inconsistent by
% 140.93/20.56 | | | | sub-proof #272.
% 140.93/20.56 | | | |
% 140.93/20.56 | | | End of split
% 140.93/20.56 | | |
% 140.93/20.56 | | End of split
% 140.93/20.56 | |
% 140.93/20.56 | End of split
% 140.93/20.56 |
% 140.93/20.56 End of proof
% 140.93/20.56
% 140.93/20.56 Sub-proof #69 shows that the following formulas are inconsistent:
% 140.93/20.56 ----------------------------------------------------------------
% 140.93/20.56 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.56 (2) op(e2, e2) = e3
% 140.93/20.56 (3) op(e2, e2) = e1
% 140.93/20.56 (4) ~ (e3 = e1)
% 140.93/20.56
% 140.93/20.56 Begin of proof
% 140.93/20.56 |
% 140.93/20.56 | GROUND_INST: instantiating (1) with e3, e1, e2, e2, simplifying with (2), (3)
% 140.93/20.56 | gives:
% 140.93/20.56 | (5) e3 = e1
% 140.93/20.56 |
% 140.93/20.56 | REDUCE: (4), (5) imply:
% 140.93/20.56 | (6) $false
% 140.93/20.56 |
% 140.93/20.56 | CLOSE: (6) is inconsistent.
% 140.93/20.56 |
% 140.93/20.56 End of proof
% 140.93/20.56
% 140.93/20.56 Sub-proof #70 shows that the following formulas are inconsistent:
% 140.93/20.56 ----------------------------------------------------------------
% 140.93/20.56 (1) ~ (all_52_4 = e3)
% 140.93/20.56 (2) op(e1, e1) = e2
% 140.93/20.56 (3) op(e3, e2) = all_52_4
% 140.93/20.56 (4) ~ (e3 = e2)
% 140.93/20.56 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.56 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.56 (6) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 140.93/20.56 all_56_9 & $i(all_56_9))
% 140.93/20.56 (7) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 140.93/20.56 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 140.93/20.56 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 140.93/20.56 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 140.93/20.56 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 140.93/20.56 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 140.93/20.56 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 140.93/20.56 op(e1, e1) = e3 & $i(all_56_6))
% 140.93/20.56
% 140.93/20.56 Begin of proof
% 140.93/20.56 |
% 140.93/20.56 | BETA: splitting (7) gives:
% 140.93/20.56 |
% 140.93/20.56 | Case 1:
% 140.93/20.56 | |
% 140.93/20.56 | | (8) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.93/20.56 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 140.93/20.56 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.93/20.56 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 140.93/20.56 | |
% 140.93/20.56 | | BETA: splitting (8) gives:
% 140.93/20.56 | |
% 140.93/20.56 | | Case 1:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (9) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 140.93/20.56 | | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 140.93/20.56 | | |
% 140.93/20.56 | | | ALPHA: (9) implies:
% 140.93/20.56 | | | (10) all_56_9 = e2
% 140.93/20.56 | | |
% 140.93/20.56 | | | REF_CLOSE: (1), (3), (5), (6), (10) are inconsistent by sub-proof #345.
% 140.93/20.56 | | |
% 140.93/20.56 | | Case 2:
% 140.93/20.56 | | |
% 140.93/20.56 | | | (11) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 140.93/20.56 | | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 140.93/20.56 | | |
% 140.93/20.56 | | | ALPHA: (11) implies:
% 140.93/20.56 | | | (12) all_56_9 = e2
% 140.93/20.56 | | |
% 140.93/20.56 | | | REF_CLOSE: (1), (3), (5), (6), (12) are inconsistent by sub-proof #345.
% 140.93/20.56 | | |
% 140.93/20.56 | | End of split
% 140.93/20.56 | |
% 140.93/20.56 | Case 2:
% 140.93/20.56 | |
% 140.93/20.57 | | (13) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 140.93/20.57 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 140.93/20.57 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 140.93/20.57 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (2), (4), (5), (13) are inconsistent by sub-proof #76.
% 140.93/20.57 | |
% 140.93/20.57 | End of split
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #71 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) op(e1, e1) = e2
% 140.93/20.57 (2) ~ (e3 = e2)
% 140.93/20.57 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (4) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) = e2)
% 140.93/20.57 | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.93/20.57 ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 140.93/20.57 all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 140.93/20.57 ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 140.93/20.57 ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 140.93/20.57 all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.93/20.57 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.93/20.57 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 140.93/20.57 all_56_10 & $i(all_56_10)))
% 140.93/20.57 (5) op(e1, e3) = e1
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (4) implies:
% 140.93/20.57 | (6) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 140.93/20.57 | all_56_6 & $i(all_56_6))
% 140.93/20.57 |
% 140.93/20.57 | BETA: splitting (6) gives:
% 140.93/20.57 |
% 140.93/20.57 | Case 1:
% 140.93/20.57 | |
% 140.93/20.57 | | (7) all_56_13 = e3 & op(e1, e1) = e3
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (7) implies:
% 140.93/20.57 | | (8) op(e1, e1) = e3
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (1), (2), (3), (8) are inconsistent by sub-proof #77.
% 140.93/20.57 | |
% 140.93/20.57 | Case 2:
% 140.93/20.57 | |
% 140.93/20.57 | | (9) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (9) implies:
% 140.93/20.57 | | (10) ~ (all_56_6 = e1)
% 140.93/20.57 | | (11) op(e1, e3) = all_56_6
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (3), (5), (10), (11) are inconsistent by sub-proof #435.
% 140.93/20.57 | |
% 140.93/20.57 | End of split
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #72 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) = all_32_1
% 140.93/20.57 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2) =
% 140.93/20.57 all_32_1 & $i(all_32_1))
% 140.93/20.57 (2) op(e3, e1) = e0
% 140.93/20.57 (3) ( ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1 &
% 140.93/20.57 $i(all_4_0) & $i(all_4_1)) | ( ~ (all_4_1 = e0) & op(e1, e2) = all_4_1
% 140.93/20.57 & $i(all_4_1))
% 140.93/20.57 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (5) op(e1, e2) = e3
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | BETA: splitting (3) gives:
% 140.93/20.57 |
% 140.93/20.57 | Case 1:
% 140.93/20.57 | |
% 140.93/20.57 | | (6) ~ (all_4_0 = e3) & op(all_4_1, e1) = all_4_0 & op(e1, e2) = all_4_1
% 140.93/20.57 | | & $i(all_4_0) & $i(all_4_1)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (6) implies:
% 140.93/20.57 | | (7) op(e1, e2) = all_4_1
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #73.
% 140.93/20.57 | |
% 140.93/20.57 | Case 2:
% 140.93/20.57 | |
% 140.93/20.57 | | (8) ~ (all_4_1 = e0) & op(e1, e2) = all_4_1 & $i(all_4_1)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (8) implies:
% 140.93/20.57 | | (9) op(e1, e2) = all_4_1
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #73.
% 140.93/20.57 | |
% 140.93/20.57 | End of split
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #73 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) ( ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) = all_32_1
% 140.93/20.57 & $i(all_32_0) & $i(all_32_1)) | ( ~ (all_32_1 = e3) & op(e1, e2) =
% 140.93/20.57 all_32_1 & $i(all_32_1))
% 140.93/20.57 (2) op(e1, e2) = all_4_1
% 140.93/20.57 (3) op(e3, e1) = e0
% 140.93/20.57 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (5) op(e1, e2) = e3
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (4) with e3, all_4_1, e2, e1, simplifying with (2),
% 140.93/20.57 | (5) gives:
% 140.93/20.57 | (6) all_4_1 = e3
% 140.93/20.57 |
% 140.93/20.57 | BETA: splitting (1) gives:
% 140.93/20.57 |
% 140.93/20.57 | Case 1:
% 140.93/20.57 | |
% 140.93/20.57 | | (7) ~ (all_32_0 = e0) & op(all_32_1, e1) = all_32_0 & op(e1, e2) =
% 140.93/20.57 | | all_32_1 & $i(all_32_0) & $i(all_32_1)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (7) implies:
% 140.93/20.57 | | (8) ~ (all_32_0 = e0)
% 140.93/20.57 | | (9) op(e1, e2) = all_32_1
% 140.93/20.57 | | (10) op(all_32_1, e1) = all_32_0
% 140.93/20.57 | |
% 140.93/20.57 | | GROUND_INST: instantiating (4) with e3, all_32_1, e2, e1, simplifying with
% 140.93/20.57 | | (5), (9) gives:
% 140.93/20.57 | | (11) all_32_1 = e3
% 140.93/20.57 | |
% 140.93/20.57 | | REDUCE: (10), (11) imply:
% 140.93/20.57 | | (12) op(e3, e1) = all_32_0
% 140.93/20.57 | |
% 140.93/20.57 | | GROUND_INST: instantiating (4) with e0, all_32_0, e1, e3, simplifying with
% 140.93/20.57 | | (3), (12) gives:
% 140.93/20.57 | | (13) all_32_0 = e0
% 140.93/20.57 | |
% 140.93/20.57 | | REDUCE: (8), (13) imply:
% 140.93/20.57 | | (14) $false
% 140.93/20.57 | |
% 140.93/20.57 | | CLOSE: (14) is inconsistent.
% 140.93/20.57 | |
% 140.93/20.57 | Case 2:
% 140.93/20.57 | |
% 140.93/20.57 | | (15) ~ (all_32_1 = e3) & op(e1, e2) = all_32_1 & $i(all_32_1)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (15) implies:
% 140.93/20.57 | | (16) ~ (all_32_1 = e3)
% 140.93/20.57 | | (17) op(e1, e2) = all_32_1
% 140.93/20.57 | |
% 140.93/20.57 | | GROUND_INST: instantiating (4) with e3, all_32_1, e2, e1, simplifying with
% 140.93/20.57 | | (5), (17) gives:
% 140.93/20.57 | | (18) all_32_1 = e3
% 140.93/20.57 | |
% 140.93/20.57 | | REDUCE: (16), (18) imply:
% 140.93/20.57 | | (19) $false
% 140.93/20.57 | |
% 140.93/20.57 | | CLOSE: (19) is inconsistent.
% 140.93/20.57 | |
% 140.93/20.57 | End of split
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #74 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) all_57_4 = e1 & op(e3, e1) = e1
% 140.93/20.57 (2) all_57_4 = e0
% 140.93/20.57 (3) ~ (e1 = e0)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (1) implies:
% 140.93/20.57 | (4) all_57_4 = e1
% 140.93/20.57 |
% 140.93/20.57 | COMBINE_EQS: (2), (4) imply:
% 140.93/20.57 | (5) e1 = e0
% 140.93/20.57 |
% 140.93/20.57 | SIMP: (5) implies:
% 140.93/20.57 | (6) e1 = e0
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (3), (6) imply:
% 140.93/20.57 | (7) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (7) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #75 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) ~ (all_52_12 = e3)
% 140.93/20.57 (2) ~ (all_52_8 = e3)
% 140.93/20.57 (3) ~ (e2 = e1)
% 140.93/20.57 (4) op(e3, e3) = e3
% 140.93/20.57 (5) all_57_12 = e3
% 140.93/20.57 (6) ~ (all_52_1 = e1)
% 140.93/20.57 (7) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 140.93/20.57 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 140.93/20.57 (8) ~ (e3 = e0)
% 140.93/20.57 (9) ~ (all_52_4 = e3)
% 140.93/20.57 (10) op(e3, e1) = all_52_8
% 140.93/20.57 (11) op(e2, e3) = all_52_1
% 140.93/20.57 (12) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 140.93/20.57 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 140.93/20.57 (13) ~ (e1 = e0)
% 140.93/20.57 (14) op(e3, e2) = all_52_4
% 140.93/20.57 (15) ~ (e2 = e0)
% 140.93/20.57 (16) ~ (e3 = e2)
% 140.93/20.57 (17) all_57_0 = e3
% 140.93/20.57 (18) op(e3, e0) = all_52_12
% 140.93/20.57 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (20) ~ (e3 = e1)
% 140.93/20.57 (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 140.93/20.57 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 140.93/20.57 (22) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 140.93/20.57 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | BETA: splitting (22) gives:
% 140.93/20.57 |
% 140.93/20.57 | Case 1:
% 140.93/20.57 | |
% 140.93/20.57 | | (23) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 140.93/20.57 | | e2)
% 140.93/20.57 | |
% 140.93/20.57 | | BETA: splitting (23) gives:
% 140.93/20.57 | |
% 140.93/20.57 | | Case 1:
% 140.93/20.57 | | |
% 140.93/20.57 | | | (24) all_57_0 = e2 & op(e3, e3) = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | ALPHA: (24) implies:
% 140.93/20.57 | | | (25) op(e3, e3) = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | REF_CLOSE: (4), (16), (19), (25) are inconsistent by sub-proof #450.
% 140.93/20.57 | | |
% 140.93/20.57 | | Case 2:
% 140.93/20.57 | | |
% 140.93/20.57 | | | (26) all_57_2 = e2 & op(e2, e3) = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | ALPHA: (26) implies:
% 140.93/20.57 | | | (27) all_57_2 = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | BETA: splitting (12) gives:
% 140.93/20.57 | | |
% 140.93/20.57 | | | Case 1:
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 140.93/20.57 | | | | = e1)
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | REF_CLOSE: (4), (6), (11), (19), (20), (28) are inconsistent by
% 140.93/20.57 | | | | sub-proof #438.
% 140.93/20.57 | | | |
% 140.93/20.57 | | | Case 2:
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | (29) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 140.93/20.57 | | | | = e1)
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | BETA: splitting (29) gives:
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | Case 1:
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | (30) all_57_6 = e1 & op(e1, e3) = e1
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | ALPHA: (30) implies:
% 140.93/20.57 | | | | | (31) all_57_6 = e1
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | BETA: splitting (7) gives:
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | Case 1:
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | | (32) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2,
% 140.93/20.57 | | | | | | e3) = e0)
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | | BETA: splitting (32) gives:
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | | Case 1:
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | (33) all_57_0 = e0 & op(e3, e3) = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | ALPHA: (33) implies:
% 140.93/20.57 | | | | | | | (34) all_57_0 = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | REF_CLOSE: (1), (2), (8), (9), (10), (14), (18), (19), (21), (34)
% 140.93/20.57 | | | | | | | are inconsistent by sub-proof #1103.
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | Case 2:
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | (35) all_57_2 = e0 & op(e2, e3) = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | ALPHA: (35) implies:
% 140.93/20.57 | | | | | | | (36) all_57_2 = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | COMBINE_EQS: (27), (36) imply:
% 140.93/20.57 | | | | | | | (37) e2 = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | REDUCE: (15), (37) imply:
% 140.93/20.57 | | | | | | | (38) $false
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | CLOSE: (38) is inconsistent.
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | End of split
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | Case 2:
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | | (39) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0,
% 140.93/20.57 | | | | | | e3) = e0)
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | | BETA: splitting (39) gives:
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | | Case 1:
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | (40) all_57_6 = e0 & op(e1, e3) = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | ALPHA: (40) implies:
% 140.93/20.57 | | | | | | | (41) all_57_6 = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | REF_CLOSE: (13), (31), (41) are inconsistent by sub-proof #1026.
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | Case 2:
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | (42) all_57_12 = e0 & op(e0, e3) = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | ALPHA: (42) implies:
% 140.93/20.57 | | | | | | | (43) all_57_12 = e0
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | | REF_CLOSE: (1), (2), (5), (8), (9), (10), (14), (17), (18), (19),
% 140.93/20.57 | | | | | | | (21), (43) are inconsistent by sub-proof #892.
% 140.93/20.57 | | | | | | |
% 140.93/20.57 | | | | | | End of split
% 140.93/20.57 | | | | | |
% 140.93/20.57 | | | | | End of split
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | Case 2:
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | (44) all_57_12 = e1 & op(e0, e3) = e1
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | REF_CLOSE: (5), (20), (44) are inconsistent by sub-proof #1073.
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | End of split
% 140.93/20.57 | | | |
% 140.93/20.57 | | | End of split
% 140.93/20.57 | | |
% 140.93/20.57 | | End of split
% 140.93/20.57 | |
% 140.93/20.57 | Case 2:
% 140.93/20.57 | |
% 140.93/20.57 | | (45) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 140.93/20.57 | | e2)
% 140.93/20.57 | |
% 140.93/20.57 | | BETA: splitting (45) gives:
% 140.93/20.57 | |
% 140.93/20.57 | | Case 1:
% 140.93/20.57 | | |
% 140.93/20.57 | | | (46) all_57_6 = e2 & op(e1, e3) = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | ALPHA: (46) implies:
% 140.93/20.57 | | | (47) all_57_6 = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | BETA: splitting (12) gives:
% 140.93/20.57 | | |
% 140.93/20.57 | | | Case 1:
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | (48) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 140.93/20.57 | | | | = e1)
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | REF_CLOSE: (4), (6), (11), (19), (20), (48) are inconsistent by
% 140.93/20.57 | | | | sub-proof #438.
% 140.93/20.57 | | | |
% 140.93/20.57 | | | Case 2:
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | (49) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 140.93/20.57 | | | | = e1)
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | BETA: splitting (49) gives:
% 140.93/20.57 | | | |
% 140.93/20.57 | | | | Case 1:
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | (50) all_57_6 = e1 & op(e1, e3) = e1
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | REF_CLOSE: (3), (47), (50) are inconsistent by sub-proof #437.
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | Case 2:
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | (51) all_57_12 = e1 & op(e0, e3) = e1
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | | REF_CLOSE: (5), (20), (51) are inconsistent by sub-proof #1073.
% 140.93/20.57 | | | | |
% 140.93/20.57 | | | | End of split
% 140.93/20.57 | | | |
% 140.93/20.57 | | | End of split
% 140.93/20.57 | | |
% 140.93/20.57 | | Case 2:
% 140.93/20.57 | | |
% 140.93/20.57 | | | (52) all_57_12 = e2 & op(e0, e3) = e2
% 140.93/20.57 | | |
% 140.93/20.57 | | | REF_CLOSE: (5), (16), (52) are inconsistent by sub-proof #659.
% 140.93/20.57 | | |
% 140.93/20.57 | | End of split
% 140.93/20.57 | |
% 140.93/20.57 | End of split
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #76 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 &
% 140.93/20.57 op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 140.93/20.57 e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3)
% 140.93/20.57 = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 140.93/20.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (3) op(e1, e1) = e2
% 140.93/20.57 (4) ~ (e3 = e2)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | BETA: splitting (1) gives:
% 140.93/20.57 |
% 140.93/20.57 | Case 1:
% 140.93/20.57 | |
% 140.93/20.57 | | (5) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1
% 140.93/20.57 | | & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (5) implies:
% 140.93/20.57 | | (6) op(e1, e1) = e3
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #77.
% 140.93/20.57 | |
% 140.93/20.57 | Case 2:
% 140.93/20.57 | |
% 140.93/20.57 | | (7) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1
% 140.93/20.57 | | & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)
% 140.93/20.57 | |
% 140.93/20.57 | | ALPHA: (7) implies:
% 140.93/20.57 | | (8) op(e1, e1) = e3
% 140.93/20.57 | |
% 140.93/20.57 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #77.
% 140.93/20.57 | |
% 140.93/20.57 | End of split
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #77 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (2) op(e1, e1) = e3
% 140.93/20.57 (3) op(e1, e1) = e2
% 140.93/20.57 (4) ~ (e3 = e2)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (1) with e2, e3, e1, e1, simplifying with (2), (3)
% 140.93/20.57 | gives:
% 140.93/20.57 | (5) e3 = e2
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (5) imply:
% 140.93/20.57 | (6) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (6) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #78 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) all_57_7 = e2 & op(e1, e2) = e2
% 140.93/20.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (3) op(e1, e2) = all_52_6
% 140.93/20.57 (4) ~ (all_52_6 = e2)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (1) implies:
% 140.93/20.57 | (5) op(e1, e2) = e2
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (2) with all_52_6, e2, e2, e1, simplifying with
% 140.93/20.57 | (3), (5) gives:
% 140.93/20.57 | (6) all_52_6 = e2
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (6) imply:
% 140.93/20.57 | (7) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (7) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #79 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) all_57_6 = e2 & op(e1, e3) = e2
% 140.93/20.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (3) op(e1, e3) = all_52_2
% 140.93/20.57 (4) ~ (all_52_2 = e2)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (1) implies:
% 140.93/20.57 | (5) op(e1, e3) = e2
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (2) with all_52_2, e2, e3, e1, simplifying with
% 140.93/20.57 | (3), (5) gives:
% 140.93/20.57 | (6) all_52_2 = e2
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (6) imply:
% 140.93/20.57 | (7) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (7) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #80 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) all_57_13 = e3 & op(e0, e2) = e3
% 140.93/20.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (3) op(e0, e2) = all_52_7
% 140.93/20.57 (4) ~ (all_52_7 = e3)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (1) implies:
% 140.93/20.57 | (5) op(e0, e2) = e3
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (2) with all_52_7, e3, e2, e0, simplifying with
% 140.93/20.57 | (3), (5) gives:
% 140.93/20.57 | (6) all_52_7 = e3
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (6) imply:
% 140.93/20.57 | (7) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (7) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #81 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) all_57_10 = e3 & op(e2, e0) = e3
% 140.93/20.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (3) op(e2, e0) = all_52_13
% 140.93/20.57 (4) ~ (all_52_13 = e3)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (1) implies:
% 140.93/20.57 | (5) op(e2, e0) = e3
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (2) with all_52_13, e3, e0, e2, simplifying with
% 140.93/20.57 | (3), (5) gives:
% 140.93/20.57 | (6) all_52_13 = e3
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (6) imply:
% 140.93/20.57 | (7) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (7) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #82 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 140.93/20.57 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (3) op(e0, e0) = e1
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | ALPHA: (1) implies:
% 140.93/20.57 | (4) ~ (all_56_15 = e1)
% 140.93/20.57 | (5) op(e0, e0) = all_56_15
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (2) with e1, all_56_15, e0, e0, simplifying with
% 140.93/20.57 | (3), (5) gives:
% 140.93/20.57 | (6) all_56_15 = e1
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (6) imply:
% 140.93/20.57 | (7) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (7) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #83 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.57 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.57 (2) op(e0, e0) = all_10_2
% 140.93/20.57 (3) op(e0, e0) = e3
% 140.93/20.57 (4) ~ (all_10_2 = e3)
% 140.93/20.57
% 140.93/20.57 Begin of proof
% 140.93/20.57 |
% 140.93/20.57 | GROUND_INST: instantiating (1) with all_10_2, e3, e0, e0, simplifying with
% 140.93/20.57 | (2), (3) gives:
% 140.93/20.57 | (5) all_10_2 = e3
% 140.93/20.57 |
% 140.93/20.57 | REDUCE: (4), (5) imply:
% 140.93/20.57 | (6) $false
% 140.93/20.57 |
% 140.93/20.57 | CLOSE: (6) is inconsistent.
% 140.93/20.57 |
% 140.93/20.57 End of proof
% 140.93/20.57
% 140.93/20.57 Sub-proof #84 shows that the following formulas are inconsistent:
% 140.93/20.57 ----------------------------------------------------------------
% 140.93/20.57 (1) all_26_2 = e3
% 140.93/20.57 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 140.93/20.57 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 140.93/20.57 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 140.93/20.57 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 140.93/20.57 (4) op(e1, e3) = all_52_2
% 140.93/20.57 (5) op(e1, e1) = e3
% 140.93/20.57 (6) op(e1, e2) = all_52_6
% 140.93/20.57 (7) ~ (all_52_8 = e3)
% 140.93/20.57 (8) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 140.93/20.57 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 140.93/20.57 (9) ~ (all_52_4 = e1)
% 140.93/20.57 (10) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 140.93/20.57 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 140.93/20.57 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 140.93/20.57 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 140.93/20.57 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 140.93/20.57 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 140.93/20.57 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 140.93/20.57 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 140.93/20.57 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 140.93/20.57 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 140.93/20.57 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.93/20.57 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 140.93/20.57 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 140.93/20.57 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.93/20.57 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.93/20.57 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 140.93/20.57 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 140.93/20.57 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 140.93/20.57 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 140.93/20.57 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 140.93/20.57 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 140.93/20.57 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 140.93/20.57 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 140.93/20.57 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 140.93/20.57 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 140.93/20.57 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 140.93/20.57 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 140.93/20.57 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 140.93/20.57 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 140.93/20.57 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 140.93/20.57 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 140.93/20.57 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 140.93/20.57 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 140.93/20.57 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 140.93/20.57 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 140.93/20.57 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 140.93/20.57 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 140.93/20.57 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 140.93/20.57 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 140.93/20.57 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 140.93/20.57 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 140.93/20.57 (11) all_57_12 = e3
% 140.93/20.57 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 140.93/20.57 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 140.93/20.57 e1)
% 140.93/20.57 (13) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 140.93/20.57 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 140.93/20.57 (14) ~ (e3 = e0)
% 140.93/20.57 (15) op(e1, e1) = all_4_2
% 140.93/20.57 (16) ~ (all_52_4 = e3)
% 140.93/20.57 (17) ~ (all_52_8 = e1)
% 140.93/20.57 (18) op(e3, e1) = all_52_8
% 140.93/20.57 (19) ~ (all_52_12 = all_52_14)
% 140.93/20.57 (20) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 140.93/20.57 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 140.93/20.57 (21) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 140.93/20.57 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 140.93/20.57 e2)
% 140.93/20.57 (22) ~ (all_52_12 = e1)
% 140.93/20.57 (23) op(e0, e0) = all_10_2
% 140.93/20.57 (24) ~ (all_52_8 = all_52_12)
% 140.93/20.57 (25) ~ (e1 = e0)
% 140.93/20.57 (26) op(e3, e2) = all_52_4
% 140.93/20.57 (27) ~ (all_52_7 = all_52_11)
% 140.93/20.57 (28) ~ (e2 = e0)
% 140.93/20.57 (29) op(e0, e1) = all_52_11
% 140.93/20.57 (30) op(e3, e0) = all_52_12
% 140.93/20.57 (31) ~ (all_52_2 = e1)
% 140.93/20.57 (32) op(e2, e2) = e3
% 140.93/20.57 (33) op(e3, e3) = e1
% 140.93/20.57 (34) ~ (all_4_2 = e2)
% 140.93/20.57 (35) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 140.93/20.57 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 140.93/20.57 & $i(all_6_1))
% 140.93/20.57 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 140.93/20.58 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 140.93/20.58 (37) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 140.93/20.58 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 140.93/20.58 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 140.93/20.58 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 140.93/20.58 (38) ~ (all_52_9 = e3)
% 140.93/20.58 (39) ~ (e3 = e1)
% 140.93/20.58 (40) op(e0, e2) = all_52_7
% 140.93/20.58 (41) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 140.93/20.58 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 140.93/20.58 (42) all_57_3 = e3
% 140.93/20.58 (43) op(e2, e1) = all_52_9
% 140.93/20.58 (44) ~ (all_52_4 = all_52_12)
% 140.93/20.58 (45) ~ (all_26_2 = e3) | ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 &
% 140.93/20.58 op(e2, e3) = all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 =
% 140.93/20.58 e0) & op(e2, e3) = all_26_1 & $i(all_26_1))
% 140.93/20.58 (46) op(e1, e0) = all_52_14
% 140.93/20.58 (47) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 140.93/20.58 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 140.93/20.58
% 140.93/20.58 Begin of proof
% 140.93/20.58 |
% 140.93/20.58 | BETA: splitting (41) gives:
% 140.93/20.58 |
% 140.93/20.58 | Case 1:
% 140.93/20.58 | |
% 140.93/20.58 | | (48) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 140.93/20.58 | | e3)
% 140.93/20.58 | |
% 140.93/20.58 | | REF_CLOSE: (16), (26), (33), (36), (39), (48) are inconsistent by sub-proof
% 140.93/20.58 | | #244.
% 140.93/20.58 | |
% 140.93/20.58 | Case 2:
% 140.93/20.58 | |
% 140.93/20.58 | | (49) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 140.93/20.58 | | e3)
% 140.93/20.58 | |
% 140.93/20.58 | | BETA: splitting (49) gives:
% 140.93/20.58 | |
% 140.93/20.58 | | Case 1:
% 140.93/20.58 | | |
% 140.93/20.58 | | | (50) all_57_4 = e3 & op(e3, e1) = e3
% 140.93/20.58 | | |
% 140.93/20.58 | | | ALPHA: (50) implies:
% 140.93/20.58 | | | (51) op(e3, e1) = e3
% 140.93/20.58 | | |
% 140.93/20.58 | | | REF_CLOSE: (7), (18), (36), (51) are inconsistent by sub-proof #1106.
% 140.93/20.58 | | |
% 140.93/20.58 | | Case 2:
% 140.93/20.58 | | |
% 140.93/20.58 | | | (52) all_57_9 = e3 & op(e3, e0) = e3
% 140.93/20.58 | | |
% 140.93/20.58 | | | ALPHA: (52) implies:
% 140.93/20.58 | | | (53) all_57_9 = e3
% 140.93/20.58 | | | (54) op(e3, e0) = e3
% 140.93/20.58 | | |
% 140.93/20.58 | | | GROUND_INST: instantiating (36) with all_52_12, e3, e0, e3, simplifying
% 140.93/20.58 | | | with (30), (54) gives:
% 140.93/20.58 | | | (55) all_52_12 = e3
% 140.93/20.58 | | |
% 140.93/20.58 | | | REDUCE: (19), (55) imply:
% 140.93/20.58 | | | (56) ~ (all_52_14 = e3)
% 140.93/20.58 | | |
% 140.93/20.58 | | | SIMP: (56) implies:
% 140.93/20.58 | | | (57) ~ (all_52_14 = e3)
% 140.93/20.58 | | |
% 140.93/20.58 | | | BETA: splitting (10) gives:
% 140.93/20.58 | | |
% 140.93/20.58 | | | Case 1:
% 140.93/20.58 | | | |
% 140.93/20.58 | | | | (58) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 140.93/20.58 | | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 140.93/20.58 | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 140.93/20.58 | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.93/20.58 | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 140.93/20.58 | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.93/20.58 | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 140.93/20.58 | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 140.93/20.58 | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 140.93/20.58 | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 140.93/20.58 | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 140.93/20.58 | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 140.93/20.58 | | | | $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 140.93/20.58 | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 140.93/20.58 | | | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 140.93/20.58 | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 140.93/20.58 | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 140.93/20.58 | | | | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2)
% 140.93/20.58 | | | | = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 140.93/20.58 | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | (
% 140.93/20.58 | | | | ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)))
% 140.93/20.58 | | | | & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 140.93/20.58 | | | | op(e0, e2) = all_56_12 & $i(all_56_12))))
% 140.93/20.58 | | | |
% 140.93/20.58 | | | | BETA: splitting (58) gives:
% 140.93/20.58 | | | |
% 140.93/20.58 | | | | Case 1:
% 140.93/20.58 | | | | |
% 140.93/20.58 | | | | | (59) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 140.93/20.58 | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 140.93/20.58 | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 140.93/20.58 | | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 140.93/20.58 | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 140.93/20.58 | | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 140.93/20.58 | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 140.93/20.58 | | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 140.93/20.58 | | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 140.93/20.58 | | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 140.93/20.58 | | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 140.93/20.58 | | | | | all_56_10 & $i(all_56_10)))
% 140.93/20.58 | | | | |
% 140.93/20.58 | | | | | REF_CLOSE: (4), (5), (31), (36), (59) are inconsistent by sub-proof
% 140.93/20.58 | | | | | #214.
% 140.93/20.58 | | | | |
% 140.93/20.58 | | | | Case 2:
% 140.93/20.58 | | | | |
% 140.93/20.58 | | | | | (60) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 140.93/20.58 | | | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 140.93/20.58 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) =
% 140.93/20.58 | | | | | e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 140.93/20.58 | | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 140.93/20.58 | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 140.93/20.58 | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) &
% 140.93/20.58 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 =
% 140.93/20.58 | | | | | e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 140.93/20.58 | | | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0)
% 140.93/20.58 | | | | | = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 140.93/20.58 | | | | | $i(all_56_12)))
% 140.93/20.58 | | | | |
% 140.93/20.58 | | | | | ALPHA: (60) implies:
% 140.93/20.58 | | | | | (61) op(e2, e2) = all_56_11
% 140.93/20.58 | | | | | (62) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 140.93/20.58 | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 140.93/20.58 | | | | | (63) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) &
% 140.93/20.58 | | | | | op(e1, e2) = all_56_7 & $i(all_56_7))
% 140.93/20.58 | | | | | (64) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) &
% 140.93/20.58 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 140.93/20.58 | | | | | (65) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 140.93/20.58 | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))
% 141.03/20.58 | | | | | (66) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 141.03/20.58 | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))
% 141.03/20.58 | | | | | (67) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) &
% 141.03/20.58 | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.03/20.58 | | | | |
% 141.03/20.58 | | | | | BETA: splitting (67) gives:
% 141.03/20.58 | | | | |
% 141.03/20.58 | | | | | Case 1:
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | (68) all_56_0 = e3 & op(e3, e2) = e3
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | ALPHA: (68) implies:
% 141.03/20.58 | | | | | | (69) op(e3, e2) = e3
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | REF_CLOSE: (16), (26), (36), (69) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | #1107.
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | Case 2:
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | (70) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | ALPHA: (70) implies:
% 141.03/20.58 | | | | | | (71) ~ (all_56_9 = e2)
% 141.03/20.58 | | | | | | (72) op(e3, e3) = all_56_9
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | BETA: splitting (65) gives:
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | | Case 1:
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | (73) all_56_9 = e2 & op(e3, e3) = e2
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | ALPHA: (73) implies:
% 141.03/20.58 | | | | | | | (74) all_56_9 = e2
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | REF_CLOSE: (16), (26), (36), (67), (74) are inconsistent by
% 141.03/20.58 | | | | | | | sub-proof #345.
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | Case 2:
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | (75) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0)
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | ALPHA: (75) implies:
% 141.03/20.58 | | | | | | | (76) op(e3, e2) = all_56_0
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | BETA: splitting (63) gives:
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | (77) all_56_13 = e2 & op(e1, e1) = e2
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | ALPHA: (77) implies:
% 141.03/20.58 | | | | | | | | (78) op(e1, e1) = e2
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | REF_CLOSE: (15), (34), (36), (78) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | #1124.
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | (79) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.03/20.58 | | | | | | | | $i(all_56_7)
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | ALPHA: (79) implies:
% 141.03/20.58 | | | | | | | | (80) ~ (all_56_7 = e1)
% 141.03/20.58 | | | | | | | | (81) op(e1, e2) = all_56_7
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | BETA: splitting (66) gives:
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | (82) all_56_7 = e1 & op(e1, e2) = e1
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | ALPHA: (82) implies:
% 141.03/20.58 | | | | | | | | | (83) op(e1, e2) = e1
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | REF_CLOSE: (36), (80), (81), (83) are inconsistent by
% 141.03/20.58 | | | | | | | | | sub-proof #422.
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | (84) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.03/20.58 | | | | | | | | | $i(all_56_13)
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | ALPHA: (84) implies:
% 141.03/20.58 | | | | | | | | | (85) ~ (all_56_13 = e2)
% 141.03/20.58 | | | | | | | | | (86) op(e1, e1) = all_56_13
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | GROUND_INST: instantiating (36) with e3, all_56_13, e1, e1,
% 141.03/20.58 | | | | | | | | | simplifying with (5), (86) gives:
% 141.03/20.58 | | | | | | | | | (87) all_56_13 = e3
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | GROUND_INST: instantiating (36) with all_52_6, all_56_7, e2,
% 141.03/20.58 | | | | | | | | | e1, simplifying with (6), (81) gives:
% 141.03/20.58 | | | | | | | | | (88) all_56_7 = all_52_6
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | GROUND_INST: instantiating (36) with e3, all_56_11, e2, e2,
% 141.03/20.58 | | | | | | | | | simplifying with (32), (61) gives:
% 141.03/20.58 | | | | | | | | | (89) all_56_11 = e3
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | GROUND_INST: instantiating (36) with all_52_4, all_56_0, e2,
% 141.03/20.58 | | | | | | | | | e3, simplifying with (26), (76) gives:
% 141.03/20.58 | | | | | | | | | (90) all_56_0 = all_52_4
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | GROUND_INST: instantiating (36) with e1, all_56_9, e3, e3,
% 141.03/20.58 | | | | | | | | | simplifying with (33), (72) gives:
% 141.03/20.58 | | | | | | | | | (91) all_56_9 = e1
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | REDUCE: (80), (88) imply:
% 141.03/20.58 | | | | | | | | | (92) ~ (all_52_6 = e1)
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | REDUCE: (71), (91) imply:
% 141.03/20.58 | | | | | | | | | (93) ~ (e2 = e1)
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | SIMP: (93) implies:
% 141.03/20.58 | | | | | | | | | (94) ~ (e2 = e1)
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | REDUCE: (85), (87) imply:
% 141.03/20.58 | | | | | | | | | (95) ~ (e3 = e2)
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | BETA: splitting (2) gives:
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | (96) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 141.03/20.58 | | | | | | | | | | op(e2, e2) = e1)
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | BETA: splitting (96) gives:
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | (97) all_57_1 = e1 & op(e3, e2) = e1
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | REF_CLOSE: (9), (26), (36), (97) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | sub-proof #844.
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | (98) all_57_3 = e1 & op(e2, e2) = e1
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | REF_CLOSE: (39), (42), (98) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | #163.
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | (99) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1
% 141.03/20.58 | | | | | | | | | | & op(e0, e2) = e1)
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | BETA: splitting (99) gives:
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | (100) all_57_7 = e1 & op(e1, e2) = e1
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | ALPHA: (100) implies:
% 141.03/20.58 | | | | | | | | | | | (101) op(e1, e2) = e1
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | REF_CLOSE: (6), (36), (92), (101) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | sub-proof #341.
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | (102) all_57_13 = e1 & op(e0, e2) = e1
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | ALPHA: (102) implies:
% 141.03/20.58 | | | | | | | | | | | (103) all_57_13 = e1
% 141.03/20.58 | | | | | | | | | | | (104) op(e0, e2) = e1
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | BETA: splitting (8) gives:
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | (105) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 141.03/20.58 | | | | | | | | | | | | & op(e1, e2) = e1)
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | REF_CLOSE: (4), (6), (31), (36), (92), (105) are inconsistent
% 141.03/20.58 | | | | | | | | | | | | by sub-proof #85.
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | (106) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 141.03/20.58 | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | BETA: splitting (106) gives:
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | (107) all_57_8 = e1 & op(e1, e1) = e1
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | ALPHA: (107) implies:
% 141.03/20.58 | | | | | | | | | | | | | (108) op(e1, e1) = e1
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | REF_CLOSE: (5), (36), (39), (108) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | | | sub-proof #1096.
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | (109) all_57_11 = e1 & op(e1, e0) = e1
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | ALPHA: (109) implies:
% 141.03/20.58 | | | | | | | | | | | | | (110) op(e1, e0) = e1
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_52_7, e1, e2, e0,
% 141.03/20.58 | | | | | | | | | | | | | simplifying with (40), (104) gives:
% 141.03/20.58 | | | | | | | | | | | | | (111) all_52_7 = e1
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_52_14, e1, e0, e1,
% 141.03/20.58 | | | | | | | | | | | | | simplifying with (46), (110) gives:
% 141.03/20.58 | | | | | | | | | | | | | (112) all_52_14 = e1
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | REDUCE: (27), (111) imply:
% 141.03/20.58 | | | | | | | | | | | | | (113) ~ (all_52_11 = e1)
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | SIMP: (113) implies:
% 141.03/20.58 | | | | | | | | | | | | | (114) ~ (all_52_11 = e1)
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | REDUCE: (57), (112) imply:
% 141.03/20.58 | | | | | | | | | | | | | (115) ~ (e3 = e1)
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | BETA: splitting (20) gives:
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | (116) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1
% 141.03/20.58 | | | | | | | | | | | | | | & op(e2, e1) = e1)
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | BETA: splitting (116) gives:
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | (117) all_57_4 = e1 & op(e3, e1) = e1
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | REF_CLOSE: (17), (18), (36), (117) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | | | | | sub-proof #349.
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | (118) all_57_5 = e1 & op(e2, e1) = e1
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | ALPHA: (118) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | (119) all_57_5 = e1
% 141.03/20.58 | | | | | | | | | | | | | | | (120) op(e2, e1) = e1
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | (121) all_56_12 = e0 & op(e0, e2) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | ALPHA: (121) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | (122) op(e0, e2) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, e0, e2, e0,
% 141.03/20.58 | | | | | | | | | | | | | | | | simplifying with (104), (122) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | (123) e1 = e0
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | REDUCE: (25), (123) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | (124) $false
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | CLOSE: (124) is inconsistent.
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | (125) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.03/20.58 | | | | | | | | | | | | | | | | $i(all_56_15)
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | ALPHA: (125) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | (126) ~ (all_56_15 = e2)
% 141.03/20.58 | | | | | | | | | | | | | | | | (127) op(e0, e0) = all_56_15
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | BETA: splitting (62) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | (128) all_56_15 = e2 & op(e0, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (129) all_56_15 = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | REDUCE: (126), (129) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (130) $false
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | CLOSE: (130) is inconsistent.
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | (131) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.03/20.58 | | | | | | | | | | | | | | | | | $i(all_56_12)
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (132) ~ (all_56_12 = e0)
% 141.03/20.58 | | | | | | | | | | | | | | | | | (133) op(e0, e2) = all_56_12
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_10_2, all_56_15, e0,
% 141.03/20.58 | | | | | | | | | | | | | | | | | e0, simplifying with (23), (127) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (134) all_56_15 = all_10_2
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, all_56_12, e2, e0,
% 141.03/20.58 | | | | | | | | | | | | | | | | | simplifying with (104), (133) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (135) all_56_12 = e1
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_52_9, e1, e1, e2,
% 141.03/20.58 | | | | | | | | | | | | | | | | | simplifying with (43), (120) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (136) all_52_9 = e1
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | REDUCE: (126), (134) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | (137) ~ (all_10_2 = e2)
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | BETA: splitting (21) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | (138) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 141.03/20.58 | | | | | | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | BETA: splitting (138) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (139) all_57_12 = e2 & op(e0, e3) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | ALPHA: (139) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (140) all_57_12 = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (95), (140) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | #772.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (141) all_57_13 = e2 & op(e0, e2) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | ALPHA: (141) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (142) all_57_13 = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (94), (103), (142) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | #1057.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | (143) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 141.03/20.58 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (144) all_57_14 = e2 & op(e0, e1) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | ALPHA: (144) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (145) all_57_14 = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | (146) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (146) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (147) all_57_9 = e2 & op(e3, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (148) all_57_9 = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (53), (95), (148) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | #581.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (149) all_57_10 = e2 & op(e2, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (149) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (150) all_57_10 = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | (151) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (151) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | (152) all_57_2 = e0 & op(e2, e3) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (152) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | (153) op(e2, e3) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | (154) ~ (all_26_2 = e3)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (1), (154) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | (155) $false
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (155) is inconsistent.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | (156) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = all_26_1 & $i(all_26_0) &
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | = all_26_1 & $i(all_26_1))
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | (157) ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 &
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_26_1 & $i(all_26_0) &
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | (158) ~ (all_26_0 = e1)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | (159) op(e2, e3) = all_26_1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | (160) op(all_26_1, e2) = all_26_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (161) ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 &
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | op(e2, e3) = all_6_1 & $i(all_6_0) & $i(all_6_1)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (162) op(e2, e3) = all_6_1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (163) op(all_6_1, e2) = all_6_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_6_1, all_26_1, e3, e2,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (159), (162) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (164) all_26_1 = all_6_1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e0, all_26_1, e3, e2,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (153), (159) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (165) all_26_1 = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (164), (165) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (166) all_6_1 = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (165) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (167) op(e0, e2) = all_26_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (166) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (168) op(e0, e2) = all_6_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, all_26_0, e2, e0,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (104), (167) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (169) all_26_0 = e1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_6_0, all_26_0, e2, e0,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (167), (168) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (170) all_26_0 = all_6_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (169), (170) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (171) all_6_0 = e1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (169) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (172) $false
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (172) is inconsistent.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (173) ~ (all_6_1 = e1) & op(e2, e3) = all_6_1 &
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_6_1)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (174) op(e2, e3) = all_6_1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with all_6_1, all_26_1, e3, e2,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (159), (174) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (175) all_26_1 = all_6_1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e0, all_26_1, e3, e2,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (153), (159) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (176) all_26_1 = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (175), (176) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (177) all_6_1 = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (160), (176) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (178) op(e0, e2) = all_26_0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (36) with e1, all_26_0, e2, e0,
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | simplifying with (104), (178) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (179) all_26_0 = e1
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | REDUCE: (158), (179) imply:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | (180) $false
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | | CLOSE: (180) is inconsistent.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | (181) ~ (all_26_1 = e0) & op(e2, e3) = all_26_1 &
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | $i(all_26_1)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (153), (181) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | | #146.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | (182) all_57_3 = e0 & op(e2, e2) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (182) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | (183) op(e2, e2) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (32), (36), (183) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1119.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | (184) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (184) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | (185) all_57_5 = e0 & op(e2, e1) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (119), (185) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | #264.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | (186) all_57_10 = e0 & op(e2, e0) = e0
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (150), (186) are inconsistent by sub-proof
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | | #563.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | (187) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | BETA: splitting (187) gives:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (188) all_57_11 = e2 & op(e1, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (189) op(e1, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (36), (94), (110), (189) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | sub-proof #139.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (190) all_57_15 = e2 & op(e0, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (191) op(e0, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (12), (14), (25), (28), (36), (37), (39),
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | (94), (95), (103), (145), (191) are inconsistent
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | | by sub-proof #800.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (192) all_57_15 = e2 & op(e0, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | (193) op(e0, e0) = e2
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (23), (36), (137), (193) are inconsistent by
% 141.03/20.58 | | | | | | | | | | | | | | | | | | | sub-proof #1115.
% 141.03/20.58 | | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | Case 2:
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | (194) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 =
% 141.03/20.58 | | | | | | | | | | | | | | e1 & op(e0, e1) = e1)
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | | REF_CLOSE: (5), (29), (36), (39), (114), (194) are
% 141.03/20.58 | | | | | | | | | | | | | | inconsistent by sub-proof #193.
% 141.03/20.58 | | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | | |
% 141.03/20.58 | | | | | | | | | End of split
% 141.03/20.58 | | | | | | | | |
% 141.03/20.58 | | | | | | | | End of split
% 141.03/20.58 | | | | | | | |
% 141.03/20.58 | | | | | | | End of split
% 141.03/20.58 | | | | | | |
% 141.03/20.58 | | | | | | End of split
% 141.03/20.58 | | | | | |
% 141.03/20.58 | | | | | End of split
% 141.03/20.58 | | | | |
% 141.03/20.58 | | | | End of split
% 141.03/20.58 | | | |
% 141.03/20.58 | | | Case 2:
% 141.03/20.58 | | | |
% 141.03/20.59 | | | | (195) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.03/20.59 | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 141.03/20.59 | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.03/20.59 | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 141.03/20.59 | | | | ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.03/20.59 | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | (
% 141.03/20.59 | | | | ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.03/20.59 | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | (
% 141.03/20.59 | | | | ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 141.03/20.59 | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) | (
% 141.03/20.59 | | | | ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.03/20.59 | | | | $i(all_56_14)))) | (op(e0, e0) = all_56_15 &
% 141.03/20.59 | | | | $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 141.03/20.59 | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.03/20.59 | | | | & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 141.03/20.59 | | | | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 =
% 141.03/20.59 | | | | e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.03/20.59 | | | | = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.03/20.59 | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2
% 141.03/20.59 | | | | & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) |
% 141.03/20.59 | | | | ( ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.03/20.59 | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | (
% 141.03/20.59 | | | | ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.03/20.59 | | | | $i(all_56_8))))
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | BETA: splitting (195) gives:
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | Case 1:
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | (196) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.03/20.59 | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 141.03/20.59 | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.03/20.59 | | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 141.03/20.59 | | | | | ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.03/20.59 | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | (
% 141.03/20.59 | | | | | ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.03/20.59 | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | (
% 141.03/20.59 | | | | | ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 141.03/20.59 | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) | (
% 141.03/20.59 | | | | | ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.03/20.59 | | | | | $i(all_56_14)))
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | ALPHA: (196) implies:
% 141.03/20.59 | | | | | (197) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) &
% 141.03/20.59 | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | REF_CLOSE: (7), (18), (33), (36), (197) are inconsistent by sub-proof
% 141.03/20.59 | | | | | #295.
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | Case 2:
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | (198) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 141.03/20.59 | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 141.03/20.59 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 141.03/20.59 | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 141.03/20.59 | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 141.03/20.59 | | | | | ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.03/20.59 | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | (
% 141.03/20.59 | | | | | ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.03/20.59 | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | (
% 141.03/20.59 | | | | | ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.03/20.59 | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | (
% 141.03/20.59 | | | | | ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.03/20.59 | | | | | $i(all_56_8)))
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | ALPHA: (198) implies:
% 141.03/20.59 | | | | | (199) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) &
% 141.03/20.59 | | | | | op(e3, e0) = all_56_2 & $i(all_56_2))
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | BETA: splitting (199) gives:
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | Case 1:
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | (200) all_56_9 = e0 & op(e3, e3) = e0
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | ALPHA: (200) implies:
% 141.03/20.59 | | | | | | (201) op(e3, e3) = e0
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | REF_CLOSE: (25), (33), (36), (201) are inconsistent by sub-proof
% 141.03/20.59 | | | | | | #840.
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | Case 2:
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | (202) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2)
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | ALPHA: (202) implies:
% 141.03/20.59 | | | | | | (203) ~ (all_56_2 = e3)
% 141.03/20.59 | | | | | | (204) op(e3, e0) = all_56_2
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | REF_CLOSE: (36), (54), (203), (204) are inconsistent by sub-proof
% 141.03/20.59 | | | | | | #274.
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | End of split
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | End of split
% 141.03/20.59 | | | |
% 141.03/20.59 | | | End of split
% 141.03/20.59 | | |
% 141.03/20.59 | | End of split
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #85 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) op(e1, e3) = all_52_2
% 141.03/20.59 (2) op(e1, e2) = all_52_6
% 141.03/20.59 (3) ~ (all_52_6 = e1)
% 141.03/20.59 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 141.03/20.59 (5) ~ (all_52_2 = e1)
% 141.03/20.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (4) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (7) all_57_6 = e1 & op(e1, e3) = e1
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (7) implies:
% 141.03/20.59 | | (8) op(e1, e3) = e1
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #332.
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.59 | | (9) all_57_7 = e1 & op(e1, e2) = e1
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (9) implies:
% 141.03/20.59 | | (10) op(e1, e2) = e1
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #341.
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #86 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) ~ (all_52_14 = e3)
% 141.03/20.59 (2) ~ (e3 = e2)
% 141.03/20.59 (3) op(e0, e0) = e2
% 141.03/20.59 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (5) op(e1, e0) = all_52_14
% 141.03/20.59 (6) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (6) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #160.
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.59 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (8) implies:
% 141.03/20.59 | | (9) op(e0, e0) = e3
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1066.
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #87 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) op(e1, e3) = all_8_1
% 141.03/20.59 (2) ~ (all_12_1 = e0)
% 141.03/20.59 (3) op(e1, e3) = e0
% 141.03/20.59 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (5) op(e1, e3) = all_12_1
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | GROUND_INST: instantiating (4) with all_8_1, all_12_1, e3, e1, simplifying
% 141.03/20.59 | with (1), (5) gives:
% 141.03/20.59 | (6) all_12_1 = all_8_1
% 141.03/20.59 |
% 141.03/20.59 | GROUND_INST: instantiating (4) with e0, all_12_1, e3, e1, simplifying with
% 141.03/20.59 | (3), (5) gives:
% 141.03/20.59 | (7) all_12_1 = e0
% 141.03/20.59 |
% 141.03/20.59 | COMBINE_EQS: (6), (7) imply:
% 141.03/20.59 | (8) all_8_1 = e0
% 141.03/20.59 |
% 141.03/20.59 | REDUCE: (2), (7) imply:
% 141.03/20.59 | (9) $false
% 141.03/20.59 |
% 141.03/20.59 | CLOSE: (9) is inconsistent.
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #88 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) op(e1, e3) = all_8_1
% 141.03/20.59 (2) op(all_12_1, e1) = all_12_0
% 141.03/20.59 (3) op(e0, e1) = e2
% 141.03/20.59 (4) op(e1, e3) = e0
% 141.03/20.59 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (6) ~ (all_12_0 = e2)
% 141.03/20.59 (7) op(e1, e3) = all_12_1
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | GROUND_INST: instantiating (5) with e0, all_12_1, e3, e1, simplifying with
% 141.03/20.59 | (4), (7) gives:
% 141.03/20.59 | (8) all_12_1 = e0
% 141.03/20.59 |
% 141.03/20.59 | GROUND_INST: instantiating (5) with all_8_1, all_12_1, e3, e1, simplifying
% 141.03/20.59 | with (1), (7) gives:
% 141.03/20.59 | (9) all_12_1 = all_8_1
% 141.03/20.59 |
% 141.03/20.59 | COMBINE_EQS: (8), (9) imply:
% 141.03/20.59 | (10) all_8_1 = e0
% 141.03/20.59 |
% 141.03/20.59 | REDUCE: (2), (8) imply:
% 141.03/20.59 | (11) op(e0, e1) = all_12_0
% 141.03/20.59 |
% 141.03/20.59 | GROUND_INST: instantiating (5) with e2, all_12_0, e1, e0, simplifying with
% 141.03/20.59 | (3), (11) gives:
% 141.03/20.59 | (12) all_12_0 = e2
% 141.03/20.59 |
% 141.03/20.59 | REDUCE: (6), (12) imply:
% 141.03/20.59 | (13) $false
% 141.03/20.59 |
% 141.03/20.59 | CLOSE: (13) is inconsistent.
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #89 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) all_57_10 = e2
% 141.03/20.59 (2) ~ (all_52_8 = e3)
% 141.03/20.59 (3) all_56_9 = e2
% 141.03/20.59 (4) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.03/20.59 all_56_11 & $i(all_56_11))
% 141.03/20.59 (5) ~ (all_52_9 = e2)
% 141.03/20.59 (6) all_56_11 = e3
% 141.03/20.59 (7) op(e3, e1) = all_52_8
% 141.03/20.59 (8) all_57_9 = e3
% 141.03/20.59 (9) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.03/20.59 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (11) op(e2, e1) = all_52_9
% 141.03/20.59 (12) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 all_56_9 & $i(all_56_9))
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (9) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (13) all_57_9 = e1 & op(e3, e0) = e1
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (13) implies:
% 141.03/20.59 | | (14) all_57_9 = e1
% 141.03/20.59 | |
% 141.03/20.59 | | COMBINE_EQS: (8), (14) imply:
% 141.03/20.59 | | (15) e3 = e1
% 141.03/20.59 | |
% 141.03/20.59 | | COMBINE_EQS: (6), (15) imply:
% 141.03/20.59 | | (16) all_56_11 = e1
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (4), (5), (10), (11), (16) are inconsistent by sub-proof #91.
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.59 | | (17) all_57_10 = e1 & op(e2, e0) = e1
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (1), (2), (3), (7), (10), (12), (17) are inconsistent by
% 141.03/20.59 | | sub-proof #90.
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #90 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) all_57_10 = e2
% 141.03/20.59 (2) ~ (all_52_8 = e3)
% 141.03/20.59 (3) all_56_9 = e2
% 141.03/20.59 (4) op(e3, e1) = all_52_8
% 141.03/20.59 (5) all_57_10 = e1 & op(e2, e0) = e1
% 141.03/20.59 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (7) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 all_56_9 & $i(all_56_9))
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | ALPHA: (5) implies:
% 141.03/20.59 | (8) all_57_10 = e1
% 141.03/20.59 |
% 141.03/20.59 | COMBINE_EQS: (1), (8) imply:
% 141.03/20.59 | (9) e2 = e1
% 141.03/20.59 |
% 141.03/20.59 | SIMP: (9) implies:
% 141.03/20.59 | (10) e2 = e1
% 141.03/20.59 |
% 141.03/20.59 | COMBINE_EQS: (3), (10) imply:
% 141.03/20.59 | (11) all_56_9 = e1
% 141.03/20.59 |
% 141.03/20.59 | REF_CLOSE: (2), (4), (6), (7), (11) are inconsistent by sub-proof #898.
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #91 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.03/20.59 all_56_11 & $i(all_56_11))
% 141.03/20.59 (2) ~ (all_52_9 = e2)
% 141.03/20.59 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (4) op(e2, e1) = all_52_9
% 141.03/20.59 (5) all_56_11 = e1
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (1) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (6) all_56_4 = e2 & op(e2, e1) = e2
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (6) implies:
% 141.03/20.59 | | (7) op(e2, e1) = e2
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #890.
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.59 | | (8) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (8) implies:
% 141.03/20.59 | | (9) ~ (all_56_11 = e1)
% 141.03/20.59 | |
% 141.03/20.59 | | REDUCE: (5), (9) imply:
% 141.03/20.59 | | (10) $false
% 141.03/20.59 | |
% 141.03/20.59 | | CLOSE: (10) is inconsistent.
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #92 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.03/20.59 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.03/20.59 (2) ~ (all_52_8 = e3)
% 141.03/20.59 (3) ~ (e2 = e1)
% 141.03/20.59 (4) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.03/20.59 all_56_11 & $i(all_56_11))
% 141.03/20.59 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.03/20.59 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.03/20.59 (6) op(e3, e3) = e2
% 141.03/20.59 (7) ~ (e3 = e0)
% 141.03/20.59 (8) op(e1, e1) = all_4_2
% 141.03/20.59 (9) op(e3, e1) = all_52_8
% 141.03/20.59 (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.03/20.59 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.03/20.59 (11) ~ (e1 = e0)
% 141.03/20.59 (12) ~ (e2 = e0)
% 141.03/20.59 (13) ~ (e3 = e2)
% 141.03/20.59 (14) op(e2, e2) = e3
% 141.03/20.59 (15) ~ (all_4_2 = e2)
% 141.03/20.59 (16) op(e0, e0) = e2
% 141.03/20.59 (17) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.03/20.59 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.03/20.59 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (19) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.03/20.59 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.03/20.59 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.03/20.59 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.03/20.59 (20) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.03/20.59 all_56_4 & $i(all_56_4))
% 141.03/20.59 (21) ~ (e3 = e1)
% 141.03/20.59 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.03/20.59 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.03/20.59 (23) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.03/20.59 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.03/20.59 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.03/20.59 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.03/20.59 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.03/20.59 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.03/20.59 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.03/20.59 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.03/20.59 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.03/20.59 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.03/20.59 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.03/20.59 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.03/20.59 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.03/20.59 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.03/20.59 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.03/20.59 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.03/20.59 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.03/20.59 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.03/20.59 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.03/20.59 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.03/20.59 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.03/20.59 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.03/20.59 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.03/20.59 $i(all_56_14))))
% 141.03/20.59 (24) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.03/20.59 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.03/20.59 (25) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 all_56_9 & $i(all_56_9))
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (17) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 141.03/20.59 | | e2)
% 141.03/20.59 | |
% 141.03/20.59 | | BETA: splitting (26) gives:
% 141.03/20.59 | |
% 141.03/20.59 | | Case 1:
% 141.03/20.59 | | |
% 141.03/20.59 | | | (27) all_57_4 = e2 & op(e3, e1) = e2
% 141.03/20.59 | | |
% 141.03/20.59 | | | ALPHA: (27) implies:
% 141.03/20.59 | | | (28) all_57_4 = e2
% 141.03/20.59 | | |
% 141.03/20.59 | | | REF_CLOSE: (3), (6), (7), (10), (11), (12), (13), (18), (21), (22), (24),
% 141.03/20.59 | | | (28) are inconsistent by sub-proof #407.
% 141.03/20.59 | | |
% 141.03/20.59 | | Case 2:
% 141.03/20.59 | | |
% 141.03/20.59 | | | (29) all_57_5 = e2 & op(e2, e1) = e2
% 141.03/20.59 | | |
% 141.03/20.59 | | | ALPHA: (29) implies:
% 141.03/20.59 | | | (30) op(e2, e1) = e2
% 141.03/20.59 | | |
% 141.03/20.59 | | | BETA: splitting (20) gives:
% 141.03/20.59 | | |
% 141.03/20.59 | | | Case 1:
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | (31) all_56_11 = e1 & op(e2, e2) = e1
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | ALPHA: (31) implies:
% 141.03/20.59 | | | | (32) all_56_11 = e1
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | BETA: splitting (23) gives:
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | Case 1:
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | (33) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3,
% 141.03/20.59 | | | | | e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 &
% 141.03/20.59 | | | | | $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~
% 141.03/20.59 | | | | | (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 &
% 141.03/20.59 | | | | | op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 & all_56_13
% 141.03/20.59 | | | | | = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.03/20.59 | | | | | all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1
% 141.03/20.59 | | | | | & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 &
% 141.03/20.59 | | | | | op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | REF_CLOSE: (2), (9), (18), (21), (25), (32), (33) are inconsistent by
% 141.03/20.59 | | | | | sub-proof #93.
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | Case 2:
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | (34) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 141.03/20.59 | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 141.03/20.59 | | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 141.03/20.59 | | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 141.03/20.59 | | | | | op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.03/20.59 | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 141.03/20.59 | | | | | op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.03/20.59 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 141.03/20.59 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 141.03/20.59 | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.03/20.59 | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.03/20.59 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.03/20.59 | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 141.03/20.59 | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.03/20.59 | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 141.03/20.59 | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.03/20.59 | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.03/20.59 | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.59 | | | | | e1) = all_56_14 & $i(all_56_14))))
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | BETA: splitting (34) gives:
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | | Case 1:
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | (35) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 141.03/20.59 | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3
% 141.03/20.59 | | | | | | & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 141.03/20.59 | | | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4
% 141.03/20.59 | | | | | | & op(e1, e1) = e2 & $i(all_56_4))
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | REF_CLOSE: (4), (13), (16), (18), (35) are inconsistent by sub-proof
% 141.03/20.59 | | | | | | #118.
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | Case 2:
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | (36) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.03/20.59 | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2
% 141.03/20.59 | | | | | | & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 141.03/20.59 | | | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 141.03/20.59 | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.03/20.59 | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 =
% 141.03/20.59 | | | | | | e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0,
% 141.03/20.59 | | | | | | e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.59 | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 141.03/20.59 | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13
% 141.03/20.59 | | | | | | = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.03/20.59 | | | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.03/20.59 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 141.03/20.59 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.03/20.59 | | | | | | $i(all_56_14))))
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | BETA: splitting (36) gives:
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | | Case 1:
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | | (37) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.03/20.59 | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2
% 141.03/20.59 | | | | | | | & $i(all_56_7)
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | | ALPHA: (37) implies:
% 141.03/20.59 | | | | | | | (38) op(e1, e1) = e2
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | | REF_CLOSE: (8), (15), (18), (38) are inconsistent by sub-proof
% 141.03/20.59 | | | | | | | #1124.
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | Case 2:
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | | (39) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 141.03/20.59 | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) =
% 141.03/20.59 | | | | | | | e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.03/20.59 | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 141.03/20.59 | | | | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 141.03/20.59 | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.59 | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.03/20.59 | | | | | | | e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.03/20.59 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.03/20.59 | | | | | | | & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.03/20.59 | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 &
% 141.03/20.59 | | | | | | | ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.03/20.59 | | | | | | | all_56_14 & $i(all_56_14))))
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | | BETA: splitting (39) gives:
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | | Case 1:
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | | (40) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 141.03/20.59 | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) =
% 141.03/20.59 | | | | | | | | e2 & $i(all_56_5)
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | | ALPHA: (40) implies:
% 141.03/20.59 | | | | | | | | (41) op(e2, e2) = e0
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | | REF_CLOSE: (11), (18), (20), (30), (41) are inconsistent by
% 141.03/20.59 | | | | | | | | sub-proof #950.
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | Case 2:
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | | (42) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0
% 141.03/20.59 | | | | | | | | & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 141.03/20.59 | | | | | | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.03/20.59 | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0)
% 141.03/20.59 | | | | | | | | & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.03/20.59 | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 141.03/20.59 | | | | | | | | ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 141.03/20.59 | | | | | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.03/20.59 | | | | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 141.03/20.59 | | | | | | | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | | REF_CLOSE: (3), (7), (13), (14), (16), (18), (42) are
% 141.03/20.59 | | | | | | | | inconsistent by sub-proof #108.
% 141.03/20.59 | | | | | | | |
% 141.03/20.59 | | | | | | | End of split
% 141.03/20.59 | | | | | | |
% 141.03/20.59 | | | | | | End of split
% 141.03/20.59 | | | | | |
% 141.03/20.59 | | | | | End of split
% 141.03/20.59 | | | | |
% 141.03/20.59 | | | | End of split
% 141.03/20.59 | | | |
% 141.03/20.59 | | | Case 2:
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | (43) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | ALPHA: (43) implies:
% 141.03/20.59 | | | | (44) ~ (all_56_4 = e2)
% 141.03/20.59 | | | | (45) op(e2, e1) = all_56_4
% 141.03/20.59 | | | |
% 141.03/20.59 | | | | REF_CLOSE: (18), (30), (44), (45) are inconsistent by sub-proof #951.
% 141.03/20.59 | | | |
% 141.03/20.59 | | | End of split
% 141.03/20.59 | | |
% 141.03/20.59 | | End of split
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.59 | | (46) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 141.03/20.59 | | e2)
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (1), (3), (5), (7), (8), (11), (12), (13), (15), (16), (18),
% 141.03/20.59 | | (19), (21), (46) are inconsistent by sub-proof #766.
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #93 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) ~ (all_52_8 = e3)
% 141.03/20.59 (2) op(e3, e1) = all_52_8
% 141.03/20.59 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (4) ~ (e3 = e1)
% 141.03/20.59 (5) all_56_11 = e1
% 141.03/20.59 (6) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 all_56_9 & $i(all_56_9))
% 141.03/20.59 (7) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.03/20.59 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.03/20.59 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.03/20.59 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.03/20.59 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.03/20.59 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 141.03/20.59 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 141.03/20.59 op(e1, e1) = e3 & $i(all_56_6))
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (7) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (8) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 141.03/20.59 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.03/20.59 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 141.03/20.59 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.03/20.59 | |
% 141.03/20.59 | | BETA: splitting (8) gives:
% 141.03/20.59 | |
% 141.03/20.59 | | Case 1:
% 141.03/20.59 | | |
% 141.03/20.59 | | | (9) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 141.03/20.59 | | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 141.03/20.59 | | |
% 141.03/20.59 | | | ALPHA: (9) implies:
% 141.03/20.59 | | | (10) all_56_11 = e3
% 141.03/20.59 | | |
% 141.03/20.59 | | | COMBINE_EQS: (5), (10) imply:
% 141.03/20.59 | | | (11) e3 = e1
% 141.03/20.59 | | |
% 141.03/20.59 | | | REDUCE: (4), (11) imply:
% 141.03/20.59 | | | (12) $false
% 141.03/20.59 | | |
% 141.03/20.59 | | | CLOSE: (12) is inconsistent.
% 141.03/20.59 | | |
% 141.03/20.59 | | Case 2:
% 141.03/20.59 | | |
% 141.03/20.59 | | | (13) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 141.03/20.59 | | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 141.03/20.59 | | |
% 141.03/20.59 | | | ALPHA: (13) implies:
% 141.03/20.59 | | | (14) all_56_11 = e3
% 141.03/20.59 | | |
% 141.03/20.59 | | | COMBINE_EQS: (5), (14) imply:
% 141.03/20.59 | | | (15) e3 = e1
% 141.03/20.59 | | |
% 141.03/20.59 | | | REDUCE: (4), (15) imply:
% 141.03/20.59 | | | (16) $false
% 141.03/20.59 | | |
% 141.03/20.59 | | | CLOSE: (16) is inconsistent.
% 141.03/20.59 | | |
% 141.03/20.59 | | End of split
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.59 | | (17) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 141.03/20.59 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.03/20.59 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 141.03/20.59 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (1), (2), (3), (6), (17) are inconsistent by sub-proof #94.
% 141.03/20.59 | |
% 141.03/20.59 | End of split
% 141.03/20.59 |
% 141.03/20.59 End of proof
% 141.03/20.59
% 141.03/20.59 Sub-proof #94 shows that the following formulas are inconsistent:
% 141.03/20.59 ----------------------------------------------------------------
% 141.03/20.59 (1) ~ (all_52_8 = e3)
% 141.03/20.59 (2) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 &
% 141.03/20.59 op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 141.03/20.59 e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3)
% 141.03/20.59 = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.03/20.59 (3) op(e3, e1) = all_52_8
% 141.03/20.59 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.59 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.59 (5) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.03/20.59 all_56_9 & $i(all_56_9))
% 141.03/20.59
% 141.03/20.59 Begin of proof
% 141.03/20.59 |
% 141.03/20.59 | BETA: splitting (2) gives:
% 141.03/20.59 |
% 141.03/20.59 | Case 1:
% 141.03/20.59 | |
% 141.03/20.59 | | (6) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1
% 141.03/20.59 | | & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)
% 141.03/20.59 | |
% 141.03/20.59 | | ALPHA: (6) implies:
% 141.03/20.59 | | (7) all_56_9 = e1
% 141.03/20.59 | |
% 141.03/20.59 | | REF_CLOSE: (1), (3), (4), (5), (7) are inconsistent by sub-proof #898.
% 141.03/20.59 | |
% 141.03/20.59 | Case 2:
% 141.03/20.59 | |
% 141.03/20.60 | | (8) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1
% 141.03/20.60 | | & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (8) implies:
% 141.03/20.60 | | (9) all_56_9 = e1
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (1), (3), (4), (5), (9) are inconsistent by sub-proof #898.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #95 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) all_57_6 = e3 & op(e1, e3) = e3
% 141.03/20.60 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (3) op(e1, e3) = all_52_2
% 141.03/20.60 (4) ~ (all_52_2 = e3)
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | ALPHA: (1) implies:
% 141.03/20.60 | (5) op(e1, e3) = e3
% 141.03/20.60 |
% 141.03/20.60 | GROUND_INST: instantiating (2) with all_52_2, e3, e3, e1, simplifying with
% 141.03/20.60 | (3), (5) gives:
% 141.03/20.60 | (6) all_52_2 = e3
% 141.03/20.60 |
% 141.03/20.60 | REDUCE: (4), (6) imply:
% 141.03/20.60 | (7) $false
% 141.03/20.60 |
% 141.03/20.60 | CLOSE: (7) is inconsistent.
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #96 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) ~ (all_52_1 = e3)
% 141.03/20.60 (2) op(e3, e3) = e2
% 141.03/20.60 (3) op(e2, e3) = all_52_1
% 141.03/20.60 (4) ~ (e3 = e2)
% 141.03/20.60 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (6) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (7) implies:
% 141.03/20.60 | | (8) op(e3, e3) = e3
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #450.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | | (9) all_57_2 = e3 & op(e2, e3) = e3
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #183.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #97 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) ~ (all_52_1 = all_52_3)
% 141.03/20.60 (2) op(e1, e3) = all_52_2
% 141.03/20.60 (3) op(e2, e3) = e2
% 141.03/20.60 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.03/20.60 (5) op(e0, e3) = all_52_3
% 141.03/20.60 (6) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.03/20.60 all_56_6 & $i(all_56_6))
% 141.03/20.60 (7) op(e1, e1) = e0
% 141.03/20.60 (8) all_54_12 = all_52_3
% 141.03/20.60 (9) ~ (e3 = e0)
% 141.03/20.60 (10) op(e2, e3) = all_52_1
% 141.03/20.60 (11) op(e0, e3) = all_56_10
% 141.03/20.60 (12) ~ (all_52_3 = e1)
% 141.03/20.60 (13) ~ (all_52_1 = all_52_2)
% 141.03/20.60 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (15) ~ (all_52_2 = e0)
% 141.03/20.60 (16) ~ (all_52_2 = all_52_3)
% 141.03/20.60 (17) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.03/20.60 (18) all_54_8 = all_52_2
% 141.03/20.60 (19) ~ (all_56_10 = e0)
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (6) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (20) all_56_13 = e3 & op(e1, e1) = e3
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (20) implies:
% 141.03/20.60 | | (21) op(e1, e1) = e3
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (7), (9), (14), (21) are inconsistent by sub-proof #308.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | | (22) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6)
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (22) implies:
% 141.03/20.60 | | (23) ~ (all_56_6 = e1)
% 141.03/20.60 | | (24) op(e1, e3) = all_56_6
% 141.03/20.60 | |
% 141.03/20.60 | | GROUND_INST: instantiating (14) with all_52_3, all_56_10, e3, e0,
% 141.03/20.60 | | simplifying with (5), (11) gives:
% 141.03/20.60 | | (25) all_56_10 = all_52_3
% 141.03/20.60 | |
% 141.03/20.60 | | GROUND_INST: instantiating (14) with all_52_2, all_56_6, e3, e1, simplifying
% 141.03/20.60 | | with (2), (24) gives:
% 141.03/20.60 | | (26) all_56_6 = all_52_2
% 141.03/20.60 | |
% 141.03/20.60 | | GROUND_INST: instantiating (14) with all_52_1, e2, e3, e2, simplifying with
% 141.03/20.60 | | (3), (10) gives:
% 141.03/20.60 | | (27) all_52_1 = e2
% 141.03/20.60 | |
% 141.03/20.60 | | REDUCE: (23), (26) imply:
% 141.03/20.60 | | (28) ~ (all_52_2 = e1)
% 141.03/20.60 | |
% 141.03/20.60 | | REDUCE: (19), (25) imply:
% 141.03/20.60 | | (29) ~ (all_52_3 = e0)
% 141.03/20.60 | |
% 141.03/20.60 | | REDUCE: (13), (27) imply:
% 141.03/20.60 | | (30) ~ (all_52_2 = e2)
% 141.03/20.60 | |
% 141.03/20.60 | | SIMP: (30) implies:
% 141.03/20.60 | | (31) ~ (all_52_2 = e2)
% 141.03/20.60 | |
% 141.03/20.60 | | REDUCE: (1), (27) imply:
% 141.03/20.60 | | (32) ~ (all_52_3 = e2)
% 141.03/20.60 | |
% 141.03/20.60 | | SIMP: (32) implies:
% 141.03/20.60 | | (33) ~ (all_52_3 = e2)
% 141.03/20.60 | |
% 141.03/20.60 | | BETA: splitting (4) gives:
% 141.03/20.60 | |
% 141.03/20.60 | | Case 1:
% 141.03/20.60 | | |
% 141.03/20.60 | | | (34) all_54_12 = e3
% 141.03/20.60 | | |
% 141.03/20.60 | | | COMBINE_EQS: (8), (34) imply:
% 141.03/20.60 | | | (35) all_52_3 = e3
% 141.03/20.60 | | |
% 141.03/20.60 | | | SIMP: (35) implies:
% 141.03/20.60 | | | (36) all_52_3 = e3
% 141.03/20.60 | | |
% 141.03/20.60 | | | REDUCE: (16), (36) imply:
% 141.03/20.60 | | | (37) ~ (all_52_2 = e3)
% 141.03/20.60 | | |
% 141.03/20.60 | | | REF_CLOSE: (15), (17), (18), (28), (31), (37) are inconsistent by
% 141.03/20.60 | | | sub-proof #149.
% 141.03/20.60 | | |
% 141.03/20.60 | | Case 2:
% 141.03/20.60 | | |
% 141.03/20.60 | | | (38) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.03/20.60 | | |
% 141.03/20.60 | | | BETA: splitting (38) gives:
% 141.03/20.60 | | |
% 141.03/20.60 | | | Case 1:
% 141.03/20.60 | | | |
% 141.03/20.60 | | | | (39) all_54_12 = e2
% 141.03/20.60 | | | |
% 141.03/20.60 | | | | REF_CLOSE: (8), (33), (39) are inconsistent by sub-proof #231.
% 141.03/20.60 | | | |
% 141.03/20.60 | | | Case 2:
% 141.03/20.60 | | | |
% 141.03/20.60 | | | | (40) all_54_12 = e1 | all_54_12 = e0
% 141.03/20.60 | | | |
% 141.03/20.60 | | | | REF_CLOSE: (8), (12), (29), (40) are inconsistent by sub-proof #661.
% 141.03/20.60 | | | |
% 141.03/20.60 | | | End of split
% 141.03/20.60 | | |
% 141.03/20.60 | | End of split
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #98 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) ~ (all_52_14 = e1)
% 141.03/20.60 (2) op(e1, e1) = e0
% 141.03/20.60 (3) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 141.03/20.60 all_56_13 & $i(all_56_13))
% 141.03/20.60 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (5) op(e1, e0) = all_52_14
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (3) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (6) all_56_8 = e1 & op(e1, e0) = e1
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (6) implies:
% 141.03/20.60 | | (7) op(e1, e0) = e1
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #459.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | | (8) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (8) implies:
% 141.03/20.60 | | (9) ~ (all_56_13 = e0)
% 141.03/20.60 | | (10) op(e1, e1) = all_56_13
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #140.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #99 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) op(e0, e0) = e1
% 141.03/20.60 (2) ~ (all_52_11 = e0)
% 141.03/20.60 (3) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 141.03/20.60 all_56_14 & $i(all_56_14))
% 141.03/20.60 (4) op(e0, e1) = all_52_11
% 141.03/20.60 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (6) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.03/20.60 all_56_15 & $i(all_56_15))
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (6) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (7) all_56_14 = e0 & op(e0, e1) = e0
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (7) implies:
% 141.03/20.60 | | (8) op(e0, e1) = e0
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #886.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | | (9) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (9) implies:
% 141.03/20.60 | | (10) op(e0, e0) = all_56_15
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10) are inconsistent by sub-proof
% 141.03/20.60 | | #100.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #100 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) op(e0, e0) = e1
% 141.03/20.60 (2) ~ (all_52_11 = e0)
% 141.03/20.60 (3) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 141.03/20.60 all_56_14 & $i(all_56_14))
% 141.03/20.60 (4) op(e0, e1) = all_52_11
% 141.03/20.60 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (6) op(e0, e0) = all_56_15
% 141.03/20.60 (7) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.03/20.60 all_56_15 & $i(all_56_15))
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (3) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (8) all_56_15 = e1 & op(e0, e0) = e1
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (8) implies:
% 141.03/20.60 | | (9) all_56_15 = e1
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (4), (5), (7), (9) are inconsistent by sub-proof #432.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | |
% 141.03/20.60 | | GROUND_INST: instantiating (5) with e1, all_56_15, e0, e0, simplifying with
% 141.03/20.60 | | (1), (6) gives:
% 141.03/20.60 | | (10) all_56_15 = e1
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (4), (5), (7), (10) are inconsistent by sub-proof #432.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #101 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) all_54_7 = e1 | all_54_7 = e0
% 141.03/20.60 (2) all_54_7 = all_52_13
% 141.03/20.60 (3) ~ (all_52_13 = e1)
% 141.03/20.60 (4) ~ (all_52_13 = e0)
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (1) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (5) all_54_7 = e1
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #676.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | | (6) all_54_7 = e0
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #961.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #102 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) ~ (all_52_1 = e2)
% 141.03/20.60 (2) ~ (all_52_8 = all_52_9)
% 141.03/20.60 (3) ~ (all_52_14 = e1)
% 141.03/20.60 (4) ~ (all_52_12 = e3)
% 141.03/20.60 (5) ~ (all_52_8 = e3)
% 141.03/20.60 (6) ~ (all_52_4 = e0)
% 141.03/20.60 (7) ~ (e2 = e1)
% 141.03/20.60 (8) ~ (all_52_4 = all_52_8)
% 141.03/20.60 (9) op(e3, e3) = e3
% 141.03/20.60 (10) op(e0, e1) = e3
% 141.03/20.60 (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 141.03/20.60 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.60 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.03/20.60 all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.03/20.60 (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.03/20.60 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0)
% 141.03/20.60 & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.03/20.60 (12) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.03/20.60 (13) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.03/20.60 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.03/20.60 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.03/20.60 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.03/20.60 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.03/20.60 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.03/20.60 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.03/20.60 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.03/20.60 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.03/20.60 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.03/20.60 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.03/20.60 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.03/20.60 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.03/20.60 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.03/20.60 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.03/20.60 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.03/20.60 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.03/20.60 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.03/20.60 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.03/20.60 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.03/20.60 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.03/20.60 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.03/20.60 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.03/20.60 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.03/20.60 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.03/20.60 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.03/20.60 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.03/20.60 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.03/20.60 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.03/20.60 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.03/20.60 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.03/20.60 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.03/20.60 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.03/20.60 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.03/20.60 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.03/20.60 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.03/20.60 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.03/20.60 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.03/20.60 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.03/20.60 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.03/20.60 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.03/20.60 (14) ~ (all_52_8 = all_4_2)
% 141.03/20.60 (15) ~ (all_50_2 = e0) | ( ~ (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 &
% 141.03/20.60 op(e1, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 141.03/20.60 e3) & op(e1, e0) = all_50_1 & $i(all_50_1))
% 141.03/20.60 (16) ~ (all_52_9 = e2)
% 141.03/20.60 (17) all_48_2 = all_4_2
% 141.03/20.60 (18) ~ (e3 = e0)
% 141.03/20.60 (19) op(e1, e1) = all_4_2
% 141.03/20.60 (20) ~ (all_52_4 = e3)
% 141.03/20.60 (21) all_57_14 = e3
% 141.03/20.60 (22) op(e3, e1) = all_52_8
% 141.03/20.60 (23) all_50_2 = all_4_2
% 141.03/20.60 (24) op(e2, e3) = all_52_1
% 141.03/20.60 (25) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.03/20.60 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.03/20.60 (26) ~ (all_4_2 = e3)
% 141.03/20.60 (27) ~ (e1 = e0)
% 141.03/20.60 (28) op(e1, e0) = e3
% 141.03/20.60 (29) op(e3, e2) = all_52_4
% 141.03/20.60 (30) all_57_0 = e3
% 141.03/20.60 (31) op(e3, e0) = all_52_12
% 141.03/20.60 (32) op(e2, e2) = e3
% 141.03/20.60 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 141.03/20.60 (34) ~ (all_4_2 = e2)
% 141.03/20.60 (35) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.03/20.60 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.03/20.60 (36) all_54_10 = all_4_2
% 141.03/20.60 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (38) ~ (all_52_8 = e0)
% 141.03/20.60 (39) ~ (e3 = e1)
% 141.03/20.60 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.03/20.60 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.03/20.60 (41) ~ (all_48_2 = e0) | ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 &
% 141.03/20.60 op(e1, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 141.03/20.60 e2) & op(e1, e0) = all_48_1 & $i(all_48_1))
% 141.03/20.60 (42) all_56_15 = e1
% 141.03/20.60 (43) op(e2, e1) = all_52_9
% 141.03/20.60 (44) op(e3, e3) = all_14_2
% 141.03/20.60 (45) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.03/20.60 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.03/20.60 (46) ~ (all_14_2 = e0)
% 141.03/20.60 (47) op(e1, e0) = all_52_14
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (33) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (48) all_57_4 = e2 & op(e3, e1) = e2
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (48) implies:
% 141.03/20.60 | | (49) all_57_4 = e2
% 141.03/20.60 | | (50) op(e3, e1) = e2
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 141.03/20.60 | | (13), (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.03/20.60 | | (25), (26), (27), (28), (29), (30), (31), (32), (34), (35), (36),
% 141.03/20.60 | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 141.03/20.60 | | (49), (50) are inconsistent by sub-proof #103.
% 141.03/20.60 | |
% 141.03/20.60 | Case 2:
% 141.03/20.60 | |
% 141.03/20.60 | | (51) all_57_5 = e2 & op(e2, e1) = e2
% 141.03/20.60 | |
% 141.03/20.60 | | ALPHA: (51) implies:
% 141.03/20.60 | | (52) op(e2, e1) = e2
% 141.03/20.60 | |
% 141.03/20.60 | | REF_CLOSE: (16), (37), (43), (52) are inconsistent by sub-proof #890.
% 141.03/20.60 | |
% 141.03/20.60 | End of split
% 141.03/20.60 |
% 141.03/20.60 End of proof
% 141.03/20.60
% 141.03/20.60 Sub-proof #103 shows that the following formulas are inconsistent:
% 141.03/20.60 ----------------------------------------------------------------
% 141.03/20.60 (1) ~ (all_52_1 = e2)
% 141.03/20.60 (2) ~ (all_52_8 = all_52_9)
% 141.03/20.60 (3) ~ (all_52_14 = e1)
% 141.03/20.60 (4) all_57_4 = e2
% 141.03/20.60 (5) ~ (all_52_12 = e3)
% 141.03/20.60 (6) ~ (all_52_8 = e3)
% 141.03/20.60 (7) ~ (all_52_4 = e0)
% 141.03/20.60 (8) ~ (e2 = e1)
% 141.03/20.60 (9) ~ (all_52_4 = all_52_8)
% 141.03/20.60 (10) op(e3, e3) = e3
% 141.03/20.60 (11) op(e0, e1) = e3
% 141.03/20.60 (12) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 141.03/20.60 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.60 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.03/20.60 all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.03/20.60 (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.03/20.60 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0)
% 141.03/20.60 & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.03/20.60 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.03/20.60 (14) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.03/20.60 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.03/20.60 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.03/20.60 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.03/20.60 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.03/20.60 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.03/20.60 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.03/20.60 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.03/20.60 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.03/20.60 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.03/20.60 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.03/20.60 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.03/20.60 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.03/20.60 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.03/20.60 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.03/20.60 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.03/20.60 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.03/20.60 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.03/20.60 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.03/20.60 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.03/20.60 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.03/20.60 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.03/20.60 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.03/20.60 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.03/20.60 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.03/20.60 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.03/20.60 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.03/20.60 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.03/20.60 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.03/20.60 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.03/20.60 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.03/20.60 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.03/20.60 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.03/20.60 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.03/20.60 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.03/20.60 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.03/20.60 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.03/20.60 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.03/20.60 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.03/20.60 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.03/20.60 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.03/20.60 (15) ~ (all_52_8 = all_4_2)
% 141.03/20.60 (16) ~ (all_50_2 = e0) | ( ~ (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 &
% 141.03/20.60 op(e1, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 141.03/20.60 e3) & op(e1, e0) = all_50_1 & $i(all_50_1))
% 141.03/20.60 (17) all_48_2 = all_4_2
% 141.03/20.60 (18) ~ (e3 = e0)
% 141.03/20.60 (19) op(e1, e1) = all_4_2
% 141.03/20.60 (20) ~ (all_52_4 = e3)
% 141.03/20.60 (21) op(e3, e1) = e2
% 141.03/20.60 (22) all_57_14 = e3
% 141.03/20.60 (23) op(e3, e1) = all_52_8
% 141.03/20.60 (24) all_50_2 = all_4_2
% 141.03/20.60 (25) op(e2, e3) = all_52_1
% 141.03/20.60 (26) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.03/20.60 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.03/20.60 (27) ~ (all_4_2 = e3)
% 141.03/20.60 (28) ~ (e1 = e0)
% 141.03/20.60 (29) op(e1, e0) = e3
% 141.03/20.60 (30) op(e3, e2) = all_52_4
% 141.03/20.60 (31) all_57_0 = e3
% 141.03/20.60 (32) op(e3, e0) = all_52_12
% 141.03/20.60 (33) op(e2, e2) = e3
% 141.03/20.60 (34) ~ (all_4_2 = e2)
% 141.03/20.60 (35) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.03/20.60 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.03/20.60 (36) all_54_10 = all_4_2
% 141.03/20.60 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.60 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.60 (38) ~ (all_52_8 = e0)
% 141.03/20.60 (39) ~ (e3 = e1)
% 141.03/20.60 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.03/20.60 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.03/20.60 (41) ~ (all_48_2 = e0) | ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 &
% 141.03/20.60 op(e1, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 141.03/20.60 e2) & op(e1, e0) = all_48_1 & $i(all_48_1))
% 141.03/20.60 (42) all_56_15 = e1
% 141.03/20.60 (43) op(e2, e1) = all_52_9
% 141.03/20.60 (44) op(e3, e3) = all_14_2
% 141.03/20.60 (45) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.03/20.60 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.03/20.60 (46) ~ (all_14_2 = e0)
% 141.03/20.60 (47) op(e1, e0) = all_52_14
% 141.03/20.60
% 141.03/20.60 Begin of proof
% 141.03/20.60 |
% 141.03/20.60 | BETA: splitting (14) gives:
% 141.03/20.60 |
% 141.03/20.60 | Case 1:
% 141.03/20.60 | |
% 141.03/20.60 | | (48) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 141.03/20.60 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.03/20.60 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.03/20.60 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.03/20.60 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.03/20.60 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.03/20.60 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.03/20.60 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.03/20.60 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.03/20.60 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.03/20.60 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.03/20.60 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 141.03/20.60 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.03/20.60 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.03/20.60 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.03/20.60 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.03/20.60 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.03/20.60 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.03/20.60 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.03/20.60 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.03/20.60 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.03/20.60 | | $i(all_56_12))))
% 141.03/20.60 | |
% 141.03/20.60 | | BETA: splitting (48) gives:
% 141.03/20.60 | |
% 141.03/20.60 | | Case 1:
% 141.03/20.60 | | |
% 141.03/20.61 | | | (49) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 141.03/20.61 | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.03/20.61 | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.03/20.61 | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.03/20.61 | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.03/20.61 | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.03/20.61 | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.03/20.61 | | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.03/20.61 | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.03/20.61 | | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.03/20.61 | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 141.03/20.61 | | |
% 141.03/20.61 | | | ALPHA: (49) implies:
% 141.03/20.61 | | | (50) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2,
% 141.03/20.61 | | | e2) = all_56_11 & $i(all_56_11))
% 141.03/20.61 | | |
% 141.03/20.61 | | | REF_CLOSE: (1), (25), (33), (37), (50) are inconsistent by sub-proof #178.
% 141.03/20.61 | | |
% 141.03/20.61 | | Case 2:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (51) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 141.03/20.61 | | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.03/20.61 | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 141.03/20.61 | | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.03/20.61 | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.03/20.61 | | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.03/20.61 | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.03/20.61 | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.03/20.61 | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.03/20.61 | | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 141.03/20.61 | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 141.03/20.61 | | |
% 141.03/20.61 | | | ALPHA: (51) implies:
% 141.03/20.61 | | | (52) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.03/20.61 | | | e2) = all_56_7 & $i(all_56_7))
% 141.03/20.61 | | | (53) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.03/20.61 | | | e2) = all_56_0 & $i(all_56_0))
% 141.03/20.61 | | | (54) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.03/20.61 | | | e1) = all_56_13 & $i(all_56_13))
% 141.03/20.61 | | | (55) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3,
% 141.03/20.61 | | | e3) = all_56_9 & $i(all_56_9))
% 141.03/20.61 | | |
% 141.03/20.61 | | | BETA: splitting (53) gives:
% 141.03/20.61 | | |
% 141.03/20.61 | | | Case 1:
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | (56) all_56_9 = e2 & op(e3, e3) = e2
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | ALPHA: (56) implies:
% 141.03/20.61 | | | | (57) all_56_9 = e2
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | REF_CLOSE: (20), (30), (37), (55), (57) are inconsistent by sub-proof
% 141.03/20.61 | | | | #345.
% 141.03/20.61 | | | |
% 141.03/20.61 | | | Case 2:
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | (58) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0)
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | ALPHA: (58) implies:
% 141.03/20.61 | | | | (59) op(e3, e2) = all_56_0
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | BETA: splitting (52) gives:
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | Case 1:
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | (60) all_56_13 = e2 & op(e1, e1) = e2
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | ALPHA: (60) implies:
% 141.03/20.61 | | | | | (61) op(e1, e1) = e2
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | REF_CLOSE: (19), (34), (37), (61) are inconsistent by sub-proof #1124.
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | Case 2:
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | (62) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | ALPHA: (62) implies:
% 141.03/20.61 | | | | | (63) ~ (all_56_7 = e1)
% 141.03/20.61 | | | | | (64) op(e1, e2) = all_56_7
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | BETA: splitting (26) gives:
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | Case 1:
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | (65) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3,
% 141.03/20.61 | | | | | | e2) = e1)
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | BETA: splitting (65) gives:
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | Case 1:
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | (66) all_57_0 = e1 & op(e3, e3) = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | ALPHA: (66) implies:
% 141.03/20.61 | | | | | | | (67) op(e3, e3) = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | REF_CLOSE: (10), (37), (39), (67) are inconsistent by sub-proof
% 141.03/20.61 | | | | | | | #838.
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | Case 2:
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | (68) all_57_1 = e1 & op(e3, e2) = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | ALPHA: (68) implies:
% 141.03/20.61 | | | | | | | (69) op(e3, e2) = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | BETA: splitting (54) gives:
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | Case 1:
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | (70) all_56_7 = e1 & op(e1, e2) = e1
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | ALPHA: (70) implies:
% 141.03/20.61 | | | | | | | | (71) op(e1, e2) = e1
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | REF_CLOSE: (37), (63), (64), (71) are inconsistent by sub-proof
% 141.03/20.61 | | | | | | | | #422.
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | Case 2:
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | (72) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.03/20.61 | | | | | | | | $i(all_56_13)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | ALPHA: (72) implies:
% 141.03/20.61 | | | | | | | | (73) op(e1, e1) = all_56_13
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | GROUND_INST: instantiating (37) with all_4_2, all_56_13, e1, e1,
% 141.03/20.61 | | | | | | | | simplifying with (19), (73) gives:
% 141.03/20.61 | | | | | | | | (74) all_56_13 = all_4_2
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | GROUND_INST: instantiating (37) with all_52_8, e2, e1, e3,
% 141.03/20.61 | | | | | | | | simplifying with (21), (23) gives:
% 141.03/20.61 | | | | | | | | (75) all_52_8 = e2
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | GROUND_INST: instantiating (37) with all_52_4, all_56_0, e2, e3,
% 141.03/20.61 | | | | | | | | simplifying with (30), (59) gives:
% 141.03/20.61 | | | | | | | | (76) all_56_0 = all_52_4
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | GROUND_INST: instantiating (37) with e1, all_56_0, e2, e3,
% 141.03/20.61 | | | | | | | | simplifying with (59), (69) gives:
% 141.03/20.61 | | | | | | | | (77) all_56_0 = e1
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | COMBINE_EQS: (76), (77) imply:
% 141.03/20.61 | | | | | | | | (78) all_52_4 = e1
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | SIMP: (78) implies:
% 141.03/20.61 | | | | | | | | (79) all_52_4 = e1
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | REDUCE: (9), (75), (79) imply:
% 141.03/20.61 | | | | | | | | (80) ~ (e2 = e1)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | REDUCE: (2), (75) imply:
% 141.03/20.61 | | | | | | | | (81) ~ (all_52_9 = e2)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | SIMP: (81) implies:
% 141.03/20.61 | | | | | | | | (82) ~ (all_52_9 = e2)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | REDUCE: (15), (75) imply:
% 141.03/20.61 | | | | | | | | (83) ~ (all_4_2 = e2)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | REDUCE: (6), (75) imply:
% 141.03/20.61 | | | | | | | | (84) ~ (e3 = e2)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | SIMP: (84) implies:
% 141.03/20.61 | | | | | | | | (85) ~ (e3 = e2)
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | BETA: splitting (16) gives:
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | | Case 1:
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | (86) ~ (all_50_2 = e0)
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | REDUCE: (24), (86) imply:
% 141.03/20.61 | | | | | | | | | (87) ~ (all_4_2 = e0)
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | REF_CLOSE: (8), (12), (13), (19), (27), (34), (36), (37),
% 141.03/20.61 | | | | | | | | | (42), (44), (46), (87) are inconsistent by
% 141.03/20.61 | | | | | | | | | sub-proof #455.
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | Case 2:
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | (88) all_50_2 = e0
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | COMBINE_EQS: (24), (88) imply:
% 141.03/20.61 | | | | | | | | | (89) all_4_2 = e0
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | SIMP: (89) implies:
% 141.03/20.61 | | | | | | | | | (90) all_4_2 = e0
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | COMBINE_EQS: (17), (90) imply:
% 141.03/20.61 | | | | | | | | | (91) all_48_2 = e0
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | BETA: splitting (41) gives:
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | | Case 1:
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | | (92) ~ (all_48_2 = e0)
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | | REDUCE: (91), (92) imply:
% 141.03/20.61 | | | | | | | | | | (93) $false
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | | CLOSE: (93) is inconsistent.
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | Case 2:
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | | (94) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 &
% 141.03/20.61 | | | | | | | | | | op(e1, e0) = all_48_1 & $i(all_48_0) &
% 141.03/20.61 | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0) =
% 141.03/20.61 | | | | | | | | | | all_48_1 & $i(all_48_1))
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | | REF_CLOSE: (16), (19), (22), (23), (29), (34), (35), (37),
% 141.03/20.61 | | | | | | | | | | (43), (47), (82), (85), (88), (94) are
% 141.03/20.61 | | | | | | | | | | inconsistent by sub-proof #428.
% 141.03/20.61 | | | | | | | | | |
% 141.03/20.61 | | | | | | | | | End of split
% 141.03/20.61 | | | | | | | | |
% 141.03/20.61 | | | | | | | | End of split
% 141.03/20.61 | | | | | | | |
% 141.03/20.61 | | | | | | | End of split
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | End of split
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | Case 2:
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | (95) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3,
% 141.03/20.61 | | | | | | e0) = e1)
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | BETA: splitting (95) gives:
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | Case 1:
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | (96) all_57_4 = e1 & op(e3, e1) = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | ALPHA: (96) implies:
% 141.03/20.61 | | | | | | | (97) all_57_4 = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | REF_CLOSE: (4), (8), (97) are inconsistent by sub-proof #1088.
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | Case 2:
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | (98) all_57_9 = e1 & op(e3, e0) = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | ALPHA: (98) implies:
% 141.03/20.61 | | | | | | | (99) all_57_9 = e1
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | | REF_CLOSE: (5), (6), (7), (18), (20), (23), (28), (30), (32),
% 141.03/20.61 | | | | | | | (37), (38), (40), (45), (99) are inconsistent by
% 141.03/20.61 | | | | | | | sub-proof #226.
% 141.03/20.61 | | | | | | |
% 141.03/20.61 | | | | | | End of split
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | End of split
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | End of split
% 141.03/20.61 | | | |
% 141.03/20.61 | | | End of split
% 141.03/20.61 | | |
% 141.03/20.61 | | End of split
% 141.03/20.61 | |
% 141.03/20.61 | Case 2:
% 141.03/20.61 | |
% 141.03/20.61 | | (100) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.03/20.61 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.03/20.61 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.03/20.61 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.03/20.61 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.03/20.61 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.03/20.61 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.03/20.61 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.03/20.61 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.03/20.61 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.03/20.61 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.03/20.61 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) |
% 141.03/20.61 | | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.03/20.61 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 141.03/20.61 | | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 &
% 141.03/20.61 | | op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 141.03/20.61 | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) =
% 141.03/20.61 | | e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.03/20.61 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.03/20.61 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.03/20.61 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 141.03/20.61 | | op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.03/20.61 | |
% 141.03/20.61 | | BETA: splitting (100) gives:
% 141.03/20.61 | |
% 141.03/20.61 | | Case 1:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (101) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.03/20.61 | | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.03/20.61 | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.03/20.61 | | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.03/20.61 | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.03/20.61 | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.03/20.61 | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.03/20.61 | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.03/20.61 | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.03/20.61 | | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.03/20.61 | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.03/20.61 | | |
% 141.03/20.61 | | | ALPHA: (101) implies:
% 141.03/20.61 | | | (102) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) &
% 141.03/20.61 | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 141.03/20.61 | | |
% 141.03/20.61 | | | BETA: splitting (102) gives:
% 141.03/20.61 | | |
% 141.03/20.61 | | | Case 1:
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | (103) all_56_14 = e0 & op(e0, e1) = e0
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | ALPHA: (103) implies:
% 141.03/20.61 | | | | (104) op(e0, e1) = e0
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | BETA: splitting (12) gives:
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | Case 1:
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | (105) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.03/20.61 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.03/20.61 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 141.03/20.61 | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | REF_CLOSE: (18), (33), (37), (44), (46), (105) are inconsistent by
% 141.03/20.61 | | | | | sub-proof #124.
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | Case 2:
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | (106) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 141.03/20.61 | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.03/20.61 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 141.03/20.61 | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | BETA: splitting (106) gives:
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | | Case 1:
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | GROUND_INST: instantiating (37) with e3, e0, e1, e0, simplifying
% 141.03/20.61 | | | | | | with (11), (104) gives:
% 141.03/20.61 | | | | | | (107) e3 = e0
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | COMBINE_EQS: (31), (107) imply:
% 141.03/20.61 | | | | | | (108) all_57_0 = e0
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | REF_CLOSE: (5), (6), (18), (20), (23), (30), (32), (37), (40), (108)
% 141.03/20.61 | | | | | | are inconsistent by sub-proof #1103.
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | Case 2:
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | (109) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 141.03/20.61 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | ALPHA: (109) implies:
% 141.03/20.61 | | | | | | (110) ~ (all_56_14 = e0)
% 141.03/20.61 | | | | | | (111) op(e0, e1) = all_56_14
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | | REF_CLOSE: (37), (104), (110), (111) are inconsistent by sub-proof
% 141.03/20.61 | | | | | | #973.
% 141.03/20.61 | | | | | |
% 141.03/20.61 | | | | | End of split
% 141.03/20.61 | | | | |
% 141.03/20.61 | | | | End of split
% 141.03/20.61 | | | |
% 141.03/20.61 | | | Case 2:
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | (112) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | ALPHA: (112) implies:
% 141.03/20.61 | | | | (113) ~ (all_56_15 = e1)
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | REDUCE: (42), (113) imply:
% 141.03/20.61 | | | | (114) $false
% 141.03/20.61 | | | |
% 141.03/20.61 | | | | CLOSE: (114) is inconsistent.
% 141.03/20.61 | | | |
% 141.03/20.61 | | | End of split
% 141.03/20.61 | | |
% 141.03/20.61 | | Case 2:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (115) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.03/20.61 | | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.03/20.61 | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.03/20.61 | | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.03/20.61 | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 141.03/20.61 | | | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 &
% 141.03/20.61 | | | op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.03/20.61 | | | all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) =
% 141.03/20.61 | | | e0) | ( ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.03/20.61 | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~
% 141.03/20.61 | | | (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8)))
% 141.03/20.61 | | |
% 141.03/20.61 | | | REF_CLOSE: (3), (12), (18), (33), (37), (39), (42), (47), (115) are
% 141.03/20.61 | | | inconsistent by sub-proof #104.
% 141.03/20.61 | | |
% 141.03/20.61 | | End of split
% 141.03/20.61 | |
% 141.03/20.61 | End of split
% 141.03/20.61 |
% 141.03/20.61 End of proof
% 141.03/20.61
% 141.03/20.61 Sub-proof #104 shows that the following formulas are inconsistent:
% 141.03/20.61 ----------------------------------------------------------------
% 141.03/20.61 (1) ~ (all_52_14 = e1)
% 141.03/20.61 (2) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.03/20.61 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.03/20.61 ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.03/20.61 all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 141.03/20.61 ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.03/20.61 ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.03/20.61 all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.03/20.61 (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.03/20.61 ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.03/20.61 all_56_8 & $i(all_56_8)))
% 141.03/20.61 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.03/20.61 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.03/20.61 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.03/20.61 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.03/20.61 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.03/20.61 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.61 e1) = all_56_14 & $i(all_56_14))
% 141.03/20.61 (4) ~ (e3 = e0)
% 141.03/20.61 (5) op(e2, e2) = e3
% 141.03/20.61 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.61 (7) ~ (e3 = e1)
% 141.03/20.61 (8) all_56_15 = e1
% 141.03/20.61 (9) op(e1, e0) = all_52_14
% 141.03/20.61
% 141.03/20.61 Begin of proof
% 141.03/20.61 |
% 141.03/20.61 | ALPHA: (2) implies:
% 141.03/20.61 | (10) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.03/20.61 | = all_56_5 & $i(all_56_5))
% 141.03/20.61 | (11) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.03/20.61 | = all_56_13 & $i(all_56_13))
% 141.03/20.61 | (12) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2)
% 141.03/20.61 | = all_56_11 & $i(all_56_11))
% 141.03/20.61 |
% 141.03/20.61 | BETA: splitting (11) gives:
% 141.03/20.61 |
% 141.03/20.61 | Case 1:
% 141.03/20.61 | |
% 141.03/20.61 | | (13) all_56_8 = e1 & op(e1, e0) = e1
% 141.03/20.61 | |
% 141.03/20.61 | | ALPHA: (13) implies:
% 141.03/20.61 | | (14) op(e1, e0) = e1
% 141.03/20.61 | |
% 141.03/20.61 | | REF_CLOSE: (1), (6), (9), (14) are inconsistent by sub-proof #459.
% 141.03/20.61 | |
% 141.03/20.61 | Case 2:
% 141.03/20.61 | |
% 141.03/20.61 | | (15) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.03/20.61 | |
% 141.03/20.61 | | ALPHA: (15) implies:
% 141.03/20.61 | | (16) ~ (all_56_13 = e0)
% 141.03/20.61 | |
% 141.03/20.61 | | BETA: splitting (10) gives:
% 141.03/20.61 | |
% 141.03/20.61 | | Case 1:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (17) all_56_11 = e0 & op(e2, e2) = e0
% 141.03/20.61 | | |
% 141.03/20.61 | | | ALPHA: (17) implies:
% 141.03/20.61 | | | (18) op(e2, e2) = e0
% 141.03/20.61 | | |
% 141.03/20.61 | | | REF_CLOSE: (4), (5), (6), (18) are inconsistent by sub-proof #1119.
% 141.03/20.61 | | |
% 141.03/20.61 | | Case 2:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (19) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5)
% 141.03/20.61 | | |
% 141.03/20.61 | | | ALPHA: (19) implies:
% 141.03/20.61 | | | (20) ~ (all_56_5 = e2)
% 141.03/20.61 | | |
% 141.03/20.61 | | | REF_CLOSE: (3), (6), (7), (8), (12), (16), (20) are inconsistent by
% 141.03/20.61 | | | sub-proof #324.
% 141.03/20.61 | | |
% 141.03/20.61 | | End of split
% 141.03/20.61 | |
% 141.03/20.61 | End of split
% 141.03/20.61 |
% 141.03/20.61 End of proof
% 141.03/20.61
% 141.03/20.61 Sub-proof #105 shows that the following formulas are inconsistent:
% 141.03/20.61 ----------------------------------------------------------------
% 141.03/20.61 (1) all_54_3 = all_10_0
% 141.03/20.61 (2) all_54_3 = e1
% 141.03/20.61 (3) ~ (all_10_0 = e1)
% 141.03/20.61
% 141.03/20.61 Begin of proof
% 141.03/20.61 |
% 141.03/20.61 | COMBINE_EQS: (1), (2) imply:
% 141.03/20.61 | (4) all_10_0 = e1
% 141.03/20.61 |
% 141.03/20.61 | SIMP: (4) implies:
% 141.03/20.61 | (5) all_10_0 = e1
% 141.03/20.61 |
% 141.03/20.61 | REDUCE: (3), (5) imply:
% 141.03/20.61 | (6) $false
% 141.03/20.61 |
% 141.03/20.61 | CLOSE: (6) is inconsistent.
% 141.03/20.61 |
% 141.03/20.61 End of proof
% 141.03/20.61
% 141.03/20.61 Sub-proof #106 shows that the following formulas are inconsistent:
% 141.03/20.61 ----------------------------------------------------------------
% 141.03/20.61 (1) all_54_3 = all_10_0
% 141.03/20.61 (2) all_54_3 = e2
% 141.03/20.61 (3) ~ (all_10_0 = e2)
% 141.03/20.61
% 141.03/20.61 Begin of proof
% 141.03/20.61 |
% 141.03/20.61 | COMBINE_EQS: (1), (2) imply:
% 141.03/20.61 | (4) all_10_0 = e2
% 141.03/20.61 |
% 141.03/20.61 | SIMP: (4) implies:
% 141.03/20.61 | (5) all_10_0 = e2
% 141.03/20.61 |
% 141.03/20.61 | REDUCE: (3), (5) imply:
% 141.03/20.61 | (6) $false
% 141.03/20.61 |
% 141.03/20.61 | CLOSE: (6) is inconsistent.
% 141.03/20.61 |
% 141.03/20.61 End of proof
% 141.03/20.61
% 141.03/20.61 Sub-proof #107 shows that the following formulas are inconsistent:
% 141.03/20.61 ----------------------------------------------------------------
% 141.03/20.61 (1) ~ (e2 = e1)
% 141.03/20.61 (2) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 141.03/20.61 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.03/20.61 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 141.03/20.61 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.03/20.61 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 141.03/20.61 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.03/20.61 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.03/20.61 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.03/20.61 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 141.03/20.61 = all_56_14 & $i(all_56_14))))
% 141.03/20.61 (3) ~ (e3 = e0)
% 141.03/20.61 (4) ~ (e3 = e2)
% 141.03/20.61 (5) op(e2, e2) = e3
% 141.03/20.61 (6) op(e0, e0) = e2
% 141.03/20.61 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.61
% 141.03/20.61 Begin of proof
% 141.03/20.61 |
% 141.03/20.61 | BETA: splitting (2) gives:
% 141.03/20.61 |
% 141.03/20.61 | Case 1:
% 141.03/20.61 | |
% 141.03/20.61 | | (8) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.03/20.61 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 141.03/20.61 | |
% 141.03/20.61 | | ALPHA: (8) implies:
% 141.03/20.61 | | (9) op(e2, e2) = e0
% 141.03/20.61 | |
% 141.03/20.61 | | REF_CLOSE: (3), (5), (7), (9) are inconsistent by sub-proof #1119.
% 141.03/20.61 | |
% 141.03/20.61 | Case 2:
% 141.03/20.61 | |
% 141.03/20.61 | | (10) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 141.03/20.61 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 141.03/20.61 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 141.03/20.61 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.03/20.61 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 141.03/20.61 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.03/20.61 | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.03/20.61 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.03/20.61 | | $i(all_56_14)))
% 141.03/20.61 | |
% 141.03/20.61 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 141.03/20.61 | | #108.
% 141.03/20.61 | |
% 141.03/20.61 | End of split
% 141.03/20.61 |
% 141.03/20.61 End of proof
% 141.03/20.61
% 141.03/20.61 Sub-proof #108 shows that the following formulas are inconsistent:
% 141.03/20.61 ----------------------------------------------------------------
% 141.03/20.61 (1) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 141.03/20.61 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.03/20.61 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 141.03/20.61 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.03/20.61 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0
% 141.03/20.61 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.03/20.61 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14
% 141.03/20.61 & $i(all_56_14)))
% 141.03/20.61 (2) ~ (e2 = e1)
% 141.03/20.61 (3) ~ (e3 = e0)
% 141.03/20.61 (4) ~ (e3 = e2)
% 141.03/20.61 (5) op(e2, e2) = e3
% 141.03/20.61 (6) op(e0, e0) = e2
% 141.03/20.61 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.61 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.61
% 141.03/20.61 Begin of proof
% 141.03/20.61 |
% 141.03/20.61 | ALPHA: (1) implies:
% 141.03/20.61 | (8) op(e0, e0) = all_56_15
% 141.03/20.61 | (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 141.03/20.61 | & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.61 | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.03/20.61 | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.03/20.61 | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.03/20.61 | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 141.03/20.61 | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.03/20.61 |
% 141.03/20.61 | GROUND_INST: instantiating (7) with e2, all_56_15, e0, e0, simplifying with
% 141.03/20.61 | (6), (8) gives:
% 141.03/20.61 | (10) all_56_15 = e2
% 141.03/20.61 |
% 141.03/20.61 | BETA: splitting (9) gives:
% 141.03/20.61 |
% 141.03/20.61 | Case 1:
% 141.03/20.61 | |
% 141.03/20.61 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.03/20.61 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.61 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.03/20.61 | | e2) = all_56_12 & $i(all_56_12))
% 141.03/20.61 | |
% 141.03/20.61 | | BETA: splitting (11) gives:
% 141.03/20.61 | |
% 141.03/20.61 | | Case 1:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (12) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 141.03/20.61 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.03/20.61 | | |
% 141.03/20.61 | | | REF_CLOSE: (4), (10), (12) are inconsistent by sub-proof #528.
% 141.03/20.61 | | |
% 141.03/20.61 | | Case 2:
% 141.03/20.61 | | |
% 141.03/20.61 | | | (13) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.03/20.61 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.03/20.61 | | |
% 141.03/20.61 | | | ALPHA: (13) implies:
% 141.03/20.61 | | | (14) op(e2, e2) = e0
% 141.03/20.61 | | |
% 141.03/20.61 | | | REF_CLOSE: (3), (5), (7), (14) are inconsistent by sub-proof #1119.
% 141.03/20.61 | | |
% 141.03/20.61 | | End of split
% 141.03/20.61 | |
% 141.03/20.61 | Case 2:
% 141.03/20.61 | |
% 141.03/20.61 | | (15) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.03/20.61 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.03/20.61 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.61 | | e1) = all_56_14 & $i(all_56_14))
% 141.03/20.61 | |
% 141.03/20.61 | | REF_CLOSE: (2), (10), (15) are inconsistent by sub-proof #527.
% 141.03/20.61 | |
% 141.03/20.61 | End of split
% 141.03/20.61 |
% 141.03/20.61 End of proof
% 141.03/20.61
% 141.03/20.61 Sub-proof #109 shows that the following formulas are inconsistent:
% 141.03/20.61 ----------------------------------------------------------------
% 141.03/20.61 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.03/20.61 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.03/20.61 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.03/20.61 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.03/20.61 (3) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.03/20.61 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.03/20.61 (4) ~ (all_52_4 = e0)
% 141.03/20.61 (5) ~ (e2 = e1)
% 141.03/20.61 (6) op(e0, e0) = e3
% 141.03/20.61 (7) op(e2, e2) = all_56_11
% 141.03/20.61 (8) all_57_4 = e3
% 141.03/20.61 (9) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) = all_26_1
% 141.03/20.61 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3) =
% 141.03/20.61 all_26_1 & $i(all_26_1))
% 141.03/20.61 (10) op(e0, e3) = all_52_3
% 141.03/20.61 (11) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.03/20.61 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.03/20.61 (12) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 141.03/20.61 all_56_0 & $i(all_56_0))
% 141.03/20.61 (13) ~ (all_52_1 = e0)
% 141.03/20.61 (14) ~ (e3 = e0)
% 141.03/20.61 (15) op(e1, e1) = all_4_2
% 141.03/20.61 (16) ~ (all_52_4 = e3)
% 141.03/20.61 (17) op(e3, e1) = all_52_8
% 141.03/20.61 (18) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 141.03/20.61 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 141.03/20.61 (19) op(e2, e3) = all_52_1
% 141.03/20.61 (20) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 141.03/20.61 all_56_15 & $i(all_56_15))
% 141.03/20.62 (21) ~ (all_56_15 = e2)
% 141.03/20.62 (22) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.03/20.62 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.03/20.62 (23) ~ (e1 = e0)
% 141.03/20.62 (24) op(e3, e2) = all_52_4
% 141.03/20.62 (25) ~ (all_56_7 = e1)
% 141.03/20.62 (26) op(e2, e2) = e3
% 141.03/20.62 (27) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.03/20.62 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.03/20.62 (28) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.03/20.62 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.03/20.62 & $i(all_6_1))
% 141.03/20.62 (29) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 141.03/20.62 all_56_13 & $i(all_56_13))
% 141.03/20.62 (30) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.62 (31) ~ (all_52_3 = e0)
% 141.03/20.62 (32) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.03/20.62 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.03/20.62 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.03/20.62 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.03/20.62 (33) ~ (all_52_8 = e0)
% 141.03/20.62 (34) ~ (e3 = e1)
% 141.03/20.62 (35) op(e0, e2) = all_52_7
% 141.03/20.62 (36) op(e0, e0) = all_56_15
% 141.03/20.62 (37) all_57_3 = e3
% 141.03/20.62 (38) op(e0, e2) = all_56_12
% 141.03/20.62 (39) op(e3, e3) = e0
% 141.03/20.62 (40) op(e1, e2) = all_56_7
% 141.03/20.62 (41) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.03/20.62 all_56_9 & $i(all_56_9))
% 141.03/20.62 (42) ~ (all_56_12 = e0)
% 141.03/20.62 (43) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.03/20.62 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.03/20.62
% 141.03/20.62 Begin of proof
% 141.03/20.62 |
% 141.03/20.62 | BETA: splitting (12) gives:
% 141.03/20.62 |
% 141.03/20.62 | Case 1:
% 141.03/20.62 | |
% 141.03/20.62 | | (44) all_56_9 = e2 & op(e3, e3) = e2
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (44) implies:
% 141.03/20.62 | | (45) all_56_9 = e2
% 141.03/20.62 | |
% 141.03/20.62 | | REF_CLOSE: (16), (24), (30), (41), (45) are inconsistent by sub-proof #345.
% 141.03/20.62 | |
% 141.03/20.62 | Case 2:
% 141.03/20.62 | |
% 141.03/20.62 | | (46) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0)
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (46) implies:
% 141.03/20.62 | | (47) ~ (all_56_0 = e3)
% 141.03/20.62 | | (48) op(e3, e2) = all_56_0
% 141.03/20.62 | |
% 141.03/20.62 | | BETA: splitting (29) gives:
% 141.03/20.62 | |
% 141.03/20.62 | | Case 1:
% 141.03/20.62 | | |
% 141.03/20.62 | | | (49) all_56_7 = e1 & op(e1, e2) = e1
% 141.03/20.62 | | |
% 141.03/20.62 | | | ALPHA: (49) implies:
% 141.03/20.62 | | | (50) op(e1, e2) = e1
% 141.03/20.62 | | |
% 141.03/20.62 | | | REF_CLOSE: (25), (30), (40), (50) are inconsistent by sub-proof #422.
% 141.03/20.62 | | |
% 141.03/20.62 | | Case 2:
% 141.03/20.62 | | |
% 141.03/20.62 | | | (51) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.03/20.62 | | |
% 141.03/20.62 | | | ALPHA: (51) implies:
% 141.03/20.62 | | | (52) ~ (all_56_13 = e2)
% 141.03/20.62 | | | (53) op(e1, e1) = all_56_13
% 141.03/20.62 | | |
% 141.03/20.62 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 141.03/20.62 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.03/20.62 | | | (26), (27), (28), (30), (31), (32), (33), (34), (35), (36),
% 141.03/20.62 | | | (37), (38), (39), (41), (42), (43), (47), (48), (52), (53) are
% 141.03/20.62 | | | inconsistent by sub-proof #110.
% 141.03/20.62 | | |
% 141.03/20.62 | | End of split
% 141.03/20.62 | |
% 141.03/20.62 | End of split
% 141.03/20.62 |
% 141.03/20.62 End of proof
% 141.03/20.62
% 141.03/20.62 Sub-proof #110 shows that the following formulas are inconsistent:
% 141.03/20.62 ----------------------------------------------------------------
% 141.03/20.62 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.03/20.62 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.03/20.62 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.03/20.62 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.03/20.62 (3) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.03/20.62 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.03/20.62 (4) ~ (all_52_4 = e0)
% 141.03/20.62 (5) ~ (e2 = e1)
% 141.03/20.62 (6) op(e0, e0) = e3
% 141.03/20.62 (7) op(e2, e2) = all_56_11
% 141.03/20.62 (8) all_57_4 = e3
% 141.03/20.62 (9) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) = all_26_1
% 141.03/20.62 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3) =
% 141.03/20.62 all_26_1 & $i(all_26_1))
% 141.03/20.62 (10) op(e0, e3) = all_52_3
% 141.03/20.62 (11) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.03/20.62 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.03/20.62 (12) ~ (all_52_1 = e0)
% 141.03/20.62 (13) ~ (e3 = e0)
% 141.03/20.62 (14) op(e1, e1) = all_4_2
% 141.03/20.62 (15) op(e3, e1) = all_52_8
% 141.03/20.62 (16) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 141.03/20.62 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 141.03/20.62 (17) op(e2, e3) = all_52_1
% 141.03/20.62 (18) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 141.03/20.62 all_56_15 & $i(all_56_15))
% 141.03/20.62 (19) ~ (all_56_15 = e2)
% 141.03/20.62 (20) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.03/20.62 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.03/20.62 (21) ~ (e1 = e0)
% 141.03/20.62 (22) op(e3, e2) = all_52_4
% 141.03/20.62 (23) ~ (all_56_13 = e2)
% 141.03/20.62 (24) op(e3, e2) = all_56_0
% 141.03/20.62 (25) op(e2, e2) = e3
% 141.03/20.62 (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.03/20.62 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.03/20.62 (27) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.03/20.62 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.03/20.62 & $i(all_6_1))
% 141.03/20.62 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.62 (29) ~ (all_52_3 = e0)
% 141.03/20.62 (30) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.03/20.62 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.03/20.62 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.03/20.62 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.03/20.62 (31) ~ (all_52_8 = e0)
% 141.03/20.62 (32) ~ (e3 = e1)
% 141.03/20.62 (33) op(e0, e2) = all_52_7
% 141.03/20.62 (34) op(e0, e0) = all_56_15
% 141.03/20.62 (35) all_57_3 = e3
% 141.03/20.62 (36) op(e0, e2) = all_56_12
% 141.03/20.62 (37) op(e3, e3) = e0
% 141.03/20.62 (38) ~ (all_56_0 = e3)
% 141.03/20.62 (39) op(e1, e1) = all_56_13
% 141.03/20.62 (40) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.03/20.62 all_56_9 & $i(all_56_9))
% 141.03/20.62 (41) ~ (all_56_12 = e0)
% 141.03/20.62 (42) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.03/20.62 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.03/20.62
% 141.03/20.62 Begin of proof
% 141.03/20.62 |
% 141.03/20.62 | BETA: splitting (40) gives:
% 141.03/20.62 |
% 141.03/20.62 | Case 1:
% 141.03/20.62 | |
% 141.03/20.62 | | (43) all_56_0 = e3 & op(e3, e2) = e3
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (43) implies:
% 141.03/20.62 | | (44) op(e3, e2) = e3
% 141.03/20.62 | |
% 141.03/20.62 | | REF_CLOSE: (24), (28), (38), (44) are inconsistent by sub-proof #670.
% 141.03/20.62 | |
% 141.03/20.62 | Case 2:
% 141.03/20.62 | |
% 141.03/20.62 | | (45) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (45) implies:
% 141.03/20.62 | | (46) ~ (all_56_9 = e2)
% 141.03/20.62 | | (47) op(e3, e3) = all_56_9
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (28) with e3, all_56_15, e0, e0, simplifying with
% 141.03/20.62 | | (6), (34) gives:
% 141.03/20.62 | | (48) all_56_15 = e3
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (28) with all_52_7, all_56_12, e2, e0,
% 141.03/20.62 | | simplifying with (33), (36) gives:
% 141.03/20.62 | | (49) all_56_12 = all_52_7
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (28) with all_4_2, all_56_13, e1, e1, simplifying
% 141.03/20.62 | | with (14), (39) gives:
% 141.03/20.62 | | (50) all_56_13 = all_4_2
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (28) with e3, all_56_11, e2, e2, simplifying with
% 141.03/20.62 | | (7), (25) gives:
% 141.03/20.62 | | (51) all_56_11 = e3
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (28) with all_52_4, all_56_0, e2, e3, simplifying
% 141.03/20.62 | | with (22), (24) gives:
% 141.03/20.62 | | (52) all_56_0 = all_52_4
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (28) with e0, all_56_9, e3, e3, simplifying with
% 141.03/20.62 | | (37), (47) gives:
% 141.03/20.62 | | (53) all_56_9 = e0
% 141.03/20.62 | |
% 141.03/20.62 | | REDUCE: (46), (53) imply:
% 141.03/20.62 | | (54) ~ (e2 = e0)
% 141.03/20.62 | |
% 141.03/20.62 | | SIMP: (54) implies:
% 141.03/20.62 | | (55) ~ (e2 = e0)
% 141.03/20.62 | |
% 141.03/20.62 | | REDUCE: (41), (49) imply:
% 141.03/20.62 | | (56) ~ (all_52_7 = e0)
% 141.03/20.62 | |
% 141.03/20.62 | | REDUCE: (23), (50) imply:
% 141.03/20.62 | | (57) ~ (all_4_2 = e2)
% 141.03/20.62 | |
% 141.03/20.62 | | REDUCE: (19), (48) imply:
% 141.03/20.62 | | (58) ~ (e3 = e2)
% 141.03/20.62 | |
% 141.03/20.62 | | BETA: splitting (30) gives:
% 141.03/20.62 | |
% 141.03/20.62 | | Case 1:
% 141.03/20.62 | | |
% 141.03/20.62 | | | (59) all_57_15 = e0 & op(e0, e0) = e0
% 141.03/20.62 | | |
% 141.03/20.62 | | | ALPHA: (59) implies:
% 141.03/20.62 | | | (60) op(e0, e0) = e0
% 141.03/20.62 | | |
% 141.03/20.62 | | | REF_CLOSE: (6), (13), (28), (60) are inconsistent by sub-proof #751.
% 141.03/20.62 | | |
% 141.03/20.62 | | Case 2:
% 141.03/20.62 | | |
% 141.03/20.62 | | | (61) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 141.03/20.62 | | | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0
% 141.03/20.62 | | | & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.03/20.62 | | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.03/20.62 | | |
% 141.03/20.62 | | | ALPHA: (61) implies:
% 141.03/20.62 | | | (62) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2)
% 141.03/20.62 | | | = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.03/20.62 | | |
% 141.03/20.62 | | | BETA: splitting (62) gives:
% 141.03/20.62 | | |
% 141.03/20.62 | | | Case 1:
% 141.03/20.62 | | | |
% 141.03/20.62 | | | | (63) all_57_12 = e0 & op(e0, e3) = e0
% 141.03/20.62 | | | |
% 141.03/20.62 | | | | ALPHA: (63) implies:
% 141.03/20.62 | | | | (64) op(e0, e3) = e0
% 141.03/20.62 | | | |
% 141.03/20.62 | | | | REF_CLOSE: (10), (28), (29), (64) are inconsistent by sub-proof #986.
% 141.03/20.62 | | | |
% 141.03/20.62 | | | Case 2:
% 141.03/20.62 | | | |
% 141.03/20.62 | | | | (65) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 141.03/20.62 | | | | e1) = e0)
% 141.03/20.62 | | | |
% 141.03/20.62 | | | | BETA: splitting (65) gives:
% 141.03/20.62 | | | |
% 141.03/20.62 | | | | Case 1:
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | (66) all_57_13 = e0 & op(e0, e2) = e0
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | ALPHA: (66) implies:
% 141.03/20.62 | | | | | (67) op(e0, e2) = e0
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | REF_CLOSE: (28), (36), (41), (67) are inconsistent by sub-proof #738.
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | Case 2:
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | (68) all_57_14 = e0 & op(e0, e1) = e0
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | ALPHA: (68) implies:
% 141.03/20.62 | | | | | (69) all_57_14 = e0
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | BETA: splitting (26) gives:
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | | Case 1:
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | | (70) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2,
% 141.03/20.62 | | | | | | e1) = e2)
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | | BETA: splitting (70) gives:
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | | Case 1:
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | (71) all_57_4 = e2 & op(e3, e1) = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | ALPHA: (71) implies:
% 141.03/20.62 | | | | | | | (72) all_57_4 = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | COMBINE_EQS: (8), (72) imply:
% 141.03/20.62 | | | | | | | (73) e3 = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | SIMP: (73) implies:
% 141.03/20.62 | | | | | | | (74) e3 = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | COMBINE_EQS: (48), (74) imply:
% 141.03/20.62 | | | | | | | (75) all_56_15 = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | REF_CLOSE: (18), (28), (33), (56), (75) are inconsistent by
% 141.03/20.62 | | | | | | | sub-proof #976.
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | Case 2:
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | (76) all_57_5 = e2 & op(e2, e1) = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | ALPHA: (76) implies:
% 141.03/20.62 | | | | | | | (77) all_57_5 = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | BETA: splitting (42) gives:
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | | (78) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 141.03/20.62 | | | | | | | | op(e2, e2) = e0)
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | | REF_CLOSE: (12), (13), (17), (25), (28), (78) are inconsistent
% 141.03/20.62 | | | | | | | | by sub-proof #112.
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | | (79) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 141.03/20.62 | | | | | | | | op(e2, e0) = e0)
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | | BETA: splitting (79) gives:
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | | (80) all_57_5 = e0 & op(e2, e1) = e0
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | | REF_CLOSE: (55), (77), (80) are inconsistent by sub-proof
% 141.03/20.62 | | | | | | | | | #627.
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | | (81) all_57_10 = e0 & op(e2, e0) = e0
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | | ALPHA: (81) implies:
% 141.03/20.62 | | | | | | | | | (82) all_57_10 = e0
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | | BETA: splitting (16) gives:
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | (83) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 &
% 141.03/20.62 | | | | | | | | | | op(e2, e1) = e1)
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | BETA: splitting (83) gives:
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | (84) all_57_4 = e1 & op(e3, e1) = e1
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | ALPHA: (84) implies:
% 141.03/20.62 | | | | | | | | | | | (85) all_57_4 = e1
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | REF_CLOSE: (8), (32), (85) are inconsistent by sub-proof
% 141.03/20.62 | | | | | | | | | | | #631.
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | (86) all_57_5 = e1 & op(e2, e1) = e1
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | REF_CLOSE: (5), (77), (86) are inconsistent by sub-proof
% 141.03/20.62 | | | | | | | | | | | #938.
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | (87) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1
% 141.03/20.62 | | | | | | | | | | & op(e0, e1) = e1)
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | BETA: splitting (87) gives:
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | (88) all_57_8 = e1 & op(e1, e1) = e1
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | ALPHA: (88) implies:
% 141.03/20.62 | | | | | | | | | | | (89) all_57_8 = e1
% 141.03/20.62 | | | | | | | | | | | (90) op(e1, e1) = e1
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | BETA: splitting (20) gives:
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | (91) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 141.03/20.62 | | | | | | | | | | | | & op(e2, e2) = e0)
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (5), (13), (21), (22), (28), (32),
% 141.03/20.62 | | | | | | | | | | | | (58), (77), (82), (91) are inconsistent by
% 141.03/20.62 | | | | | | | | | | | | sub-proof #542.
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | (92) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 141.03/20.62 | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | BETA: splitting (92) gives:
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | (93) all_57_7 = e0 & op(e1, e2) = e0
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | ALPHA: (93) implies:
% 141.03/20.62 | | | | | | | | | | | | | (94) op(e1, e2) = e0
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | BETA: splitting (3) gives:
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | (95) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 141.03/20.62 | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | (96) all_57_2 = e1 & op(e2, e3) = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 141.03/20.62 | | | | | | | | | | | | | | | (97) op(e2, e3) = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | BETA: splitting (9) gives:
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | | (98) ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 &
% 141.03/20.62 | | | | | | | | | | | | | | | | op(e2, e3) = all_26_1 & $i(all_26_0) &
% 141.03/20.62 | | | | | | | | | | | | | | | | $i(all_26_1)
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | | ALPHA: (98) implies:
% 141.03/20.62 | | | | | | | | | | | | | | | | (99) op(e2, e3) = all_26_1
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (28), (94), (97), (99) are inconsistent by
% 141.03/20.62 | | | | | | | | | | | | | | | | sub-proof #111.
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | | (100) ~ (all_26_1 = e0) & op(e2, e3) = all_26_1 &
% 141.03/20.62 | | | | | | | | | | | | | | | | $i(all_26_1)
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | | ALPHA: (100) implies:
% 141.03/20.62 | | | | | | | | | | | | | | | | (101) op(e2, e3) = all_26_1
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | | REF_CLOSE: (27), (28), (94), (97), (101) are inconsistent by
% 141.03/20.62 | | | | | | | | | | | | | | | | sub-proof #111.
% 141.03/20.62 | | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | (102) all_57_3 = e1 & op(e2, e2) = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | ALPHA: (102) implies:
% 141.03/20.62 | | | | | | | | | | | | | | | (103) all_57_3 = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | COMBINE_EQS: (35), (103) imply:
% 141.03/20.62 | | | | | | | | | | | | | | | (104) e3 = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | COMBINE_EQS: (8), (104) imply:
% 141.03/20.62 | | | | | | | | | | | | | | | (105) all_57_4 = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (11), (13), (15), (21), (26), (28),
% 141.03/20.62 | | | | | | | | | | | | | | | (31), (32), (55), (58), (90), (105) are
% 141.03/20.62 | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | (106) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 141.03/20.62 | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | BETA: splitting (106) gives:
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | Case 1:
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | (107) all_57_5 = e1 & op(e2, e1) = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 141.03/20.62 | | | | | | | | | | | | | | | (108) all_57_5 = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | REF_CLOSE: (2), (5), (13), (26), (32), (55), (58), (69),
% 141.03/20.62 | | | | | | | | | | | | | | | (89), (108) are inconsistent by sub-proof #494.
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | (109) all_57_10 = e1 & op(e2, e0) = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | ALPHA: (109) implies:
% 141.03/20.62 | | | | | | | | | | | | | | | (110) all_57_10 = e1
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | | REF_CLOSE: (21), (82), (110) are inconsistent by sub-proof
% 141.03/20.62 | | | | | | | | | | | | | | | #590.
% 141.03/20.62 | | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | (111) all_57_13 = e0 & op(e0, e2) = e0
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | ALPHA: (111) implies:
% 141.03/20.62 | | | | | | | | | | | | | (112) op(e0, e2) = e0
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | | REF_CLOSE: (28), (36), (41), (112) are inconsistent by
% 141.03/20.62 | | | | | | | | | | | | | sub-proof #738.
% 141.03/20.62 | | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | Case 2:
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | (113) all_57_14 = e1 & op(e0, e1) = e1
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | | REF_CLOSE: (21), (69), (113) are inconsistent by sub-proof
% 141.03/20.62 | | | | | | | | | | | #668.
% 141.03/20.62 | | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | | |
% 141.03/20.62 | | | | | | | | | End of split
% 141.03/20.62 | | | | | | | | |
% 141.03/20.62 | | | | | | | | End of split
% 141.03/20.62 | | | | | | | |
% 141.03/20.62 | | | | | | | End of split
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | End of split
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | Case 2:
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | | (114) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 141.03/20.62 | | | | | | op(e0, e1) = e2)
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | | BETA: splitting (114) gives:
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | | Case 1:
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | (115) all_57_8 = e2 & op(e1, e1) = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | ALPHA: (115) implies:
% 141.03/20.62 | | | | | | | (116) op(e1, e1) = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | REF_CLOSE: (14), (28), (57), (116) are inconsistent by sub-proof
% 141.03/20.62 | | | | | | | #1124.
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | Case 2:
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | (117) all_57_14 = e2 & op(e0, e1) = e2
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | | REF_CLOSE: (10), (28), (29), (33), (55), (56), (62), (117) are
% 141.03/20.62 | | | | | | | inconsistent by sub-proof #652.
% 141.03/20.62 | | | | | | |
% 141.03/20.62 | | | | | | End of split
% 141.03/20.62 | | | | | |
% 141.03/20.62 | | | | | End of split
% 141.03/20.62 | | | | |
% 141.03/20.62 | | | | End of split
% 141.03/20.62 | | | |
% 141.03/20.62 | | | End of split
% 141.03/20.62 | | |
% 141.03/20.62 | | End of split
% 141.03/20.62 | |
% 141.03/20.62 | End of split
% 141.03/20.62 |
% 141.03/20.62 End of proof
% 141.03/20.62
% 141.03/20.62 Sub-proof #111 shows that the following formulas are inconsistent:
% 141.03/20.62 ----------------------------------------------------------------
% 141.03/20.62 (1) op(e1, e2) = e0
% 141.03/20.62 (2) op(e2, e3) = all_26_1
% 141.03/20.62 (3) op(e2, e3) = e1
% 141.03/20.62 (4) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.03/20.62 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.03/20.62 & $i(all_6_1))
% 141.03/20.62 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.62
% 141.03/20.62 Begin of proof
% 141.03/20.62 |
% 141.03/20.62 | BETA: splitting (4) gives:
% 141.03/20.62 |
% 141.03/20.62 | Case 1:
% 141.03/20.62 | |
% 141.03/20.62 | | (6) ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1
% 141.03/20.62 | | & $i(all_6_0) & $i(all_6_1)
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (6) implies:
% 141.03/20.62 | | (7) ~ (all_6_0 = e0)
% 141.03/20.62 | | (8) op(e2, e3) = all_6_1
% 141.03/20.62 | | (9) op(all_6_1, e2) = all_6_0
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (5) with e1, all_26_1, e3, e2, simplifying with
% 141.03/20.62 | | (2), (3) gives:
% 141.03/20.62 | | (10) all_26_1 = e1
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (5) with all_6_1, all_26_1, e3, e2, simplifying
% 141.03/20.62 | | with (2), (8) gives:
% 141.03/20.62 | | (11) all_26_1 = all_6_1
% 141.03/20.62 | |
% 141.03/20.62 | | COMBINE_EQS: (10), (11) imply:
% 141.03/20.62 | | (12) all_6_1 = e1
% 141.03/20.62 | |
% 141.03/20.62 | | SIMP: (12) implies:
% 141.03/20.62 | | (13) all_6_1 = e1
% 141.03/20.62 | |
% 141.03/20.62 | | REDUCE: (9), (13) imply:
% 141.03/20.62 | | (14) op(e1, e2) = all_6_0
% 141.03/20.62 | |
% 141.03/20.62 | | GROUND_INST: instantiating (5) with e0, all_6_0, e2, e1, simplifying with
% 141.03/20.62 | | (1), (14) gives:
% 141.03/20.62 | | (15) all_6_0 = e0
% 141.03/20.62 | |
% 141.03/20.62 | | REDUCE: (7), (15) imply:
% 141.03/20.62 | | (16) $false
% 141.03/20.62 | |
% 141.03/20.62 | | CLOSE: (16) is inconsistent.
% 141.03/20.62 | |
% 141.03/20.62 | Case 2:
% 141.03/20.62 | |
% 141.03/20.62 | | (17) ~ (all_6_1 = e1) & op(e2, e3) = all_6_1 & $i(all_6_1)
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (17) implies:
% 141.03/20.62 | | (18) ~ (all_6_1 = e1)
% 141.03/20.62 | | (19) op(e2, e3) = all_6_1
% 141.03/20.62 | |
% 141.03/20.62 | | REF_CLOSE: (2), (3), (5), (18), (19) are inconsistent by sub-proof #173.
% 141.03/20.62 | |
% 141.03/20.62 | End of split
% 141.03/20.62 |
% 141.03/20.62 End of proof
% 141.03/20.62
% 141.03/20.62 Sub-proof #112 shows that the following formulas are inconsistent:
% 141.03/20.62 ----------------------------------------------------------------
% 141.03/20.62 (1) ~ (all_52_1 = e0)
% 141.03/20.62 (2) ~ (e3 = e0)
% 141.03/20.62 (3) op(e2, e3) = all_52_1
% 141.03/20.62 (4) op(e2, e2) = e3
% 141.03/20.62 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.62 (6) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 141.03/20.62
% 141.03/20.62 Begin of proof
% 141.03/20.62 |
% 141.03/20.62 | BETA: splitting (6) gives:
% 141.03/20.62 |
% 141.03/20.62 | Case 1:
% 141.03/20.62 | |
% 141.03/20.62 | | (7) all_57_2 = e0 & op(e2, e3) = e0
% 141.03/20.62 | |
% 141.03/20.62 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #1028.
% 141.03/20.62 | |
% 141.03/20.62 | Case 2:
% 141.03/20.62 | |
% 141.03/20.62 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 141.03/20.62 | |
% 141.03/20.62 | | ALPHA: (8) implies:
% 141.03/20.62 | | (9) op(e2, e2) = e0
% 141.03/20.62 | |
% 141.03/20.62 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1119.
% 141.03/20.62 | |
% 141.03/20.62 | End of split
% 141.03/20.62 |
% 141.03/20.62 End of proof
% 141.03/20.62
% 141.03/20.62 Sub-proof #113 shows that the following formulas are inconsistent:
% 141.03/20.62 ----------------------------------------------------------------
% 141.03/20.62 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.03/20.62 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.03/20.62 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.03/20.62 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.03/20.62 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.03/20.62 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.62 e1) = all_56_14 & $i(all_56_14))
% 141.03/20.62 (2) ~ (all_10_2 = e1)
% 141.03/20.62 (3) ~ (e3 = e0)
% 141.03/20.62 (4) op(e0, e0) = all_10_2
% 141.03/20.62 (5) ~ (e1 = e0)
% 141.03/20.62 (6) op(e2, e2) = e3
% 141.03/20.62 (7) op(e3, e3) = e1
% 141.03/20.62 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.62 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.62 (9) op(e0, e0) = all_56_15
% 141.03/20.62
% 141.03/20.62 Begin of proof
% 141.03/20.62 |
% 141.03/20.62 | GROUND_INST: instantiating (8) with all_10_2, all_56_15, e0, e0, simplifying
% 141.03/20.62 | with (4), (9) gives:
% 141.03/20.62 | (10) all_56_15 = all_10_2
% 141.03/20.62 |
% 141.03/20.62 | BETA: splitting (1) gives:
% 141.03/20.62 |
% 141.03/20.62 | Case 1:
% 141.03/20.62 | |
% 141.03/20.62 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.03/20.62 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.62 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.03/20.62 | | e2) = all_56_12 & $i(all_56_12))
% 141.03/20.62 | |
% 141.03/20.62 | | BETA: splitting (11) gives:
% 141.03/20.62 | |
% 141.03/20.62 | | Case 1:
% 141.03/20.62 | | |
% 141.03/20.62 | | | (12) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 141.03/20.62 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.03/20.62 | | |
% 141.03/20.62 | | | ALPHA: (12) implies:
% 141.03/20.63 | | | (13) op(e3, e3) = e0
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (5), (7), (8), (13) are inconsistent by sub-proof #840.
% 141.03/20.63 | | |
% 141.03/20.63 | | Case 2:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (14) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.03/20.63 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.03/20.63 | | |
% 141.03/20.63 | | | ALPHA: (14) implies:
% 141.03/20.63 | | | (15) op(e2, e2) = e0
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (3), (6), (8), (15) are inconsistent by sub-proof #1119.
% 141.03/20.63 | | |
% 141.03/20.63 | | End of split
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (16) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.03/20.63 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.03/20.63 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.63 | | e1) = all_56_14 & $i(all_56_14))
% 141.03/20.63 | |
% 141.03/20.63 | | BETA: splitting (16) gives:
% 141.03/20.63 | |
% 141.03/20.63 | | Case 1:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (17) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1)
% 141.03/20.63 | | | = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 141.03/20.63 | | |
% 141.03/20.63 | | | ALPHA: (17) implies:
% 141.03/20.63 | | | (18) all_56_15 = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (2), (10), (18) are inconsistent by sub-proof #114.
% 141.03/20.63 | | |
% 141.03/20.63 | | Case 2:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (19) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1)
% 141.03/20.63 | | | = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 141.03/20.63 | | |
% 141.03/20.63 | | | ALPHA: (19) implies:
% 141.03/20.63 | | | (20) all_56_15 = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (2), (10), (20) are inconsistent by sub-proof #114.
% 141.03/20.63 | | |
% 141.03/20.63 | | End of split
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #114 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) all_56_15 = all_10_2
% 141.03/20.63 (2) all_56_15 = e1
% 141.03/20.63 (3) ~ (all_10_2 = e1)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | COMBINE_EQS: (1), (2) imply:
% 141.03/20.63 | (4) all_10_2 = e1
% 141.03/20.63 |
% 141.03/20.63 | SIMP: (4) implies:
% 141.03/20.63 | (5) all_10_2 = e1
% 141.03/20.63 |
% 141.03/20.63 | REDUCE: (3), (5) imply:
% 141.03/20.63 | (6) $false
% 141.03/20.63 |
% 141.03/20.63 | CLOSE: (6) is inconsistent.
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #115 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ~ (e3 = e0)
% 141.03/20.63 (2) all_57_1 = e1
% 141.03/20.63 (3) ~ (e1 = e0)
% 141.03/20.63 (4) op(e2, e2) = e3
% 141.03/20.63 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (6) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (6) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (7) all_57_1 = e0 & op(e3, e2) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #416.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (8) implies:
% 141.03/20.63 | | (9) op(e2, e2) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1119.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #116 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) = all_24_1
% 141.03/20.63 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2) =
% 141.03/20.63 all_24_1 & $i(all_24_1))
% 141.03/20.63 (2) all_57_13 = e1 & op(e0, e2) = e1
% 141.03/20.63 (3) all_40_2 = e2
% 141.03/20.63 (4) op(e1, e0) = e3
% 141.03/20.63 (5) ~ (all_40_2 = e2) | ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 141.03/20.63 op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 141.03/20.63 e1) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 141.03/20.63 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | ALPHA: (2) implies:
% 141.03/20.63 | (7) op(e0, e2) = e1
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (5) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (8) ~ (all_40_2 = e2)
% 141.03/20.63 | |
% 141.03/20.63 | | REDUCE: (3), (8) imply:
% 141.03/20.63 | | (9) $false
% 141.03/20.63 | |
% 141.03/20.63 | | CLOSE: (9) is inconsistent.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (10) ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 141.03/20.63 | | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e1) &
% 141.03/20.63 | | op(e0, e2) = all_40_1 & $i(all_40_1))
% 141.03/20.63 | |
% 141.03/20.63 | | BETA: splitting (1) gives:
% 141.03/20.63 | |
% 141.03/20.63 | | Case 1:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (11) ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 141.03/20.63 | | | all_24_1 & $i(all_24_0) & $i(all_24_1)
% 141.03/20.63 | | |
% 141.03/20.63 | | | ALPHA: (11) implies:
% 141.03/20.63 | | | (12) op(e0, e2) = all_24_1
% 141.03/20.63 | | | (13) op(all_24_1, e0) = all_24_0
% 141.03/20.63 | | |
% 141.03/20.63 | | | GROUND_INST: instantiating (6) with e1, all_24_1, e2, e0, simplifying with
% 141.03/20.63 | | | (7), (12) gives:
% 141.03/20.63 | | | (14) all_24_1 = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | REDUCE: (13), (14) imply:
% 141.03/20.63 | | | (15) op(e1, e0) = all_24_0
% 141.03/20.63 | | |
% 141.03/20.63 | | | BETA: splitting (10) gives:
% 141.03/20.63 | | |
% 141.03/20.63 | | | Case 1:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | (16) ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 141.03/20.63 | | | | all_40_1 & $i(all_40_0) & $i(all_40_1)
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | ALPHA: (16) implies:
% 141.03/20.63 | | | | (17) ~ (all_40_0 = e3)
% 141.03/20.63 | | | | (18) op(e0, e2) = all_40_1
% 141.03/20.63 | | | | (19) op(all_40_1, e0) = all_40_0
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | GROUND_INST: instantiating (6) with e1, all_40_1, e2, e0, simplifying
% 141.03/20.63 | | | | with (7), (18) gives:
% 141.03/20.63 | | | | (20) all_40_1 = e1
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | GROUND_INST: instantiating (6) with e3, all_24_0, e0, e1, simplifying
% 141.03/20.63 | | | | with (4), (15) gives:
% 141.03/20.63 | | | | (21) all_24_0 = e3
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | REDUCE: (19), (20) imply:
% 141.03/20.63 | | | | (22) op(e1, e0) = all_40_0
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | GROUND_INST: instantiating (6) with e3, all_40_0, e0, e1, simplifying
% 141.03/20.63 | | | | with (4), (22) gives:
% 141.03/20.63 | | | | (23) all_40_0 = e3
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | REDUCE: (17), (23) imply:
% 141.03/20.63 | | | | (24) $false
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | CLOSE: (24) is inconsistent.
% 141.03/20.63 | | | |
% 141.03/20.63 | | | Case 2:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | (25) ~ (all_40_1 = e1) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | REF_CLOSE: (6), (7), (25) are inconsistent by sub-proof #788.
% 141.03/20.63 | | | |
% 141.03/20.63 | | | End of split
% 141.03/20.63 | | |
% 141.03/20.63 | | Case 2:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (26) ~ (all_24_1 = e3) & op(e0, e2) = all_24_1 & $i(all_24_1)
% 141.03/20.63 | | |
% 141.03/20.63 | | | ALPHA: (26) implies:
% 141.03/20.63 | | | (27) op(e0, e2) = all_24_1
% 141.03/20.63 | | |
% 141.03/20.63 | | | GROUND_INST: instantiating (6) with e1, all_24_1, e2, e0, simplifying with
% 141.03/20.63 | | | (7), (27) gives:
% 141.03/20.63 | | | (28) all_24_1 = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | BETA: splitting (10) gives:
% 141.03/20.63 | | |
% 141.03/20.63 | | | Case 1:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | (29) ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 141.03/20.63 | | | | all_40_1 & $i(all_40_0) & $i(all_40_1)
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | ALPHA: (29) implies:
% 141.03/20.63 | | | | (30) ~ (all_40_0 = e3)
% 141.03/20.63 | | | | (31) op(e0, e2) = all_40_1
% 141.03/20.63 | | | | (32) op(all_40_1, e0) = all_40_0
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | GROUND_INST: instantiating (6) with e1, all_40_1, e2, e0, simplifying
% 141.03/20.63 | | | | with (7), (31) gives:
% 141.03/20.63 | | | | (33) all_40_1 = e1
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | REDUCE: (32), (33) imply:
% 141.03/20.63 | | | | (34) op(e1, e0) = all_40_0
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | GROUND_INST: instantiating (6) with e3, all_40_0, e0, e1, simplifying
% 141.03/20.63 | | | | with (4), (34) gives:
% 141.03/20.63 | | | | (35) all_40_0 = e3
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | REDUCE: (30), (35) imply:
% 141.03/20.63 | | | | (36) $false
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | CLOSE: (36) is inconsistent.
% 141.03/20.63 | | | |
% 141.03/20.63 | | | Case 2:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | (37) ~ (all_40_1 = e1) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | REF_CLOSE: (6), (7), (37) are inconsistent by sub-proof #788.
% 141.03/20.63 | | | |
% 141.03/20.63 | | | End of split
% 141.03/20.63 | | |
% 141.03/20.63 | | End of split
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #117 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (2) op(e1, e0) = e3
% 141.03/20.63 (3) op(e1, e0) = e1
% 141.03/20.63 (4) ~ (e3 = e1)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | GROUND_INST: instantiating (1) with e3, e1, e0, e1, simplifying with (2), (3)
% 141.03/20.63 | gives:
% 141.03/20.63 | (5) e3 = e1
% 141.03/20.63 |
% 141.03/20.63 | REDUCE: (4), (5) imply:
% 141.03/20.63 | (6) $false
% 141.03/20.63 |
% 141.03/20.63 | CLOSE: (6) is inconsistent.
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #118 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.03/20.63 all_56_11 & $i(all_56_11))
% 141.03/20.63 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.03/20.63 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.03/20.63 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.03/20.63 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.03/20.63 (3) ~ (e3 = e2)
% 141.03/20.63 (4) op(e0, e0) = e2
% 141.03/20.63 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (2) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (6) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 141.03/20.63 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (6) implies:
% 141.03/20.63 | | (7) op(e0, e0) = e3
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1066.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (8) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.03/20.63 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (8) implies:
% 141.03/20.63 | | (9) all_56_11 = e1
% 141.03/20.63 | | (10) ~ (all_56_4 = e2)
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (9), (10) are inconsistent by sub-proof #646.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #119 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.03/20.63 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.03/20.63 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.03/20.63 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.03/20.63 (2) all_56_11 = e1
% 141.03/20.63 (3) ~ (e3 = e1)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (1) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (4) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2
% 141.03/20.63 | | & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (4) implies:
% 141.03/20.63 | | (5) all_56_11 = e3
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #120.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (6) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2
% 141.03/20.63 | | & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (6) implies:
% 141.03/20.63 | | (7) all_56_11 = e3
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #120.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #120 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) all_56_11 = e3
% 141.03/20.63 (2) all_56_11 = e1
% 141.03/20.63 (3) ~ (e3 = e1)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | COMBINE_EQS: (1), (2) imply:
% 141.03/20.63 | (4) e3 = e1
% 141.03/20.63 |
% 141.03/20.63 | SIMP: (4) implies:
% 141.03/20.63 | (5) e3 = e1
% 141.03/20.63 |
% 141.03/20.63 | REDUCE: (3), (5) imply:
% 141.03/20.63 | (6) $false
% 141.03/20.63 |
% 141.03/20.63 | CLOSE: (6) is inconsistent.
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #121 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) all_57_4 = e1 & op(e3, e1) = e1
% 141.03/20.63 (2) all_57_4 = e0
% 141.03/20.63 (3) ~ (e1 = e0)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | ALPHA: (1) implies:
% 141.03/20.63 | (4) all_57_4 = e1
% 141.03/20.63 |
% 141.03/20.63 | COMBINE_EQS: (2), (4) imply:
% 141.03/20.63 | (5) e1 = e0
% 141.03/20.63 |
% 141.03/20.63 | REDUCE: (3), (5) imply:
% 141.03/20.63 | (6) $false
% 141.03/20.63 |
% 141.03/20.63 | CLOSE: (6) is inconsistent.
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #122 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.03/20.63 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.03/20.63 (2) ~ (e2 = e1)
% 141.03/20.63 (3) all_57_7 = e2
% 141.03/20.63 (4) ~ (e3 = e0)
% 141.03/20.63 (5) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.03/20.63 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.03/20.63 (6) ~ (e1 = e0)
% 141.03/20.63 (7) ~ (e2 = e0)
% 141.03/20.63 (8) op(e2, e2) = e3
% 141.03/20.63 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (10) ~ (e3 = e1)
% 141.03/20.63 (11) all_57_1 = e2
% 141.03/20.63 (12) all_57_3 = e3
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (1) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (13) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 141.03/20.63 | | e1)
% 141.03/20.63 | |
% 141.03/20.63 | | BETA: splitting (13) gives:
% 141.03/20.63 | |
% 141.03/20.63 | | Case 1:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (14) all_57_1 = e1 & op(e3, e2) = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (2), (11), (14) are inconsistent by sub-proof #1092.
% 141.03/20.63 | | |
% 141.03/20.63 | | Case 2:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (15) all_57_3 = e1 & op(e2, e2) = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (10), (12), (15) are inconsistent by sub-proof #163.
% 141.03/20.63 | | |
% 141.03/20.63 | | End of split
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (16) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 141.03/20.63 | | e1)
% 141.03/20.63 | |
% 141.03/20.63 | | BETA: splitting (16) gives:
% 141.03/20.63 | |
% 141.03/20.63 | | Case 1:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (17) all_57_7 = e1 & op(e1, e2) = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | REF_CLOSE: (2), (3), (17) are inconsistent by sub-proof #864.
% 141.03/20.63 | | |
% 141.03/20.63 | | Case 2:
% 141.03/20.63 | | |
% 141.03/20.63 | | | (18) all_57_13 = e1 & op(e0, e2) = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | ALPHA: (18) implies:
% 141.03/20.63 | | | (19) all_57_13 = e1
% 141.03/20.63 | | |
% 141.03/20.63 | | | BETA: splitting (5) gives:
% 141.03/20.63 | | |
% 141.03/20.63 | | | Case 1:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | (20) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 141.03/20.63 | | | | = e0)
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | BETA: splitting (20) gives:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | Case 1:
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | (21) all_57_1 = e0 & op(e3, e2) = e0
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | REF_CLOSE: (7), (11), (21) are inconsistent by sub-proof #267.
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | Case 2:
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | (22) all_57_3 = e0 & op(e2, e2) = e0
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | ALPHA: (22) implies:
% 141.03/20.63 | | | | | (23) op(e2, e2) = e0
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | REF_CLOSE: (4), (8), (9), (23) are inconsistent by sub-proof #1119.
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | End of split
% 141.03/20.63 | | | |
% 141.03/20.63 | | | Case 2:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | (24) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 141.03/20.63 | | | | = e0)
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | BETA: splitting (24) gives:
% 141.03/20.63 | | | |
% 141.03/20.63 | | | | Case 1:
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | (25) all_57_7 = e0 & op(e1, e2) = e0
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | REF_CLOSE: (3), (7), (25) are inconsistent by sub-proof #1017.
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | Case 2:
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | (26) all_57_13 = e0 & op(e0, e2) = e0
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | | REF_CLOSE: (6), (19), (26) are inconsistent by sub-proof #519.
% 141.03/20.63 | | | | |
% 141.03/20.63 | | | | End of split
% 141.03/20.63 | | | |
% 141.03/20.63 | | | End of split
% 141.03/20.63 | | |
% 141.03/20.63 | | End of split
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #123 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ~ (e2 = e1)
% 141.03/20.63 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.03/20.63 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.03/20.63 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.03/20.63 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.03/20.63 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.03/20.63 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.63 e1) = all_56_14 & $i(all_56_14))
% 141.03/20.63 (3) ~ (e3 = e0)
% 141.03/20.63 (4) op(e2, e2) = e3
% 141.03/20.63 (5) op(e0, e0) = e2
% 141.03/20.63 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (7) op(e0, e0) = all_56_15
% 141.03/20.63 (8) op(e3, e3) = all_14_2
% 141.03/20.63 (9) ~ (all_14_2 = e0)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | GROUND_INST: instantiating (6) with e2, all_56_15, e0, e0, simplifying with
% 141.03/20.63 | (5), (7) gives:
% 141.03/20.63 | (10) all_56_15 = e2
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (2) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.03/20.63 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.03/20.63 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.03/20.63 | | e2) = all_56_12 & $i(all_56_12))
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (3), (4), (6), (8), (9), (11) are inconsistent by sub-proof #124.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (12) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.03/20.63 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.03/20.63 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.03/20.63 | | e1) = all_56_14 & $i(all_56_14))
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (10), (12) are inconsistent by sub-proof #527.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #124 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ~ (e3 = e0)
% 141.03/20.63 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.03/20.63 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.03/20.63 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.03/20.63 $i(all_56_12))
% 141.03/20.63 (3) op(e2, e2) = e3
% 141.03/20.63 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (5) op(e3, e3) = all_14_2
% 141.03/20.63 (6) ~ (all_14_2 = e0)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (2) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (7) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.03/20.63 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (7) implies:
% 141.03/20.63 | | (8) op(e3, e3) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #1125.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (9) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.03/20.63 | | e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (9) implies:
% 141.03/20.63 | | (10) op(e2, e2) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (3), (4), (10) are inconsistent by sub-proof #1119.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #125 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.03/20.63 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.03/20.63 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.03/20.63 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.03/20.63 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (3) op(e3, e3) = e3
% 141.03/20.63 (4) ~ (e3 = e2)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (1) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (5) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2
% 141.03/20.63 | | & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (5) implies:
% 141.03/20.63 | | (6) op(e3, e3) = e2
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #450.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (7) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2
% 141.03/20.63 | | & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (7) implies:
% 141.03/20.63 | | (8) op(e3, e3) = e2
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #450.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #126 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ~ (all_52_11 = e3)
% 141.03/20.63 (2) op(e1, e1) = all_4_2
% 141.03/20.63 (3) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.03/20.63 (4) ~ (all_4_2 = e3)
% 141.03/20.63 (5) op(e0, e1) = all_52_11
% 141.03/20.63 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (3) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (7) implies:
% 141.03/20.63 | | (8) op(e1, e1) = e3
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1127.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (9) all_57_14 = e3 & op(e0, e1) = e3
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #184.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #127 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) op(e3, e3) = e2
% 141.03/20.63 (2) ~ (e2 = e0)
% 141.03/20.63 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (4) all_57_1 = e2
% 141.03/20.63 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (5) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (6) all_57_0 = e0 & op(e3, e3) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | ALPHA: (6) implies:
% 141.03/20.63 | | (7) op(e3, e3) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #880.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (8) all_57_1 = e0 & op(e3, e2) = e0
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #267.
% 141.03/20.63 | |
% 141.03/20.63 | End of split
% 141.03/20.63 |
% 141.03/20.63 End of proof
% 141.03/20.63
% 141.03/20.63 Sub-proof #128 shows that the following formulas are inconsistent:
% 141.03/20.63 ----------------------------------------------------------------
% 141.03/20.63 (1) ~ (e2 = e1)
% 141.03/20.63 (2) all_57_12 = e3
% 141.03/20.63 (3) op(e3, e3) = e2
% 141.03/20.63 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.03/20.63 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.03/20.63 (5) ~ (e3 = e0)
% 141.03/20.63 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.03/20.63 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.03/20.63 (7) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.03/20.63 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.03/20.63 (8) ~ (e1 = e0)
% 141.03/20.63 (9) ~ (e2 = e0)
% 141.03/20.63 (10) all_57_6 = e2
% 141.03/20.63 (11) ~ (e3 = e2)
% 141.03/20.63 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.03/20.63 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.03/20.63 (13) ~ (e3 = e1)
% 141.03/20.63
% 141.03/20.63 Begin of proof
% 141.03/20.63 |
% 141.03/20.63 | BETA: splitting (7) gives:
% 141.03/20.63 |
% 141.03/20.63 | Case 1:
% 141.03/20.63 | |
% 141.03/20.63 | | (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 141.03/20.63 | | e1)
% 141.03/20.63 | |
% 141.03/20.63 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (14)
% 141.03/20.63 | | are inconsistent by sub-proof #402.
% 141.03/20.63 | |
% 141.03/20.63 | Case 2:
% 141.03/20.63 | |
% 141.03/20.63 | | (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 141.17/20.64 | | e1)
% 141.17/20.64 | |
% 141.17/20.64 | | BETA: splitting (15) gives:
% 141.17/20.64 | |
% 141.17/20.64 | | Case 1:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (16) all_57_6 = e1 & op(e1, e3) = e1
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (1), (10), (16) are inconsistent by sub-proof #437.
% 141.17/20.64 | | |
% 141.17/20.64 | | Case 2:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (17) all_57_12 = e1 & op(e0, e3) = e1
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (2), (13), (17) are inconsistent by sub-proof #1073.
% 141.17/20.64 | | |
% 141.17/20.64 | | End of split
% 141.17/20.64 | |
% 141.17/20.64 | End of split
% 141.17/20.64 |
% 141.17/20.64 End of proof
% 141.17/20.64
% 141.17/20.64 Sub-proof #129 shows that the following formulas are inconsistent:
% 141.17/20.64 ----------------------------------------------------------------
% 141.17/20.64 (1) ~ (all_52_14 = e3)
% 141.17/20.64 (2) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.17/20.64 (3) op(e1, e1) = all_4_2
% 141.17/20.64 (4) ~ (all_4_2 = e3)
% 141.17/20.64 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.64 (6) op(e1, e0) = all_52_14
% 141.17/20.64
% 141.17/20.64 Begin of proof
% 141.17/20.64 |
% 141.17/20.64 | BETA: splitting (2) gives:
% 141.17/20.64 |
% 141.17/20.64 | Case 1:
% 141.17/20.64 | |
% 141.17/20.64 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 141.17/20.64 | |
% 141.17/20.64 | | ALPHA: (7) implies:
% 141.17/20.64 | | (8) op(e1, e1) = e3
% 141.17/20.64 | |
% 141.17/20.64 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1127.
% 141.17/20.64 | |
% 141.17/20.64 | Case 2:
% 141.17/20.64 | |
% 141.17/20.64 | | (9) all_57_11 = e3 & op(e1, e0) = e3
% 141.17/20.64 | |
% 141.17/20.64 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #160.
% 141.17/20.64 | |
% 141.17/20.64 | End of split
% 141.17/20.64 |
% 141.17/20.64 End of proof
% 141.17/20.64
% 141.17/20.64 Sub-proof #130 shows that the following formulas are inconsistent:
% 141.17/20.64 ----------------------------------------------------------------
% 141.17/20.64 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.17/20.64 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.17/20.64 (2) ~ (e3 = e0)
% 141.17/20.64 (3) ~ (e3 = e2)
% 141.17/20.64 (4) all_57_10 = e0
% 141.17/20.64 (5) all_57_5 = e2
% 141.17/20.64 (6) ~ (e3 = e1)
% 141.17/20.64 (7) e3 = e1
% 141.17/20.64 (8) all_57_3 = e3
% 141.17/20.64 (9) all_57_2 = e3
% 141.17/20.64
% 141.17/20.64 Begin of proof
% 141.17/20.64 |
% 141.17/20.64 | COMBINE_EQS: (7), (8) imply:
% 141.17/20.64 | (10) all_57_3 = e1
% 141.17/20.64 |
% 141.17/20.64 | COMBINE_EQS: (7), (9) imply:
% 141.17/20.64 | (11) all_57_2 = e1
% 141.17/20.64 |
% 141.17/20.64 | BETA: splitting (1) gives:
% 141.17/20.64 |
% 141.17/20.64 | Case 1:
% 141.17/20.64 | |
% 141.17/20.64 | | (12) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.17/20.64 | | e3)
% 141.17/20.64 | |
% 141.17/20.64 | | BETA: splitting (12) gives:
% 141.17/20.64 | |
% 141.17/20.64 | | Case 1:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (13) all_57_2 = e3 & op(e2, e3) = e3
% 141.17/20.64 | | |
% 141.17/20.64 | | | REDUCE: (6), (7) imply:
% 141.17/20.64 | | | (14) $false
% 141.17/20.64 | | |
% 141.17/20.64 | | | CLOSE: (14) is inconsistent.
% 141.17/20.64 | | |
% 141.17/20.64 | | Case 2:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (15) all_57_3 = e3 & op(e2, e2) = e3
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (6), (8), (10) are inconsistent by sub-proof #591.
% 141.17/20.64 | | |
% 141.17/20.64 | | End of split
% 141.17/20.64 | |
% 141.17/20.64 | Case 2:
% 141.17/20.64 | |
% 141.17/20.64 | | (16) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 141.17/20.64 | | e3)
% 141.17/20.64 | |
% 141.17/20.64 | | BETA: splitting (16) gives:
% 141.17/20.64 | |
% 141.17/20.64 | | Case 1:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (17) all_57_5 = e3 & op(e2, e1) = e3
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (3), (5), (17) are inconsistent by sub-proof #489.
% 141.17/20.64 | | |
% 141.17/20.64 | | Case 2:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (18) all_57_10 = e3 & op(e2, e0) = e3
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (2), (4), (18) are inconsistent by sub-proof #351.
% 141.17/20.64 | | |
% 141.17/20.64 | | End of split
% 141.17/20.64 | |
% 141.17/20.64 | End of split
% 141.17/20.64 |
% 141.17/20.64 End of proof
% 141.17/20.64
% 141.17/20.64 Sub-proof #131 shows that the following formulas are inconsistent:
% 141.17/20.64 ----------------------------------------------------------------
% 141.17/20.64 (1) ~ (e2 = e1)
% 141.17/20.64 (2) op(e3, e3) = e2
% 141.17/20.64 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.17/20.64 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.17/20.64 (4) ~ (e3 = e0)
% 141.17/20.64 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.17/20.64 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.17/20.64 (6) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.17/20.64 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.17/20.64 (7) ~ (e1 = e0)
% 141.17/20.64 (8) ~ (e2 = e0)
% 141.17/20.64 (9) all_57_6 = e2
% 141.17/20.64 (10) ~ (e3 = e2)
% 141.17/20.64 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.64 (12) ~ (e3 = e1)
% 141.17/20.64 (13) all_57_2 = e3
% 141.17/20.64
% 141.17/20.64 Begin of proof
% 141.17/20.64 |
% 141.17/20.64 | BETA: splitting (3) gives:
% 141.17/20.64 |
% 141.17/20.64 | Case 1:
% 141.17/20.64 | |
% 141.17/20.64 | | (14) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 141.17/20.64 | | e0)
% 141.17/20.64 | |
% 141.17/20.64 | | REF_CLOSE: (2), (4), (8), (11), (13), (14) are inconsistent by sub-proof
% 141.17/20.64 | | #132.
% 141.17/20.64 | |
% 141.17/20.64 | Case 2:
% 141.17/20.64 | |
% 141.17/20.64 | | (15) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 141.17/20.64 | | e0)
% 141.17/20.64 | |
% 141.17/20.64 | | BETA: splitting (15) gives:
% 141.17/20.64 | |
% 141.17/20.64 | | Case 1:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (16) all_57_6 = e0 & op(e1, e3) = e0
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (8), (9), (16) are inconsistent by sub-proof #994.
% 141.17/20.64 | | |
% 141.17/20.64 | | Case 2:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (17) all_57_12 = e0 & op(e0, e3) = e0
% 141.17/20.64 | | |
% 141.17/20.64 | | | ALPHA: (17) implies:
% 141.17/20.64 | | | (18) all_57_12 = e0
% 141.17/20.64 | | |
% 141.17/20.64 | | | BETA: splitting (6) gives:
% 141.17/20.64 | | |
% 141.17/20.64 | | | Case 1:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 141.17/20.64 | | | | = e1)
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | BETA: splitting (19) gives:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | Case 1:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | (20) all_57_0 = e1 & op(e3, e3) = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | ALPHA: (20) implies:
% 141.17/20.64 | | | | | (21) op(e3, e3) = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | REF_CLOSE: (1), (2), (11), (21) are inconsistent by sub-proof #818.
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | Case 2:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | (22) all_57_2 = e1 & op(e2, e3) = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | ALPHA: (22) implies:
% 141.17/20.64 | | | | | (23) all_57_2 = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | REF_CLOSE: (2), (4), (5), (9), (10), (11), (12), (18), (23) are
% 141.17/20.64 | | | | | inconsistent by sub-proof #404.
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | End of split
% 141.17/20.64 | | | |
% 141.17/20.64 | | | Case 2:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | (24) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 141.17/20.64 | | | | = e1)
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | BETA: splitting (24) gives:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | Case 1:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | (25) all_57_6 = e1 & op(e1, e3) = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | REF_CLOSE: (1), (9), (25) are inconsistent by sub-proof #437.
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | Case 2:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | (26) all_57_12 = e1 & op(e0, e3) = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | ALPHA: (26) implies:
% 141.17/20.64 | | | | | (27) all_57_12 = e1
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | REF_CLOSE: (7), (18), (27) are inconsistent by sub-proof #1002.
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | End of split
% 141.17/20.64 | | | |
% 141.17/20.64 | | | End of split
% 141.17/20.64 | | |
% 141.17/20.64 | | End of split
% 141.17/20.64 | |
% 141.17/20.64 | End of split
% 141.17/20.64 |
% 141.17/20.64 End of proof
% 141.17/20.64
% 141.17/20.64 Sub-proof #132 shows that the following formulas are inconsistent:
% 141.17/20.64 ----------------------------------------------------------------
% 141.17/20.64 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 141.17/20.64 (2) op(e3, e3) = e2
% 141.17/20.64 (3) ~ (e3 = e0)
% 141.17/20.64 (4) ~ (e2 = e0)
% 141.17/20.64 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.64 (6) all_57_2 = e3
% 141.17/20.64
% 141.17/20.64 Begin of proof
% 141.17/20.64 |
% 141.17/20.64 | BETA: splitting (1) gives:
% 141.17/20.64 |
% 141.17/20.64 | Case 1:
% 141.17/20.64 | |
% 141.17/20.64 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 141.17/20.64 | |
% 141.17/20.64 | | ALPHA: (7) implies:
% 141.17/20.64 | | (8) op(e3, e3) = e0
% 141.17/20.64 | |
% 141.17/20.64 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #880.
% 141.17/20.64 | |
% 141.17/20.64 | Case 2:
% 141.17/20.64 | |
% 141.17/20.64 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 141.17/20.64 | |
% 141.17/20.64 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #697.
% 141.17/20.64 | |
% 141.17/20.64 | End of split
% 141.17/20.64 |
% 141.17/20.64 End of proof
% 141.17/20.64
% 141.17/20.64 Sub-proof #133 shows that the following formulas are inconsistent:
% 141.17/20.64 ----------------------------------------------------------------
% 141.17/20.64 (1) ~ (e2 = e1)
% 141.17/20.64 (2) all_57_4 = e3
% 141.17/20.64 (3) op(e3, e3) = e2
% 141.17/20.64 (4) ~ (e3 = e0)
% 141.17/20.64 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.17/20.64 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.17/20.64 (6) ~ (e1 = e0)
% 141.17/20.64 (7) ~ (e2 = e0)
% 141.17/20.64 (8) ~ (e3 = e2)
% 141.17/20.64 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.64 (10) ~ (e3 = e1)
% 141.17/20.64 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.17/20.64 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.17/20.64 (12) all_57_7 = e3
% 141.17/20.64 (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.17/20.64 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.17/20.64 (14) all_57_7 = e2 & op(e1, e2) = e2
% 141.17/20.64
% 141.17/20.64 Begin of proof
% 141.17/20.64 |
% 141.17/20.64 | ALPHA: (14) implies:
% 141.17/20.64 | (15) all_57_7 = e2
% 141.17/20.64 |
% 141.17/20.64 | COMBINE_EQS: (12), (15) imply:
% 141.17/20.64 | (16) e3 = e2
% 141.17/20.64 |
% 141.17/20.64 | COMBINE_EQS: (2), (16) imply:
% 141.17/20.64 | (17) all_57_4 = e2
% 141.17/20.64 |
% 141.17/20.64 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13), (17) are
% 141.17/20.64 | inconsistent by sub-proof #407.
% 141.17/20.64 |
% 141.17/20.64 End of proof
% 141.17/20.64
% 141.17/20.64 Sub-proof #134 shows that the following formulas are inconsistent:
% 141.17/20.64 ----------------------------------------------------------------
% 141.17/20.64 (1) ~ (all_10_2 = e2)
% 141.17/20.64 (2) ~ (all_52_1 = e2)
% 141.17/20.64 (3) op(e1, e3) = all_52_2
% 141.17/20.64 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.17/20.64 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.17/20.64 (5) all_46_2 = e3
% 141.17/20.64 (6) ~ (all_52_2 = all_52_14)
% 141.17/20.64 (7) ~ (e2 = e1)
% 141.17/20.64 (8) ~ (all_52_4 = all_52_8)
% 141.17/20.64 (9) op(e0, e0) = e3
% 141.17/20.64 (10) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.17/20.64 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.17/20.64 (11) all_57_6 = e3 & op(e1, e3) = e3
% 141.17/20.64 (12) ~ (all_52_14 = all_4_2)
% 141.17/20.64 (13) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.17/20.64 (14) all_57_4 = e3
% 141.17/20.64 (15) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.17/20.64 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.17/20.64 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.17/20.64 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.17/20.64 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.17/20.64 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.17/20.64 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.17/20.64 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.17/20.64 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.17/20.64 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.17/20.64 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.17/20.64 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.17/20.64 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.17/20.64 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.17/20.64 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.17/20.64 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.17/20.64 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.17/20.64 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.17/20.64 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.17/20.64 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.17/20.64 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.17/20.64 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.17/20.64 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.17/20.64 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.17/20.64 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.17/20.64 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.17/20.64 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.17/20.64 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.17/20.64 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.17/20.64 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.17/20.64 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.17/20.64 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.17/20.64 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.17/20.64 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.17/20.64 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.17/20.64 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.17/20.64 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.17/20.64 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.17/20.64 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.17/20.64 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.17/20.64 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.17/20.64 (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.17/20.64 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.17/20.64 (17) ~ (all_10_2 = e1)
% 141.17/20.64 (18) ~ (all_52_7 = e3)
% 141.17/20.64 (19) ~ (all_52_8 = all_4_2)
% 141.17/20.64 (20) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.17/20.64 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.17/20.64 e1)
% 141.17/20.64 (21) ~ (all_14_2 = e1)
% 141.17/20.64 (22) op(e3, e3) = e2
% 141.17/20.64 (23) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.17/20.64 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.17/20.64 (24) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.17/20.64 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.17/20.64 (25) ~ (e3 = e0)
% 141.17/20.64 (26) op(e1, e1) = all_4_2
% 141.17/20.64 (27) op(e3, e1) = all_52_8
% 141.17/20.64 (28) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.17/20.64 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.17/20.64 (29) op(e2, e3) = all_52_1
% 141.17/20.64 (30) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.17/20.64 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.17/20.64 (31) op(e0, e0) = all_10_2
% 141.17/20.64 (32) ~ (all_52_8 = all_52_12)
% 141.17/20.64 (33) ~ (e1 = e0)
% 141.17/20.64 (34) op(e3, e2) = all_52_4
% 141.17/20.64 (35) ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 &
% 141.17/20.64 op(e0, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 141.17/20.64 e1) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 141.17/20.64 (36) op(e3, e0) = all_52_12
% 141.17/20.64 (37) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.17/20.64 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.17/20.64 (38) op(e2, e2) = e3
% 141.17/20.64 (39) ~ (all_4_2 = e2)
% 141.17/20.64 (40) all_54_10 = all_4_2
% 141.17/20.64 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.64 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.64 (42) ~ (e3 = e1)
% 141.17/20.64 (43) op(e0, e2) = all_52_7
% 141.17/20.64 (44) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 141.17/20.64 all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0,
% 141.17/20.64 e3) = all_42_1 & $i(all_42_1))
% 141.17/20.64 (45) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.17/20.64 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.17/20.64 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.17/20.64 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.17/20.64 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.17/20.64 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.17/20.64 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.17/20.64 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.17/20.64 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.17/20.64 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.17/20.64 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.17/20.64 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.17/20.64 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.17/20.64 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.17/20.64 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.17/20.64 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.17/20.64 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.17/20.64 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.17/20.64 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.17/20.64 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.17/20.64 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.17/20.64 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.17/20.64 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.17/20.64 $i(all_56_14))))
% 141.17/20.64 (46) op(e3, e1) = e3
% 141.17/20.64 (47) op(e3, e3) = all_14_2
% 141.17/20.64 (48) ~ (all_52_8 = e2)
% 141.17/20.64 (49) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.17/20.64 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.17/20.64 (50) op(e2, e0) = all_52_13
% 141.17/20.64 (51) ~ (all_14_2 = e0)
% 141.17/20.64 (52) op(e1, e0) = all_52_14
% 141.17/20.64
% 141.17/20.64 Begin of proof
% 141.17/20.64 |
% 141.17/20.64 | ALPHA: (11) implies:
% 141.17/20.64 | (53) all_57_6 = e3
% 141.17/20.64 | (54) op(e1, e3) = e3
% 141.17/20.64 |
% 141.17/20.64 | GROUND_INST: instantiating (41) with all_52_2, e3, e3, e1, simplifying with
% 141.17/20.64 | (3), (54) gives:
% 141.17/20.64 | (55) all_52_2 = e3
% 141.17/20.64 |
% 141.17/20.64 | GROUND_INST: instantiating (41) with all_52_8, e3, e1, e3, simplifying with
% 141.17/20.64 | (27), (46) gives:
% 141.17/20.64 | (56) all_52_8 = e3
% 141.17/20.64 |
% 141.17/20.64 | REDUCE: (6), (55) imply:
% 141.17/20.64 | (57) ~ (all_52_14 = e3)
% 141.17/20.64 |
% 141.17/20.64 | SIMP: (57) implies:
% 141.17/20.64 | (58) ~ (all_52_14 = e3)
% 141.17/20.64 |
% 141.17/20.64 | REDUCE: (8), (56) imply:
% 141.17/20.64 | (59) ~ (all_52_4 = e3)
% 141.17/20.64 |
% 141.17/20.64 | REDUCE: (32), (56) imply:
% 141.17/20.64 | (60) ~ (all_52_12 = e3)
% 141.17/20.64 |
% 141.17/20.64 | SIMP: (60) implies:
% 141.17/20.64 | (61) ~ (all_52_12 = e3)
% 141.17/20.64 |
% 141.17/20.64 | REDUCE: (19), (56) imply:
% 141.17/20.64 | (62) ~ (all_4_2 = e3)
% 141.17/20.64 |
% 141.17/20.64 | SIMP: (62) implies:
% 141.17/20.64 | (63) ~ (all_4_2 = e3)
% 141.17/20.64 |
% 141.17/20.64 | REDUCE: (48), (56) imply:
% 141.17/20.64 | (64) ~ (e3 = e2)
% 141.17/20.64 |
% 141.17/20.64 | BETA: splitting (15) gives:
% 141.17/20.64 |
% 141.17/20.64 | Case 1:
% 141.17/20.64 | |
% 141.17/20.64 | | (65) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 141.17/20.64 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.17/20.64 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.17/20.64 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.17/20.64 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.17/20.64 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.17/20.64 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.17/20.64 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.17/20.64 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.17/20.64 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.17/20.64 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.17/20.64 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 141.17/20.64 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.17/20.64 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.17/20.64 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.17/20.64 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.17/20.64 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.17/20.64 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.17/20.64 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.17/20.64 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.17/20.64 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.17/20.64 | | $i(all_56_12))))
% 141.17/20.64 | |
% 141.17/20.64 | | REF_CLOSE: (2), (22), (29), (34), (38), (41), (59), (65) are inconsistent by
% 141.17/20.64 | | sub-proof #177.
% 141.17/20.64 | |
% 141.17/20.64 | Case 2:
% 141.17/20.64 | |
% 141.17/20.64 | | (66) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.17/20.64 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.17/20.64 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.17/20.64 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.17/20.64 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.17/20.64 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.17/20.64 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.17/20.64 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.17/20.64 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.17/20.64 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.17/20.64 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.17/20.64 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | (
% 141.17/20.64 | | ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.17/20.64 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.17/20.64 | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 141.17/20.64 | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.17/20.64 | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.17/20.64 | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.17/20.64 | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 141.17/20.64 | | e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.17/20.64 | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.17/20.64 | | $i(all_56_8))))
% 141.17/20.64 | |
% 141.17/20.64 | | BETA: splitting (66) gives:
% 141.17/20.64 | |
% 141.17/20.64 | | Case 1:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (67) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.17/20.64 | | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.17/20.64 | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.17/20.64 | | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.17/20.64 | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.17/20.64 | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.17/20.64 | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.17/20.64 | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.17/20.64 | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.17/20.64 | | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.17/20.64 | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.17/20.64 | | |
% 141.17/20.64 | | | ALPHA: (67) implies:
% 141.17/20.64 | | | (68) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.17/20.64 | | | e1) = all_56_1 & $i(all_56_1))
% 141.17/20.64 | | |
% 141.17/20.64 | | | REF_CLOSE: (7), (22), (41), (46), (68) are inconsistent by sub-proof #153.
% 141.17/20.64 | | |
% 141.17/20.64 | | Case 2:
% 141.17/20.64 | | |
% 141.17/20.64 | | | (69) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.17/20.64 | | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.17/20.64 | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.17/20.64 | | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.17/20.64 | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.17/20.64 | | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.17/20.64 | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.17/20.64 | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.17/20.64 | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.17/20.64 | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.17/20.64 | | | e0) = all_56_8 & $i(all_56_8)))
% 141.17/20.64 | | |
% 141.17/20.64 | | | ALPHA: (69) implies:
% 141.17/20.64 | | | (70) op(e0, e0) = all_56_15
% 141.17/20.64 | | | (71) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.17/20.64 | | | e0) = all_56_8 & $i(all_56_8))
% 141.17/20.64 | | | (72) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 141.17/20.64 | | | e0) = all_56_5 & $i(all_56_5))
% 141.17/20.64 | | | (73) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.17/20.64 | | | e1) = all_56_13 & $i(all_56_13))
% 141.17/20.64 | | | (74) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.17/20.64 | | | e2) = all_56_11 & $i(all_56_11))
% 141.17/20.64 | | | (75) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3,
% 141.17/20.64 | | | e3) = all_56_9 & $i(all_56_9))
% 141.17/20.64 | | |
% 141.17/20.64 | | | BETA: splitting (75) gives:
% 141.17/20.64 | | |
% 141.17/20.64 | | | Case 1:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | (76) all_56_2 = e3 & op(e3, e0) = e3
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | ALPHA: (76) implies:
% 141.17/20.64 | | | | (77) op(e3, e0) = e3
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | REF_CLOSE: (36), (41), (61), (77) are inconsistent by sub-proof #1105.
% 141.17/20.64 | | | |
% 141.17/20.64 | | | Case 2:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | (78) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | ALPHA: (78) implies:
% 141.17/20.64 | | | | (79) ~ (all_56_9 = e0)
% 141.17/20.64 | | | | (80) op(e3, e3) = all_56_9
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | BETA: splitting (72) gives:
% 141.17/20.64 | | | |
% 141.17/20.64 | | | | Case 1:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | (81) all_56_11 = e0 & op(e2, e2) = e0
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | ALPHA: (81) implies:
% 141.17/20.64 | | | | | (82) op(e2, e2) = e0
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | REF_CLOSE: (1), (17), (21), (25), (31), (33), (41), (45), (47), (51),
% 141.17/20.64 | | | | | (82) are inconsistent by sub-proof #235.
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | Case 2:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | (83) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5)
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | ALPHA: (83) implies:
% 141.17/20.64 | | | | | (84) ~ (all_56_5 = e2)
% 141.17/20.64 | | | | | (85) op(e2, e0) = all_56_5
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | BETA: splitting (74) gives:
% 141.17/20.64 | | | | |
% 141.17/20.64 | | | | | Case 1:
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | (86) all_56_5 = e2 & op(e2, e0) = e2
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | ALPHA: (86) implies:
% 141.17/20.64 | | | | | | (87) all_56_5 = e2
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | REDUCE: (84), (87) imply:
% 141.17/20.64 | | | | | | (88) $false
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | CLOSE: (88) is inconsistent.
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | Case 2:
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | (89) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | ALPHA: (89) implies:
% 141.17/20.64 | | | | | | (90) ~ (all_56_11 = e0)
% 141.17/20.64 | | | | | | (91) op(e2, e2) = all_56_11
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | GROUND_INST: instantiating (41) with e3, all_56_15, e0, e0,
% 141.17/20.64 | | | | | | simplifying with (9), (70) gives:
% 141.17/20.64 | | | | | | (92) all_56_15 = e3
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | GROUND_INST: instantiating (41) with all_52_13, all_56_5, e0, e2,
% 141.17/20.64 | | | | | | simplifying with (50), (85) gives:
% 141.17/20.64 | | | | | | (93) all_56_5 = all_52_13
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | GROUND_INST: instantiating (41) with e3, all_56_11, e2, e2,
% 141.17/20.64 | | | | | | simplifying with (38), (91) gives:
% 141.17/20.64 | | | | | | (94) all_56_11 = e3
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | GROUND_INST: instantiating (41) with e2, all_56_9, e3, e3,
% 141.17/20.64 | | | | | | simplifying with (22), (80) gives:
% 141.17/20.64 | | | | | | (95) all_56_9 = e2
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | REDUCE: (84), (93) imply:
% 141.17/20.64 | | | | | | (96) ~ (all_52_13 = e2)
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | REDUCE: (79), (95) imply:
% 141.17/20.64 | | | | | | (97) ~ (e2 = e0)
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | BETA: splitting (4) gives:
% 141.17/20.64 | | | | | |
% 141.17/20.64 | | | | | | Case 1:
% 141.17/20.64 | | | | | | |
% 141.17/20.65 | | | | | | | (98) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 141.17/20.65 | | | | | | | op(e2, e2) = e2)
% 141.17/20.65 | | | | | | |
% 141.17/20.65 | | | | | | | REF_CLOSE: (2), (29), (38), (41), (64), (98) are inconsistent by
% 141.17/20.65 | | | | | | | sub-proof #154.
% 141.17/20.65 | | | | | | |
% 141.17/20.65 | | | | | | Case 2:
% 141.17/20.65 | | | | | | |
% 141.17/20.65 | | | | | | | (99) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 141.17/20.65 | | | | | | | op(e2, e0) = e2)
% 141.17/20.65 | | | | | | |
% 141.17/20.65 | | | | | | | BETA: splitting (99) gives:
% 141.17/20.65 | | | | | | |
% 141.17/20.65 | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | (100) all_57_5 = e2 & op(e2, e1) = e2
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | ALPHA: (100) implies:
% 141.17/20.65 | | | | | | | | (101) all_57_5 = e2
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | BETA: splitting (23) gives:
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | | (102) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 141.17/20.65 | | | | | | | | | op(e2, e0) = e2)
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | | BETA: splitting (102) gives:
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | (103) all_57_9 = e2 & op(e3, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | ALPHA: (103) implies:
% 141.17/20.65 | | | | | | | | | | (104) all_57_9 = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | BETA: splitting (49) gives:
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | (105) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 141.17/20.65 | | | | | | | | | | | & op(e3, e2) = e0)
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | BETA: splitting (105) gives:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (106) all_57_0 = e0 & op(e3, e3) = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (106) implies:
% 141.17/20.65 | | | | | | | | | | | | (107) op(e3, e3) = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | REF_CLOSE: (9), (26), (33), (39), (41), (42), (45), (64),
% 141.17/20.65 | | | | | | | | | | | | (79), (97), (107) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | #531.
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (108) all_57_1 = e0 & op(e3, e2) = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (108) implies:
% 141.17/20.65 | | | | | | | | | | | | (109) all_57_1 = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | BETA: splitting (30) gives:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (110) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 141.17/20.65 | | | | | | | | | | | | | & op(e3, e2) = e1)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | REF_CLOSE: (7), (22), (33), (41), (109), (110) are
% 141.17/20.65 | | | | | | | | | | | | | inconsistent by sub-proof #144.
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (111) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 141.17/20.65 | | | | | | | | | | | | | & op(e3, e0) = e1)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | BETA: splitting (111) gives:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (112) all_57_4 = e1 & op(e3, e1) = e1
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (112) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | #143.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (113) all_57_9 = e1 & op(e3, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (113) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (114) all_57_9 = e1
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (7), (104), (114) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | #815.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | (115) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 141.17/20.65 | | | | | | | | | | | & op(e3, e0) = e0)
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | BETA: splitting (115) gives:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (116) all_57_4 = e0 & op(e3, e1) = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (116) implies:
% 141.17/20.65 | | | | | | | | | | | | (117) all_57_4 = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | REF_CLOSE: (14), (25), (117) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | #831.
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (118) all_57_9 = e0 & op(e3, e0) = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (118) implies:
% 141.17/20.65 | | | | | | | | | | | | (119) all_57_9 = e0
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | REF_CLOSE: (97), (104), (119) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | #1018.
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | (120) all_57_10 = e2 & op(e2, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | ALPHA: (120) implies:
% 141.17/20.65 | | | | | | | | | | (121) op(e2, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | REF_CLOSE: (41), (50), (96), (121) are inconsistent by
% 141.17/20.65 | | | | | | | | | | sub-proof #1030.
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | | (122) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2
% 141.17/20.65 | | | | | | | | | & op(e0, e0) = e2)
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | | BETA: splitting (122) gives:
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | (123) all_57_11 = e2 & op(e1, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | ALPHA: (123) implies:
% 141.17/20.65 | | | | | | | | | | (124) all_57_11 = e2
% 141.17/20.65 | | | | | | | | | | (125) op(e1, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | GROUND_INST: instantiating (41) with all_52_14, e2, e0, e1,
% 141.17/20.65 | | | | | | | | | | simplifying with (52), (125) gives:
% 141.17/20.65 | | | | | | | | | | (126) all_52_14 = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | REDUCE: (12), (126) imply:
% 141.17/20.65 | | | | | | | | | | (127) ~ (all_4_2 = e2)
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | REDUCE: (58), (126) imply:
% 141.17/20.65 | | | | | | | | | | (128) ~ (e3 = e2)
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | BETA: splitting (24) gives:
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | (129) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2
% 141.17/20.65 | | | | | | | | | | | & op(e2, e2) = e2)
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | BETA: splitting (129) gives:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (130) all_57_1 = e2 & op(e3, e2) = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (130) implies:
% 141.17/20.65 | | | | | | | | | | | | (131) all_57_1 = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | BETA: splitting (30) gives:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (132) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 141.17/20.65 | | | | | | | | | | | | | & op(e3, e2) = e1)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | REF_CLOSE: (7), (22), (41), (131), (132) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | sub-proof #142.
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (133) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 141.17/20.65 | | | | | | | | | | | | | & op(e3, e0) = e1)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | BETA: splitting (133) gives:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (134) all_57_4 = e1 & op(e3, e1) = e1
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (134) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | #143.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (135) all_57_9 = e1 & op(e3, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (135) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (136) all_57_9 = e1
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | BETA: splitting (49) gives:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | (137) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | & op(e3, e2) = e0)
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | BETA: splitting (137) gives:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (138) all_57_0 = e0 & op(e3, e3) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | (139) op(e3, e3) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (26), (33), (39), (41), (42), (45), (64),
% 141.17/20.65 | | | | | | | | | | | | | | | | (79), (97), (139) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | #531.
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (140) all_57_1 = e0 & op(e3, e2) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | REF_CLOSE: (97), (131), (140) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | #267.
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | (141) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | & op(e3, e0) = e0)
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | BETA: splitting (141) gives:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (142) all_57_4 = e0 & op(e3, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (142) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | #337.
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (143) all_57_9 = e0 & op(e3, e0) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | REF_CLOSE: (33), (136), (143) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | #813.
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (144) all_57_3 = e2 & op(e2, e2) = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (144) implies:
% 141.17/20.65 | | | | | | | | | | | | (145) op(e2, e2) = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | REF_CLOSE: (38), (41), (64), (145) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | sub-proof #728.
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | (146) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 =
% 141.17/20.65 | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | BETA: splitting (146) gives:
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (147) all_57_7 = e2 & op(e1, e2) = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (147) implies:
% 141.17/20.65 | | | | | | | | | | | | (148) all_57_7 = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | BETA: splitting (28) gives:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (149) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 141.17/20.65 | | | | | | | | | | | | | & op(e1, e2) = e0)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | BETA: splitting (149) gives:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (150) all_57_6 = e0 & op(e1, e3) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (150) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (151) all_57_6 = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (25), (53), (151) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | #873.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (152) all_57_7 = e0 & op(e1, e2) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (152) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (153) all_57_7 = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (97), (148), (153) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | #578.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (154) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 141.17/20.65 | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | BETA: splitting (154) gives:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (155) all_57_8 = e0 & op(e1, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (155) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (156) op(e1, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | BETA: splitting (73) gives:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | (157) all_56_8 = e1 & op(e1, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | ALPHA: (157) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | (158) all_56_8 = e1
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (159) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | BETA: splitting (159) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | (160) all_57_6 = e1 & op(e1, e3) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (53), (160) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | | #865.
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | (161) all_57_7 = e1 & op(e1, e2) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | ALPHA: (161) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | (162) all_57_7 = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (148), (162) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | | #872.
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (163) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 141.17/20.65 | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | (164) all_57_8 = e1 & op(e1, e1) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | (165) op(e1, e1) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (41), (71), (158), (165) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | | | | | sub-proof #141.
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | (166) all_57_11 = e1 & op(e1, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (124), (166) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | | #862.
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | (167) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.17/20.65 | | | | | | | | | | | | | | | $i(all_56_13)
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | (168) ~ (all_56_13 = e0)
% 141.17/20.65 | | | | | | | | | | | | | | | (169) op(e1, e1) = all_56_13
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | REF_CLOSE: (41), (156), (168), (169) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | | | sub-proof #140.
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (170) all_57_11 = e0 & op(e1, e0) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (170) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (171) all_57_11 = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (97), (124), (171) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | #996.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | (172) all_57_13 = e2 & op(e0, e2) = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | ALPHA: (172) implies:
% 141.17/20.65 | | | | | | | | | | | | (173) all_57_13 = e2
% 141.17/20.65 | | | | | | | | | | | | (174) op(e0, e2) = e2
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | BETA: splitting (73) gives:
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (175) all_56_8 = e1 & op(e1, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | ALPHA: (175) implies:
% 141.17/20.65 | | | | | | | | | | | | | (176) op(e1, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | REF_CLOSE: (7), (41), (125), (176) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | sub-proof #139.
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | (177) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.17/20.65 | | | | | | | | | | | | | $i(all_56_13)
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | ALPHA: (177) implies:
% 141.17/20.65 | | | | | | | | | | | | | (178) ~ (all_56_13 = e0)
% 141.17/20.65 | | | | | | | | | | | | | (179) op(e1, e1) = all_56_13
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | BETA: splitting (71) gives:
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (180) all_56_13 = e0 & op(e1, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (180) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (181) op(e1, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REF_CLOSE: (41), (178), (179), (181) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | | sub-proof #140.
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | (182) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.17/20.65 | | | | | | | | | | | | | | $i(all_56_8)
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | ALPHA: (182) implies:
% 141.17/20.65 | | | | | | | | | | | | | | (183) ~ (all_56_8 = e1)
% 141.17/20.65 | | | | | | | | | | | | | | (184) op(e1, e0) = all_56_8
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with all_52_7, e2, e2, e0,
% 141.17/20.65 | | | | | | | | | | | | | | simplifying with (43), (174) gives:
% 141.17/20.65 | | | | | | | | | | | | | | (185) all_52_7 = e2
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with e2, all_56_8, e0, e1,
% 141.17/20.65 | | | | | | | | | | | | | | simplifying with (125), (184) gives:
% 141.17/20.65 | | | | | | | | | | | | | | (186) all_56_8 = e2
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | GROUND_INST: instantiating (41) with all_4_2, all_56_13, e1,
% 141.17/20.65 | | | | | | | | | | | | | | e1, simplifying with (26), (179) gives:
% 141.17/20.65 | | | | | | | | | | | | | | (187) all_56_13 = all_4_2
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | REDUCE: (178), (187) imply:
% 141.17/20.65 | | | | | | | | | | | | | | (188) ~ (all_4_2 = e0)
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | BETA: splitting (13) gives:
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | (189) all_54_10 = e3
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | REF_CLOSE: (40), (63), (189) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | #1112.
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | (190) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (191) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | BETA: splitting (191) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | (192) all_57_6 = e0 & op(e1, e3) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | REF_CLOSE: (25), (53), (192) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | | #603.
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | (193) all_57_7 = e0 & op(e1, e2) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | ALPHA: (193) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | (194) all_57_7 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | (195) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (25), (97), (101), (195) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | | | | | | sub-proof #138.
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | (196) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 141.17/20.65 | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | BETA: splitting (196) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | (197) all_57_8 = e0 & op(e1, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | (198) all_57_8 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (10), (25), (33), (37), (42), (64), (124),
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | (194), (198) are inconsistent by sub-proof #436.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | (199) all_57_14 = e0 & op(e0, e1) = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | ALPHA: (199) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | (200) all_57_14 = e0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | (201) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (201) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (202) all_57_12 = e1 & op(e0, e3) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (202) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (203) op(e0, e3) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (35) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | (204) ~ (all_46_2 = e3)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (5), (204) imply:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | (205) $false
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (205) is inconsistent.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | (206) ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | & op(e0, e3) = all_46_1 & $i(all_46_0) &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | $i(all_46_1)) | ( ~ (all_46_1 = e1) & op(e0, e3)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | = all_46_1 & $i(all_46_1))
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (206) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | (207) ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_46_1 & $i(all_46_0) &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_1)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (207) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | (208) ~ (all_46_0 = e2)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | (209) op(e0, e3) = all_46_1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | (210) op(all_46_1, e0) = all_46_0
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (44) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | (211) ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_42_1 & $i(all_42_0) &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (211) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | (212) op(e0, e3) = all_42_1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (125), (203), (208), (209), (210), (212) are
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #137.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | (213) ~ (all_42_1 = e2) & op(e0, e3) = all_42_1 &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | $i(all_42_1)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (213) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | (214) op(e0, e3) = all_42_1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (125), (203), (208), (209), (210), (214) are
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #137.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | (215) ~ (all_46_1 = e1) & op(e0, e3) = all_46_1 &
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | $i(all_46_1)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (203), (215) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | | #555.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (216) all_57_13 = e1 & op(e0, e2) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (216) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (217) all_57_13 = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (173), (217) imply:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (218) e2 = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (186), (218) imply:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (219) all_56_8 = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (39), (40), (41), (71), (188), (190), (219)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #136.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | (220) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | BETA: splitting (220) gives:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (221) all_57_14 = e1 & op(e0, e1) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (221) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (222) all_57_14 = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (33), (200), (222) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | #1071.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (223) all_57_15 = e1 & op(e0, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | ALPHA: (223) implies:
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | (224) op(e0, e0) = e1
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (41), (42), (224) are inconsistent by
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | | sub-proof #732.
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | (225) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 141.17/20.65 | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | | REF_CLOSE: (41), (97), (124), (178), (179), (225) are
% 141.17/20.65 | | | | | | | | | | | | | | | | inconsistent by sub-proof #135.
% 141.17/20.65 | | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | (226) all_57_15 = e2 & op(e0, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | ALPHA: (226) implies:
% 141.17/20.65 | | | | | | | | | | (227) op(e0, e0) = e2
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | | REF_CLOSE: (9), (41), (64), (227) are inconsistent by
% 141.17/20.65 | | | | | | | | | | sub-proof #1066.
% 141.17/20.65 | | | | | | | | | |
% 141.17/20.65 | | | | | | | | | End of split
% 141.17/20.65 | | | | | | | | |
% 141.17/20.65 | | | | | | | | End of split
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | Case 2:
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | (228) all_57_10 = e2 & op(e2, e0) = e2
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | ALPHA: (228) implies:
% 141.17/20.65 | | | | | | | | (229) op(e2, e0) = e2
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | | REF_CLOSE: (41), (50), (96), (229) are inconsistent by sub-proof
% 141.17/20.65 | | | | | | | | #1030.
% 141.17/20.65 | | | | | | | |
% 141.17/20.65 | | | | | | | End of split
% 141.17/20.65 | | | | | | |
% 141.17/20.65 | | | | | | End of split
% 141.17/20.65 | | | | | |
% 141.17/20.65 | | | | | End of split
% 141.17/20.65 | | | | |
% 141.17/20.65 | | | | End of split
% 141.17/20.65 | | | |
% 141.17/20.65 | | | End of split
% 141.17/20.65 | | |
% 141.17/20.65 | | End of split
% 141.17/20.65 | |
% 141.17/20.65 | End of split
% 141.17/20.65 |
% 141.17/20.65 End of proof
% 141.17/20.65
% 141.17/20.65 Sub-proof #135 shows that the following formulas are inconsistent:
% 141.17/20.65 ----------------------------------------------------------------
% 141.17/20.65 (1) ~ (all_56_13 = e0)
% 141.17/20.65 (2) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.17/20.65 (3) all_57_11 = e2
% 141.17/20.65 (4) ~ (e2 = e0)
% 141.17/20.65 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.65 (6) op(e1, e1) = all_56_13
% 141.17/20.65
% 141.17/20.65 Begin of proof
% 141.17/20.65 |
% 141.17/20.65 | BETA: splitting (2) gives:
% 141.17/20.65 |
% 141.17/20.65 | Case 1:
% 141.17/20.65 | |
% 141.17/20.65 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 141.17/20.65 | |
% 141.17/20.65 | | ALPHA: (7) implies:
% 141.17/20.65 | | (8) op(e1, e1) = e0
% 141.17/20.65 | |
% 141.17/20.65 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #140.
% 141.17/20.65 | |
% 141.17/20.65 | Case 2:
% 141.17/20.65 | |
% 141.17/20.65 | | (9) all_57_11 = e0 & op(e1, e0) = e0
% 141.17/20.65 | |
% 141.17/20.65 | | ALPHA: (9) implies:
% 141.17/20.65 | | (10) all_57_11 = e0
% 141.17/20.65 | |
% 141.17/20.65 | | REF_CLOSE: (3), (4), (10) are inconsistent by sub-proof #996.
% 141.17/20.65 | |
% 141.17/20.65 | End of split
% 141.17/20.65 |
% 141.17/20.65 End of proof
% 141.17/20.65
% 141.17/20.65 Sub-proof #136 shows that the following formulas are inconsistent:
% 141.17/20.65 ----------------------------------------------------------------
% 141.17/20.65 (1) ~ (all_4_2 = e0)
% 141.17/20.65 (2) op(e1, e1) = all_4_2
% 141.17/20.65 (3) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.17/20.65 all_56_8 & $i(all_56_8))
% 141.17/20.65 (4) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.17/20.65 (5) all_56_8 = e1
% 141.17/20.65 (6) ~ (all_4_2 = e2)
% 141.17/20.65 (7) all_54_10 = all_4_2
% 141.17/20.65 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.65
% 141.17/20.65 Begin of proof
% 141.17/20.65 |
% 141.17/20.65 | BETA: splitting (4) gives:
% 141.17/20.65 |
% 141.17/20.65 | Case 1:
% 141.17/20.65 | |
% 141.17/20.65 | | (9) all_54_10 = e2
% 141.17/20.65 | |
% 141.17/20.65 | | REF_CLOSE: (6), (7), (9) are inconsistent by sub-proof #1111.
% 141.17/20.65 | |
% 141.17/20.65 | Case 2:
% 141.17/20.65 | |
% 141.17/20.65 | | (10) all_54_10 = e1 | all_54_10 = e0
% 141.17/20.65 | |
% 141.17/20.65 | | BETA: splitting (10) gives:
% 141.17/20.65 | |
% 141.17/20.65 | | Case 1:
% 141.17/20.65 | | |
% 141.17/20.65 | | | (11) all_54_10 = e1
% 141.17/20.65 | | |
% 141.17/20.65 | | | COMBINE_EQS: (7), (11) imply:
% 141.17/20.65 | | | (12) all_4_2 = e1
% 141.17/20.65 | | |
% 141.17/20.65 | | | SIMP: (12) implies:
% 141.17/20.65 | | | (13) all_4_2 = e1
% 141.17/20.65 | | |
% 141.17/20.65 | | | REDUCE: (1), (13) imply:
% 141.17/20.65 | | | (14) ~ (e1 = e0)
% 141.17/20.65 | | |
% 141.17/20.65 | | | REDUCE: (2), (13) imply:
% 141.17/20.65 | | | (15) op(e1, e1) = e1
% 141.17/20.65 | | |
% 141.17/20.65 | | | REF_CLOSE: (3), (5), (8), (14), (15) are inconsistent by sub-proof #141.
% 141.17/20.65 | | |
% 141.17/20.65 | | Case 2:
% 141.17/20.65 | | |
% 141.17/20.65 | | | (16) all_54_10 = e0
% 141.17/20.65 | | |
% 141.17/20.65 | | | REF_CLOSE: (1), (7), (16) are inconsistent by sub-proof #899.
% 141.17/20.65 | | |
% 141.17/20.65 | | End of split
% 141.17/20.65 | |
% 141.17/20.65 | End of split
% 141.17/20.65 |
% 141.17/20.65 End of proof
% 141.17/20.65
% 141.17/20.65 Sub-proof #137 shows that the following formulas are inconsistent:
% 141.17/20.65 ----------------------------------------------------------------
% 141.17/20.65 (1) op(e0, e3) = e1
% 141.17/20.65 (2) op(e1, e0) = e2
% 141.17/20.65 (3) op(e0, e3) = all_42_1
% 141.17/20.65 (4) op(all_46_1, e0) = all_46_0
% 141.17/20.65 (5) op(e0, e3) = all_46_1
% 141.17/20.65 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.17/20.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.17/20.65 (7) ~ (all_46_0 = e2)
% 141.17/20.65
% 141.17/20.65 Begin of proof
% 141.17/20.65 |
% 141.17/20.65 | GROUND_INST: instantiating (6) with all_42_1, all_46_1, e3, e0, simplifying
% 141.17/20.65 | with (3), (5) gives:
% 141.17/20.65 | (8) all_46_1 = all_42_1
% 141.17/20.65 |
% 141.17/20.65 | GROUND_INST: instantiating (6) with e1, all_46_1, e3, e0, simplifying with
% 141.17/20.65 | (1), (5) gives:
% 141.17/20.65 | (9) all_46_1 = e1
% 141.17/20.65 |
% 141.17/20.65 | COMBINE_EQS: (8), (9) imply:
% 141.17/20.65 | (10) all_42_1 = e1
% 141.17/20.65 |
% 141.17/20.65 | REDUCE: (4), (9) imply:
% 141.17/20.65 | (11) op(e1, e0) = all_46_0
% 141.17/20.65 |
% 141.17/20.65 | GROUND_INST: instantiating (6) with e2, all_46_0, e0, e1, simplifying with
% 141.17/20.65 | (2), (11) gives:
% 141.17/20.65 | (12) all_46_0 = e2
% 141.17/20.65 |
% 141.17/20.65 | REDUCE: (7), (12) imply:
% 141.17/20.65 | (13) $false
% 141.17/20.65 |
% 141.17/20.65 | CLOSE: (13) is inconsistent.
% 141.17/20.65 |
% 141.17/20.65 End of proof
% 141.17/20.65
% 141.17/20.65 Sub-proof #138 shows that the following formulas are inconsistent:
% 141.17/20.65 ----------------------------------------------------------------
% 141.17/20.65 (1) all_57_4 = e3
% 141.17/20.65 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 141.17/20.65 (3) ~ (e3 = e0)
% 141.17/20.65 (4) ~ (e2 = e0)
% 141.17/20.65 (5) all_57_5 = e2
% 141.17/20.65
% 141.17/20.65 Begin of proof
% 141.17/20.65 |
% 141.17/20.65 | BETA: splitting (2) gives:
% 141.17/20.65 |
% 141.17/20.65 | Case 1:
% 141.17/20.65 | |
% 141.17/20.65 | | (6) all_57_4 = e0 & op(e3, e1) = e0
% 141.17/20.65 | |
% 141.17/20.65 | | ALPHA: (6) implies:
% 141.17/20.65 | | (7) all_57_4 = e0
% 141.17/20.65 | |
% 141.17/20.65 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #831.
% 141.17/20.65 | |
% 141.17/20.65 | Case 2:
% 141.17/20.65 | |
% 141.17/20.65 | | (8) all_57_5 = e0 & op(e2, e1) = e0
% 141.17/20.65 | |
% 141.17/20.65 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #627.
% 141.17/20.65 | |
% 141.17/20.65 | End of split
% 141.17/20.65 |
% 141.17/20.65 End of proof
% 141.17/20.65
% 141.17/20.65 Sub-proof #139 shows that the following formulas are inconsistent:
% 141.17/20.65 ----------------------------------------------------------------
% 141.21/20.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.65 (2) op(e1, e0) = e2
% 141.21/20.65 (3) op(e1, e0) = e1
% 141.21/20.65 (4) ~ (e2 = e1)
% 141.21/20.65
% 141.21/20.65 Begin of proof
% 141.21/20.65 |
% 141.21/20.65 | GROUND_INST: instantiating (1) with e2, e1, e0, e1, simplifying with (2), (3)
% 141.21/20.65 | gives:
% 141.21/20.65 | (5) e2 = e1
% 141.21/20.65 |
% 141.21/20.65 | REDUCE: (4), (5) imply:
% 141.21/20.65 | (6) $false
% 141.21/20.65 |
% 141.21/20.65 | CLOSE: (6) is inconsistent.
% 141.21/20.65 |
% 141.21/20.65 End of proof
% 141.21/20.65
% 141.21/20.65 Sub-proof #140 shows that the following formulas are inconsistent:
% 141.21/20.65 ----------------------------------------------------------------
% 141.21/20.65 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.65 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.65 (2) op(e1, e1) = all_56_13
% 141.21/20.65 (3) op(e1, e1) = e0
% 141.21/20.65 (4) ~ (all_56_13 = e0)
% 141.21/20.65
% 141.21/20.65 Begin of proof
% 141.21/20.65 |
% 141.21/20.65 | GROUND_INST: instantiating (1) with e0, all_56_13, e1, e1, simplifying with
% 141.21/20.65 | (2), (3) gives:
% 141.21/20.65 | (5) all_56_13 = e0
% 141.21/20.65 |
% 141.21/20.65 | REDUCE: (4), (5) imply:
% 141.21/20.65 | (6) $false
% 141.21/20.65 |
% 141.21/20.65 | CLOSE: (6) is inconsistent.
% 141.21/20.65 |
% 141.21/20.65 End of proof
% 141.21/20.65
% 141.21/20.65 Sub-proof #141 shows that the following formulas are inconsistent:
% 141.21/20.65 ----------------------------------------------------------------
% 141.21/20.65 (1) op(e1, e1) = e1
% 141.21/20.66 (2) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.21/20.66 all_56_8 & $i(all_56_8))
% 141.21/20.66 (3) ~ (e1 = e0)
% 141.21/20.66 (4) all_56_8 = e1
% 141.21/20.66 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (2) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (6) all_56_13 = e0 & op(e1, e1) = e0
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (6) implies:
% 141.21/20.66 | | (7) op(e1, e1) = e0
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #1089.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (8) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8)
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (8) implies:
% 141.21/20.66 | | (9) ~ (all_56_8 = e1)
% 141.21/20.66 | |
% 141.21/20.66 | | REDUCE: (4), (9) imply:
% 141.21/20.66 | | (10) $false
% 141.21/20.66 | |
% 141.21/20.66 | | CLOSE: (10) is inconsistent.
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #142 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (e2 = e1)
% 141.21/20.66 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 141.21/20.66 (3) op(e3, e3) = e2
% 141.21/20.66 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (5) all_57_1 = e2
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (2) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (6) all_57_0 = e1 & op(e3, e3) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (6) implies:
% 141.21/20.66 | | (7) op(e3, e3) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #818.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (8) all_57_1 = e1 & op(e3, e2) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1092.
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #143 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) all_57_4 = e1 & op(e3, e1) = e1
% 141.21/20.66 (2) all_57_4 = e3
% 141.21/20.66 (3) ~ (e3 = e1)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | ALPHA: (1) implies:
% 141.21/20.66 | (4) all_57_4 = e1
% 141.21/20.66 |
% 141.21/20.66 | COMBINE_EQS: (2), (4) imply:
% 141.21/20.66 | (5) e3 = e1
% 141.21/20.66 |
% 141.21/20.66 | REDUCE: (3), (5) imply:
% 141.21/20.66 | (6) $false
% 141.21/20.66 |
% 141.21/20.66 | CLOSE: (6) is inconsistent.
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #144 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (e2 = e1)
% 141.21/20.66 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 141.21/20.66 (3) op(e3, e3) = e2
% 141.21/20.66 (4) ~ (e1 = e0)
% 141.21/20.66 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (6) all_57_1 = e0
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (2) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (7) implies:
% 141.21/20.66 | | (8) op(e3, e3) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #818.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (9) all_57_1 = e1 & op(e3, e2) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #145.
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #145 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) all_57_1 = e1 & op(e3, e2) = e1
% 141.21/20.66 (2) all_57_1 = e0
% 141.21/20.66 (3) ~ (e1 = e0)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | ALPHA: (1) implies:
% 141.21/20.66 | (4) all_57_1 = e1
% 141.21/20.66 |
% 141.21/20.66 | COMBINE_EQS: (2), (4) imply:
% 141.21/20.66 | (5) e1 = e0
% 141.21/20.66 |
% 141.21/20.66 | SIMP: (5) implies:
% 141.21/20.66 | (6) e1 = e0
% 141.21/20.66 |
% 141.21/20.66 | REDUCE: (3), (6) imply:
% 141.21/20.66 | (7) $false
% 141.21/20.66 |
% 141.21/20.66 | CLOSE: (7) is inconsistent.
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #146 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (all_26_1 = e0) & op(e2, e3) = all_26_1 & $i(all_26_1)
% 141.21/20.66 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (3) op(e2, e3) = e0
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | ALPHA: (1) implies:
% 141.21/20.66 | (4) ~ (all_26_1 = e0)
% 141.21/20.66 | (5) op(e2, e3) = all_26_1
% 141.21/20.66 |
% 141.21/20.66 | GROUND_INST: instantiating (2) with e0, all_26_1, e3, e2, simplifying with
% 141.21/20.66 | (3), (5) gives:
% 141.21/20.66 | (6) all_26_1 = e0
% 141.21/20.66 |
% 141.21/20.66 | REDUCE: (4), (6) imply:
% 141.21/20.66 | (7) $false
% 141.21/20.66 |
% 141.21/20.66 | CLOSE: (7) is inconsistent.
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #147 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 141.21/20.66 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (3) op(e3, e2) = all_36_1
% 141.21/20.66 (4) op(e3, e2) = e0
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | ALPHA: (1) implies:
% 141.21/20.66 | (5) ~ (all_44_1 = e0)
% 141.21/20.66 | (6) op(e3, e2) = all_44_1
% 141.21/20.66 |
% 141.21/20.66 | GROUND_INST: instantiating (2) with all_36_1, all_44_1, e2, e3, simplifying
% 141.21/20.66 | with (3), (6) gives:
% 141.21/20.66 | (7) all_44_1 = all_36_1
% 141.21/20.66 |
% 141.21/20.66 | GROUND_INST: instantiating (2) with e0, all_44_1, e2, e3, simplifying with
% 141.21/20.66 | (4), (6) gives:
% 141.21/20.66 | (8) all_44_1 = e0
% 141.21/20.66 |
% 141.21/20.66 | COMBINE_EQS: (7), (8) imply:
% 141.21/20.66 | (9) all_36_1 = e0
% 141.21/20.66 |
% 141.21/20.66 | REDUCE: (5), (8) imply:
% 141.21/20.66 | (10) $false
% 141.21/20.66 |
% 141.21/20.66 | CLOSE: (10) is inconsistent.
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #148 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (all_52_6 = all_26_0)
% 141.21/20.66 (2) ~ (all_52_2 = all_52_6)
% 141.21/20.66 (3) ~ (all_52_6 = e3)
% 141.21/20.66 (4) all_54_9 = all_52_6
% 141.21/20.66 (5) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.66 (6) all_54_13 = all_26_0
% 141.21/20.66 (7) ~ (all_52_2 = e0)
% 141.21/20.66 (8) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.66 (9) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.66 (10) all_54_8 = all_52_2
% 141.21/20.66 (11) ~ (all_52_2 = e2)
% 141.21/20.66 (12) ~ (all_26_0 = e0)
% 141.21/20.66 (13) ~ (all_26_0 = e3)
% 141.21/20.66 (14) ~ (all_52_2 = e3)
% 141.21/20.66 (15) ~ (all_52_6 = e0)
% 141.21/20.66 (16) ~ (all_26_0 = e1)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | SIMP: (13) implies:
% 141.21/20.66 | (17) ~ (all_26_0 = e3)
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (8) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (18) all_54_13 = e3
% 141.21/20.66 | |
% 141.21/20.66 | | COMBINE_EQS: (6), (18) imply:
% 141.21/20.66 | | (19) all_26_0 = e3
% 141.21/20.66 | |
% 141.21/20.66 | | SIMP: (19) implies:
% 141.21/20.66 | | (20) all_26_0 = e3
% 141.21/20.66 | |
% 141.21/20.66 | | REDUCE: (17), (20) imply:
% 141.21/20.66 | | (21) $false
% 141.21/20.66 | |
% 141.21/20.66 | | CLOSE: (21) is inconsistent.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (22) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.66 | |
% 141.21/20.66 | | BETA: splitting (22) gives:
% 141.21/20.66 | |
% 141.21/20.66 | | Case 1:
% 141.21/20.66 | | |
% 141.21/20.66 | | | (23) all_54_13 = e2
% 141.21/20.66 | | |
% 141.21/20.66 | | | COMBINE_EQS: (6), (23) imply:
% 141.21/20.66 | | | (24) all_26_0 = e2
% 141.21/20.66 | | |
% 141.21/20.66 | | | SIMP: (24) implies:
% 141.21/20.66 | | | (25) all_26_0 = e2
% 141.21/20.66 | | |
% 141.21/20.66 | | | REDUCE: (1), (25) imply:
% 141.21/20.66 | | | (26) ~ (all_52_6 = e2)
% 141.21/20.66 | | |
% 141.21/20.66 | | | BETA: splitting (5) gives:
% 141.21/20.66 | | |
% 141.21/20.66 | | | Case 1:
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | (27) all_54_9 = e3
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | COMBINE_EQS: (4), (27) imply:
% 141.21/20.66 | | | | (28) all_52_6 = e3
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | REDUCE: (3), (28) imply:
% 141.21/20.66 | | | | (29) $false
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | CLOSE: (29) is inconsistent.
% 141.21/20.66 | | | |
% 141.21/20.66 | | | Case 2:
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | (30) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | BETA: splitting (30) gives:
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | Case 1:
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | (31) all_54_9 = e2
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | COMBINE_EQS: (4), (31) imply:
% 141.21/20.66 | | | | | (32) all_52_6 = e2
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | REDUCE: (26), (32) imply:
% 141.21/20.66 | | | | | (33) $false
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | CLOSE: (33) is inconsistent.
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | Case 2:
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | (34) all_54_9 = e1 | all_54_9 = e0
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | BETA: splitting (34) gives:
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | | Case 1:
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | (35) all_54_9 = e1
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | COMBINE_EQS: (4), (35) imply:
% 141.21/20.66 | | | | | | (36) all_52_6 = e1
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | REDUCE: (2), (36) imply:
% 141.21/20.66 | | | | | | (37) ~ (all_52_2 = e1)
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | REF_CLOSE: (7), (9), (10), (11), (14), (37) are inconsistent by
% 141.21/20.66 | | | | | | sub-proof #149.
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | Case 2:
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | (38) all_54_9 = e0
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | COMBINE_EQS: (4), (38) imply:
% 141.21/20.66 | | | | | | (39) all_52_6 = e0
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | REDUCE: (15), (39) imply:
% 141.21/20.66 | | | | | | (40) $false
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | | CLOSE: (40) is inconsistent.
% 141.21/20.66 | | | | | |
% 141.21/20.66 | | | | | End of split
% 141.21/20.66 | | | | |
% 141.21/20.66 | | | | End of split
% 141.21/20.66 | | | |
% 141.21/20.66 | | | End of split
% 141.21/20.66 | | |
% 141.21/20.66 | | Case 2:
% 141.21/20.66 | | |
% 141.21/20.66 | | | (41) all_54_13 = e1 | all_54_13 = e0
% 141.21/20.66 | | |
% 141.21/20.66 | | | BETA: splitting (41) gives:
% 141.21/20.66 | | |
% 141.21/20.66 | | | Case 1:
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | (42) all_54_13 = e1
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | COMBINE_EQS: (6), (42) imply:
% 141.21/20.66 | | | | (43) all_26_0 = e1
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | SIMP: (43) implies:
% 141.21/20.66 | | | | (44) all_26_0 = e1
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | REDUCE: (16), (44) imply:
% 141.21/20.66 | | | | (45) $false
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | CLOSE: (45) is inconsistent.
% 141.21/20.66 | | | |
% 141.21/20.66 | | | Case 2:
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | (46) all_54_13 = e0
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | COMBINE_EQS: (6), (46) imply:
% 141.21/20.66 | | | | (47) all_26_0 = e0
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | SIMP: (47) implies:
% 141.21/20.66 | | | | (48) all_26_0 = e0
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | REDUCE: (12), (48) imply:
% 141.21/20.66 | | | | (49) $false
% 141.21/20.66 | | | |
% 141.21/20.66 | | | | CLOSE: (49) is inconsistent.
% 141.21/20.66 | | | |
% 141.21/20.66 | | | End of split
% 141.21/20.66 | | |
% 141.21/20.66 | | End of split
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #149 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (all_52_2 = e1)
% 141.21/20.66 (2) ~ (all_52_2 = e0)
% 141.21/20.66 (3) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.66 (4) all_54_8 = all_52_2
% 141.21/20.66 (5) ~ (all_52_2 = e2)
% 141.21/20.66 (6) ~ (all_52_2 = e3)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (3) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (7) all_54_8 = e3
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #989.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (8) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (2), (4), (5), (8) are inconsistent by sub-proof #790.
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #150 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (all_10_2 = e2)
% 141.21/20.66 (2) ~ (all_52_1 = e2)
% 141.21/20.66 (3) ~ (e2 = e1)
% 141.21/20.66 (4) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.21/20.66 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.21/20.66 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.21/20.66 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.66 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.21/20.66 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.21/20.66 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.21/20.66 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.21/20.66 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.21/20.66 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.21/20.66 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.21/20.66 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.21/20.66 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.21/20.66 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.21/20.66 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.21/20.66 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.21/20.66 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.21/20.66 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.21/20.66 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.21/20.66 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.21/20.66 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.21/20.66 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.21/20.66 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.21/20.66 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.21/20.66 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.21/20.66 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.21/20.66 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.21/20.66 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.21/20.66 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.21/20.66 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.21/20.66 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.21/20.66 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.21/20.66 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.21/20.66 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.21/20.66 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.21/20.66 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.21/20.66 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.21/20.66 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.21/20.66 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.21/20.66 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.21/20.66 (5) ~ (all_10_2 = e1)
% 141.21/20.66 (6) ~ (all_14_2 = e1)
% 141.21/20.66 (7) op(e3, e3) = e2
% 141.21/20.66 (8) ~ (e3 = e0)
% 141.21/20.66 (9) ~ (all_52_4 = e3)
% 141.21/20.66 (10) op(e2, e3) = all_52_1
% 141.21/20.66 (11) op(e0, e0) = all_10_2
% 141.21/20.66 (12) ~ (e1 = e0)
% 141.21/20.66 (13) op(e3, e2) = all_52_4
% 141.21/20.66 (14) op(e2, e2) = e3
% 141.21/20.66 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (16) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.21/20.66 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.21/20.66 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.21/20.66 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.21/20.66 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.21/20.66 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.21/20.66 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.21/20.66 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.21/20.66 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.21/20.66 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.21/20.66 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.21/20.66 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.21/20.66 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.21/20.66 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.21/20.66 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.21/20.66 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.21/20.66 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.21/20.66 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.66 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.21/20.66 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.66 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.21/20.66 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.21/20.66 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.21/20.66 $i(all_56_14))))
% 141.21/20.66 (17) op(e3, e1) = e3
% 141.21/20.66 (18) op(e3, e3) = all_14_2
% 141.21/20.66 (19) op(e2, e0) = e2
% 141.21/20.66 (20) ~ (all_14_2 = e0)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (4) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (21) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 141.21/20.66 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.21/20.66 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.21/20.66 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.66 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.21/20.66 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.21/20.66 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.21/20.66 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.21/20.66 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.21/20.66 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.21/20.66 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.21/20.66 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 141.21/20.66 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.21/20.66 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.21/20.66 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.21/20.66 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.21/20.66 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.21/20.66 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.21/20.66 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.21/20.66 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.21/20.66 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.21/20.66 | | $i(all_56_12))))
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (2), (7), (9), (10), (13), (14), (15), (21) are inconsistent by
% 141.21/20.66 | | sub-proof #177.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (22) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.21/20.66 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.21/20.66 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.21/20.66 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.21/20.66 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.21/20.66 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.21/20.66 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.21/20.66 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.21/20.66 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.21/20.66 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.21/20.66 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.21/20.66 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | (
% 141.21/20.66 | | ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.21/20.66 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.21/20.66 | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 141.21/20.66 | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.21/20.66 | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.21/20.66 | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.21/20.66 | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 141.21/20.66 | | e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.21/20.66 | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.21/20.66 | | $i(all_56_8))))
% 141.21/20.66 | |
% 141.21/20.66 | | BETA: splitting (22) gives:
% 141.21/20.66 | |
% 141.21/20.66 | | Case 1:
% 141.21/20.66 | | |
% 141.21/20.66 | | | (23) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.21/20.66 | | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.21/20.66 | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.21/20.66 | | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.21/20.66 | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.21/20.66 | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.21/20.66 | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.21/20.66 | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.21/20.66 | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.21/20.66 | | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.21/20.66 | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.21/20.66 | | |
% 141.21/20.66 | | | ALPHA: (23) implies:
% 141.21/20.66 | | | (24) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.21/20.66 | | | e1) = all_56_1 & $i(all_56_1))
% 141.21/20.66 | | |
% 141.21/20.66 | | | REF_CLOSE: (3), (7), (15), (17), (24) are inconsistent by sub-proof #153.
% 141.21/20.66 | | |
% 141.21/20.66 | | Case 2:
% 141.21/20.66 | | |
% 141.21/20.66 | | | (25) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.21/20.66 | | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.21/20.66 | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.21/20.66 | | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.21/20.66 | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.21/20.66 | | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.21/20.66 | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.21/20.66 | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.21/20.66 | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.21/20.66 | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.21/20.66 | | | e0) = all_56_8 & $i(all_56_8)))
% 141.21/20.66 | | |
% 141.21/20.66 | | | REF_CLOSE: (1), (5), (6), (8), (11), (12), (15), (16), (18), (19), (20),
% 141.21/20.66 | | | (25) are inconsistent by sub-proof #151.
% 141.21/20.66 | | |
% 141.21/20.66 | | End of split
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #151 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (all_10_2 = e2)
% 141.21/20.66 (2) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.21/20.66 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.21/20.66 ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.21/20.66 all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 141.21/20.66 ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.66 ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.21/20.66 all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.21/20.66 (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.21/20.66 ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.21/20.66 all_56_8 & $i(all_56_8)))
% 141.21/20.66 (3) ~ (all_10_2 = e1)
% 141.21/20.66 (4) ~ (all_14_2 = e1)
% 141.21/20.66 (5) ~ (e3 = e0)
% 141.21/20.66 (6) op(e0, e0) = all_10_2
% 141.21/20.66 (7) ~ (e1 = e0)
% 141.21/20.66 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (9) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.21/20.66 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.21/20.66 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.21/20.66 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.21/20.66 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.21/20.66 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 141.21/20.66 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 141.21/20.66 op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 & all_56_15 = e3 & ~
% 141.21/20.66 (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 141.21/20.66 = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4
% 141.21/20.66 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 141.21/20.66 $i(all_56_4)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.21/20.66 op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 141.21/20.66 $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 141.21/20.66 op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 141.21/20.66 $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 141.21/20.66 e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.21/20.66 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.21/20.66 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 141.21/20.66 = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 141.21/20.66 ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.21/20.66 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 141.21/20.66 e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.21/20.66 (10) op(e3, e3) = all_14_2
% 141.21/20.66 (11) op(e2, e0) = e2
% 141.21/20.66 (12) ~ (all_14_2 = e0)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | ALPHA: (2) implies:
% 141.21/20.66 | (13) (all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.21/20.66 | = all_56_5 & $i(all_56_5))
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (13) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (14) all_56_11 = e0 & op(e2, e2) = e0
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (14) implies:
% 141.21/20.66 | | (15) op(e2, e2) = e0
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (15) are
% 141.21/20.66 | | inconsistent by sub-proof #235.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (16) ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5)
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (16) implies:
% 141.21/20.66 | | (17) ~ (all_56_5 = e2)
% 141.21/20.66 | | (18) op(e2, e0) = all_56_5
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (8), (11), (17), (18) are inconsistent by sub-proof #152.
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #152 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (2) op(e2, e0) = all_56_5
% 141.21/20.66 (3) op(e2, e0) = e2
% 141.21/20.66 (4) ~ (all_56_5 = e2)
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | GROUND_INST: instantiating (1) with e2, all_56_5, e0, e2, simplifying with
% 141.21/20.66 | (2), (3) gives:
% 141.21/20.66 | (5) all_56_5 = e2
% 141.21/20.66 |
% 141.21/20.66 | REDUCE: (4), (5) imply:
% 141.21/20.66 | (6) $false
% 141.21/20.66 |
% 141.21/20.66 | CLOSE: (6) is inconsistent.
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #153 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.66 (1) ~ (e2 = e1)
% 141.21/20.66 (2) op(e3, e3) = e2
% 141.21/20.66 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.66 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.66 (4) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 141.21/20.66 all_56_1 & $i(all_56_1))
% 141.21/20.66 (5) op(e3, e1) = e3
% 141.21/20.66
% 141.21/20.66 Begin of proof
% 141.21/20.66 |
% 141.21/20.66 | BETA: splitting (4) gives:
% 141.21/20.66 |
% 141.21/20.66 | Case 1:
% 141.21/20.66 | |
% 141.21/20.66 | | (6) all_56_9 = e1 & op(e3, e3) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (6) implies:
% 141.21/20.66 | | (7) op(e3, e3) = e1
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #818.
% 141.21/20.66 | |
% 141.21/20.66 | Case 2:
% 141.21/20.66 | |
% 141.21/20.66 | | (8) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1)
% 141.21/20.66 | |
% 141.21/20.66 | | ALPHA: (8) implies:
% 141.21/20.66 | | (9) ~ (all_56_1 = e3)
% 141.21/20.66 | | (10) op(e3, e1) = all_56_1
% 141.21/20.66 | |
% 141.21/20.66 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #734.
% 141.21/20.66 | |
% 141.21/20.66 | End of split
% 141.21/20.66 |
% 141.21/20.66 End of proof
% 141.21/20.66
% 141.21/20.66 Sub-proof #154 shows that the following formulas are inconsistent:
% 141.21/20.66 ----------------------------------------------------------------
% 141.21/20.67 (1) ~ (all_52_1 = e2)
% 141.21/20.67 (2) op(e2, e3) = all_52_1
% 141.21/20.67 (3) ~ (e3 = e2)
% 141.21/20.67 (4) op(e2, e2) = e3
% 141.21/20.67 (5) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 141.21/20.67 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (5) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (7) all_57_2 = e2 & op(e2, e3) = e2
% 141.21/20.67 | |
% 141.21/20.67 | | ALPHA: (7) implies:
% 141.21/20.67 | | (8) op(e2, e3) = e2
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (1), (2), (6), (8) are inconsistent by sub-proof #882.
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (9) all_57_3 = e2 & op(e2, e2) = e2
% 141.21/20.67 | |
% 141.21/20.67 | | ALPHA: (9) implies:
% 141.21/20.67 | | (10) op(e2, e2) = e2
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #728.
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #155 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) ~ (e2 = e1)
% 141.21/20.67 (2) all_57_6 = e3 & op(e1, e3) = e3
% 141.21/20.67 (3) all_57_12 = e3
% 141.21/20.67 (4) op(e3, e3) = e2
% 141.21/20.67 (5) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.21/20.67 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.21/20.67 (6) ~ (e3 = e0)
% 141.21/20.67 (7) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.21/20.67 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.21/20.67 (8) ~ (e1 = e0)
% 141.21/20.67 (9) ~ (e2 = e0)
% 141.21/20.67 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67 (11) ~ (e3 = e1)
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | ALPHA: (2) implies:
% 141.21/20.67 | (12) all_57_6 = e3
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (5) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 141.21/20.67 | | e0)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (13) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (14) all_57_0 = e0 & op(e3, e3) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | ALPHA: (14) implies:
% 141.21/20.67 | | | (15) op(e3, e3) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (4), (9), (10), (15) are inconsistent by sub-proof #880.
% 141.21/20.67 | | |
% 141.21/20.67 | | Case 2:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (16) all_57_2 = e0 & op(e2, e3) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | ALPHA: (16) implies:
% 141.21/20.67 | | | (17) all_57_2 = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | BETA: splitting (7) gives:
% 141.21/20.67 | | |
% 141.21/20.67 | | | Case 1:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | (18) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 141.21/20.67 | | | | = e1)
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | BETA: splitting (18) gives:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | Case 1:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (19) all_57_0 = e1 & op(e3, e3) = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | ALPHA: (19) implies:
% 141.21/20.67 | | | | | (20) op(e3, e3) = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (1), (4), (10), (20) are inconsistent by sub-proof #818.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | Case 2:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (21) all_57_2 = e1 & op(e2, e3) = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (8), (17), (21) are inconsistent by sub-proof #878.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | End of split
% 141.21/20.67 | | | |
% 141.21/20.67 | | | Case 2:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | (22) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 141.21/20.67 | | | | = e1)
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | BETA: splitting (22) gives:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | Case 1:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (23) all_57_6 = e1 & op(e1, e3) = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (11), (12), (23) are inconsistent by sub-proof #865.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | Case 2:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (24) all_57_12 = e1 & op(e0, e3) = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (3), (11), (24) are inconsistent by sub-proof #1073.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | End of split
% 141.21/20.67 | | | |
% 141.21/20.67 | | | End of split
% 141.21/20.67 | | |
% 141.21/20.67 | | End of split
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (25) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 141.21/20.67 | | e0)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (25) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (26) all_57_6 = e0 & op(e1, e3) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (6), (12), (26) are inconsistent by sub-proof #603.
% 141.21/20.67 | | |
% 141.21/20.67 | | Case 2:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (27) all_57_12 = e0 & op(e0, e3) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (3), (6), (27) are inconsistent by sub-proof #156.
% 141.21/20.67 | | |
% 141.21/20.67 | | End of split
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #156 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) all_57_12 = e0 & op(e0, e3) = e0
% 141.21/20.67 (2) all_57_12 = e3
% 141.21/20.67 (3) ~ (e3 = e0)
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | ALPHA: (1) implies:
% 141.21/20.67 | (4) all_57_12 = e0
% 141.21/20.67 |
% 141.21/20.67 | COMBINE_EQS: (2), (4) imply:
% 141.21/20.67 | (5) e3 = e0
% 141.21/20.67 |
% 141.21/20.67 | REDUCE: (3), (5) imply:
% 141.21/20.67 | (6) $false
% 141.21/20.67 |
% 141.21/20.67 | CLOSE: (6) is inconsistent.
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #157 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) all_54_3 = all_52_12
% 141.21/20.67 (2) ~ (all_52_12 = e0)
% 141.21/20.67 (3) ~ (all_52_12 = e1)
% 141.21/20.67 (4) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.21/20.67 (5) ~ (all_52_12 = e2)
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (4) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (6) all_54_3 = e2
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (1), (5), (6) are inconsistent by sub-proof #983.
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (7) all_54_3 = e1 | all_54_3 = e0
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #418.
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #158 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.21/20.67 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.21/20.67 ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.21/20.67 all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 141.21/20.67 ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.67 ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.21/20.67 all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.21/20.67 (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.21/20.67 ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.21/20.67 all_56_8 & $i(all_56_8)))
% 141.21/20.67 (2) op(e3, e3) = e2
% 141.21/20.67 (3) ~ (e2 = e0)
% 141.21/20.67 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67 (5) op(e3, e0) = e3
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | ALPHA: (1) implies:
% 141.21/20.67 | (6) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.21/20.67 | all_56_2 & $i(all_56_2))
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (6) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (7) all_56_9 = e0 & op(e3, e3) = e0
% 141.21/20.67 | |
% 141.21/20.67 | | ALPHA: (7) implies:
% 141.21/20.67 | | (8) op(e3, e3) = e0
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #880.
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (9) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2)
% 141.21/20.67 | |
% 141.21/20.67 | | ALPHA: (9) implies:
% 141.21/20.67 | | (10) ~ (all_56_2 = e3)
% 141.21/20.67 | | (11) op(e3, e0) = all_56_2
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (4), (5), (10), (11) are inconsistent by sub-proof #274.
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #159 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) ~ (all_52_14 = e3)
% 141.21/20.67 (2) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.21/20.67 (3) op(e1, e1) = e1
% 141.21/20.67 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67 (5) ~ (e3 = e1)
% 141.21/20.67 (6) op(e1, e0) = all_52_14
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (2) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 141.21/20.67 | |
% 141.21/20.67 | | ALPHA: (7) implies:
% 141.21/20.67 | | (8) op(e1, e1) = e3
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #1096.
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (9) all_57_11 = e3 & op(e1, e0) = e3
% 141.21/20.67 | |
% 141.21/20.67 | | REF_CLOSE: (1), (4), (6), (9) are inconsistent by sub-proof #160.
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #160 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) all_57_11 = e3 & op(e1, e0) = e3
% 141.21/20.67 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67 (3) op(e1, e0) = all_52_14
% 141.21/20.67 (4) ~ (all_52_14 = e3)
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | ALPHA: (1) implies:
% 141.21/20.67 | (5) op(e1, e0) = e3
% 141.21/20.67 |
% 141.21/20.67 | GROUND_INST: instantiating (2) with all_52_14, e3, e0, e1, simplifying with
% 141.21/20.67 | (3), (5) gives:
% 141.21/20.67 | (6) all_52_14 = e3
% 141.21/20.67 |
% 141.21/20.67 | REDUCE: (4), (6) imply:
% 141.21/20.67 | (7) $false
% 141.21/20.67 |
% 141.21/20.67 | CLOSE: (7) is inconsistent.
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #161 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) ~ (all_10_2 = e2)
% 141.21/20.67 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.21/20.67 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.67 (3) ~ (e2 = e1)
% 141.21/20.67 (4) ~ (all_10_2 = e1)
% 141.21/20.67 (5) ~ (all_14_2 = e1)
% 141.21/20.67 (6) ~ (e3 = e0)
% 141.21/20.67 (7) op(e0, e0) = all_10_2
% 141.21/20.67 (8) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.21/20.67 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.21/20.67 (9) ~ (e1 = e0)
% 141.21/20.67 (10) ~ (e2 = e0)
% 141.21/20.67 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67 (12) ~ (e3 = e1)
% 141.21/20.67 (13) all_57_1 = e2
% 141.21/20.67 (14) all_57_3 = e3
% 141.21/20.67 (15) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.21/20.67 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.21/20.67 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.21/20.67 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.21/20.67 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.21/20.67 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.21/20.67 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.21/20.67 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.21/20.67 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.21/20.67 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.21/20.67 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.21/20.67 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.21/20.67 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.21/20.67 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.21/20.67 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.21/20.67 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.21/20.67 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.21/20.67 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.67 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.21/20.67 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.67 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.21/20.67 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.21/20.67 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.21/20.67 $i(all_56_14))))
% 141.21/20.67 (16) op(e3, e3) = all_14_2
% 141.21/20.67 (17) all_57_7 = e3
% 141.21/20.67 (18) ~ (all_14_2 = e0)
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (8) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (19) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 141.21/20.67 | | e0)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (19) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (20) all_57_1 = e0 & op(e3, e2) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (10), (13), (20) are inconsistent by sub-proof #267.
% 141.21/20.67 | | |
% 141.21/20.67 | | Case 2:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (21) all_57_3 = e0 & op(e2, e2) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | ALPHA: (21) implies:
% 141.21/20.67 | | | (22) op(e2, e2) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (1), (4), (5), (6), (7), (9), (11), (15), (16), (18), (22) are
% 141.21/20.67 | | | inconsistent by sub-proof #235.
% 141.21/20.67 | | |
% 141.21/20.67 | | End of split
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (23) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.21/20.67 | | e0)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (23) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (24) all_57_7 = e0 & op(e1, e2) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (6), (17), (24) are inconsistent by sub-proof #1061.
% 141.21/20.67 | | |
% 141.21/20.67 | | Case 2:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (25) all_57_13 = e0 & op(e0, e2) = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | ALPHA: (25) implies:
% 141.21/20.67 | | | (26) all_57_13 = e0
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (2), (3), (9), (12), (13), (14), (17), (26) are inconsistent by
% 141.21/20.67 | | | sub-proof #162.
% 141.21/20.67 | | |
% 141.21/20.67 | | End of split
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #162 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.21/20.67 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.67 (2) ~ (e2 = e1)
% 141.21/20.67 (3) all_57_13 = e0
% 141.21/20.67 (4) ~ (e1 = e0)
% 141.21/20.67 (5) ~ (e3 = e1)
% 141.21/20.67 (6) all_57_1 = e2
% 141.21/20.67 (7) all_57_3 = e3
% 141.21/20.67 (8) all_57_7 = e3
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (1) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (9) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (9) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (10) all_57_1 = e1 & op(e3, e2) = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #1092.
% 141.21/20.67 | | |
% 141.21/20.67 | | Case 2:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (11) all_57_3 = e1 & op(e2, e2) = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (5), (7), (11) are inconsistent by sub-proof #163.
% 141.21/20.67 | | |
% 141.21/20.67 | | End of split
% 141.21/20.67 | |
% 141.21/20.67 | Case 2:
% 141.21/20.67 | |
% 141.21/20.67 | | (12) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 141.21/20.67 | | e1)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (12) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (13) all_57_7 = e1 & op(e1, e2) = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | ALPHA: (13) implies:
% 141.21/20.67 | | | (14) all_57_7 = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (5), (8), (14) are inconsistent by sub-proof #915.
% 141.21/20.67 | | |
% 141.21/20.67 | | Case 2:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (15) all_57_13 = e1 & op(e0, e2) = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | REF_CLOSE: (3), (4), (15) are inconsistent by sub-proof #805.
% 141.21/20.67 | | |
% 141.21/20.67 | | End of split
% 141.21/20.67 | |
% 141.21/20.67 | End of split
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #163 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) all_57_3 = e1 & op(e2, e2) = e1
% 141.21/20.67 (2) all_57_3 = e3
% 141.21/20.67 (3) ~ (e3 = e1)
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | ALPHA: (1) implies:
% 141.21/20.67 | (4) all_57_3 = e1
% 141.21/20.67 |
% 141.21/20.67 | COMBINE_EQS: (2), (4) imply:
% 141.21/20.67 | (5) e3 = e1
% 141.21/20.67 |
% 141.21/20.67 | REDUCE: (3), (5) imply:
% 141.21/20.67 | (6) $false
% 141.21/20.67 |
% 141.21/20.67 | CLOSE: (6) is inconsistent.
% 141.21/20.67 |
% 141.21/20.67 End of proof
% 141.21/20.67
% 141.21/20.67 Sub-proof #164 shows that the following formulas are inconsistent:
% 141.21/20.67 ----------------------------------------------------------------
% 141.21/20.67 (1) ~ (all_10_2 = e2)
% 141.21/20.67 (2) ~ (all_52_4 = all_52_7)
% 141.21/20.67 (3) ~ (all_52_1 = all_52_3)
% 141.21/20.67 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.21/20.67 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.67 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.21/20.67 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.67 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.21/20.67 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.21/20.67 (7) ~ (all_52_3 = all_52_7)
% 141.21/20.67 (8) op(e1, e3) = all_52_2
% 141.21/20.67 (9) ~ (all_52_7 = e1)
% 141.21/20.67 (10) all_57_6 = e3
% 141.21/20.67 (11) op(e1, e2) = all_52_6
% 141.21/20.67 (12) ~ (all_52_6 = e1)
% 141.21/20.67 (13) ~ (all_52_8 = e3)
% 141.21/20.67 (14) ~ (e2 = e1)
% 141.21/20.67 (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.21/20.67 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.21/20.67 (16) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.67 (17) ~ (all_52_7 = e0)
% 141.21/20.67 (18) all_54_13 = all_52_7
% 141.21/20.67 (19) ~ (all_52_9 = all_52_13)
% 141.21/20.67 (20) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.21/20.67 all_56_11 & $i(all_56_11))
% 141.21/20.67 (21) ~ (all_52_2 = all_52_6)
% 141.21/20.67 (22) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 141.21/20.67 all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2,
% 141.21/20.67 e3) = all_26_1 & $i(all_26_1))
% 141.21/20.67 (23) op(e0, e3) = all_52_3
% 141.21/20.67 (24) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 141.21/20.67 all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3,
% 141.21/20.67 e2) = all_36_1 & $i(all_36_1))
% 141.21/20.67 (25) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.21/20.67 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.21/20.67 (26) ~ (all_10_2 = e1)
% 141.21/20.67 (27) ~ (all_52_7 = e3)
% 141.21/20.67 (28) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.67 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.21/20.67 e1)
% 141.21/20.67 (29) ~ (all_52_4 = all_52_6)
% 141.21/20.67 (30) all_54_12 = all_52_3
% 141.21/20.67 (31) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.21/20.67 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.21/20.67 (32) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.21/20.67 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.21/20.67 (33) ~ (e3 = e0)
% 141.21/20.67 (34) op(e1, e1) = e1
% 141.21/20.67 (35) all_57_14 = e3
% 141.21/20.67 (36) op(e3, e1) = all_52_8
% 141.21/20.67 (37) all_54_9 = all_52_6
% 141.21/20.67 (38) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.21/20.67 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.21/20.67 (39) ~ (all_52_6 = all_52_7)
% 141.21/20.67 (40) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.21/20.67 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.21/20.67 e2)
% 141.21/20.67 (41) op(e2, e3) = all_52_1
% 141.21/20.67 (42) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.21/20.67 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.21/20.67 (43) op(e0, e0) = all_10_2
% 141.21/20.67 (44) ~ (e1 = e0)
% 141.21/20.67 (45) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.67 (46) op(e3, e2) = all_52_4
% 141.21/20.67 (47) ~ (e2 = e0)
% 141.21/20.67 (48) ~ (e3 = e2)
% 141.21/20.67 (49) ~ (all_52_2 = e1)
% 141.21/20.67 (50) ~ (all_52_1 = all_52_2)
% 141.21/20.67 (51) all_57_9 = e3
% 141.21/20.67 (52) op(e2, e2) = e3
% 141.21/20.67 (53) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.21/20.67 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.21/20.67 (54) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.21/20.67 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.21/20.67 & $i(all_6_1))
% 141.21/20.67 (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.67 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.67 (56) all_57_5 = e2
% 141.21/20.67 (57) ~ (all_52_3 = e0)
% 141.21/20.67 (58) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.21/20.67 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.21/20.67 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.67 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.21/20.67 (59) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.21/20.67 all_56_4 & $i(all_56_4))
% 141.21/20.67 (60) ~ (all_52_9 = e3)
% 141.21/20.67 (61) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.67 (62) ~ (e3 = e1)
% 141.21/20.67 (63) op(e0, e2) = all_52_7
% 141.21/20.67 (64) all_57_3 = e3
% 141.21/20.67 (65) ~ (all_52_2 = all_52_3)
% 141.21/20.67 (66) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.67 (67) all_54_8 = all_52_2
% 141.21/20.67 (68) ~ (all_52_2 = e2)
% 141.21/20.67 (69) ~ (all_52_9 = e1)
% 141.21/20.67 (70) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.21/20.67 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.21/20.67 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.21/20.67 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.21/20.67 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.21/20.67 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.21/20.67 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.21/20.67 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.21/20.67 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.21/20.67 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.21/20.67 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.21/20.67 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.21/20.67 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.21/20.67 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.21/20.67 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.21/20.67 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.21/20.67 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.21/20.67 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.67 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.21/20.67 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.67 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.21/20.67 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.21/20.67 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.21/20.67 $i(all_56_14))))
% 141.21/20.67 (71) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 141.21/20.67 (72) op(e2, e1) = all_52_9
% 141.21/20.67 (73) op(e3, e3) = all_14_2
% 141.21/20.67 (74) all_57_7 = e0
% 141.21/20.67 (75) all_54_6 = all_52_9
% 141.21/20.67 (76) ~ (all_52_3 = e2)
% 141.21/20.67 (77) op(e2, e0) = all_52_13
% 141.21/20.67 (78) ~ (all_14_2 = e0)
% 141.21/20.67 (79) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.21/20.67 all_56_9 & $i(all_56_9))
% 141.21/20.67 (80) ~ (all_52_9 = e0)
% 141.21/20.67 (81) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 141.21/20.67 all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3,
% 141.21/20.67 e2) = all_44_1 & $i(all_44_1))
% 141.21/20.67
% 141.21/20.67 Begin of proof
% 141.21/20.67 |
% 141.21/20.67 | BETA: splitting (4) gives:
% 141.21/20.67 |
% 141.21/20.67 | Case 1:
% 141.21/20.67 | |
% 141.21/20.67 | | (82) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 141.21/20.67 | | e1)
% 141.21/20.67 | |
% 141.21/20.67 | | BETA: splitting (82) gives:
% 141.21/20.67 | |
% 141.21/20.67 | | Case 1:
% 141.21/20.67 | | |
% 141.21/20.67 | | | (83) all_57_1 = e1 & op(e3, e2) = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | ALPHA: (83) implies:
% 141.21/20.67 | | | (84) all_57_1 = e1
% 141.21/20.67 | | | (85) op(e3, e2) = e1
% 141.21/20.67 | | |
% 141.21/20.67 | | | BETA: splitting (32) gives:
% 141.21/20.67 | | |
% 141.21/20.67 | | | Case 1:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | (86) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 141.21/20.67 | | | | = e2)
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | BETA: splitting (86) gives:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | Case 1:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (87) all_57_1 = e2 & op(e3, e2) = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | ALPHA: (87) implies:
% 141.21/20.67 | | | | | (88) all_57_1 = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | COMBINE_EQS: (84), (88) imply:
% 141.21/20.67 | | | | | (89) e2 = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | SIMP: (89) implies:
% 141.21/20.67 | | | | | (90) e2 = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | COMBINE_EQS: (56), (90) imply:
% 141.21/20.67 | | | | | (91) all_57_5 = e1
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (6), (14), (25), (33), (34), (44), (47), (48), (53), (55),
% 141.21/20.67 | | | | | (62), (72), (80), (91) are inconsistent by sub-proof #336.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | Case 2:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (92) all_57_3 = e2 & op(e2, e2) = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | ALPHA: (92) implies:
% 141.21/20.67 | | | | | (93) op(e2, e2) = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (48), (52), (55), (93) are inconsistent by sub-proof #728.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | End of split
% 141.21/20.67 | | | |
% 141.21/20.67 | | | Case 2:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | (94) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2)
% 141.21/20.67 | | | | = e2)
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | BETA: splitting (94) gives:
% 141.21/20.67 | | | |
% 141.21/20.67 | | | | Case 1:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (95) all_57_7 = e2 & op(e1, e2) = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | ALPHA: (95) implies:
% 141.21/20.67 | | | | | (96) all_57_7 = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | REF_CLOSE: (47), (74), (96) are inconsistent by sub-proof #578.
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | Case 2:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | (97) all_57_13 = e2 & op(e0, e2) = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | ALPHA: (97) implies:
% 141.21/20.67 | | | | | (98) all_57_13 = e2
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | BETA: splitting (71) gives:
% 141.21/20.67 | | | | |
% 141.21/20.67 | | | | | Case 1:
% 141.21/20.67 | | | | | |
% 141.21/20.67 | | | | | | (99) all_54_6 = e2
% 141.21/20.67 | | | | | |
% 141.21/20.67 | | | | | | COMBINE_EQS: (75), (99) imply:
% 141.21/20.67 | | | | | | (100) all_52_9 = e2
% 141.21/20.67 | | | | | |
% 141.21/20.67 | | | | | | SIMP: (100) implies:
% 141.21/20.67 | | | | | | (101) all_52_9 = e2
% 141.21/20.67 | | | | | |
% 141.21/20.67 | | | | | | REDUCE: (19), (101) imply:
% 141.21/20.67 | | | | | | (102) ~ (all_52_13 = e2)
% 141.21/20.67 | | | | | |
% 141.21/20.67 | | | | | | SIMP: (102) implies:
% 141.21/20.67 | | | | | | (103) ~ (all_52_13 = e2)
% 141.21/20.67 | | | | | |
% 141.21/20.67 | | | | | | REDUCE: (60), (101) imply:
% 141.21/20.67 | | | | | | (104) ~ (e3 = e2)
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | REDUCE: (72), (101) imply:
% 141.21/20.68 | | | | | | (105) op(e2, e1) = e2
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (13),
% 141.21/20.68 | | | | | | (14), (15), (16), (17), (18), (20), (21), (22), (23),
% 141.21/20.68 | | | | | | (24), (25), (26), (27), (28), (29), (30), (31), (33),
% 141.21/20.68 | | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 141.21/20.68 | | | | | | (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 141.21/20.68 | | | | | | (53), (54), (55), (57), (58), (59), (61), (62), (63),
% 141.21/20.68 | | | | | | (65), (66), (67), (68), (70), (73), (76), (77), (78),
% 141.21/20.68 | | | | | | (79), (81), (85), (98), (103), (105) are inconsistent by
% 141.21/20.68 | | | | | | sub-proof #167.
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | Case 2:
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | (106) all_54_6 = e1 | all_54_6 = e0
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | REF_CLOSE: (69), (75), (80), (106) are inconsistent by sub-proof
% 141.21/20.68 | | | | | | #166.
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | End of split
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | End of split
% 141.21/20.68 | | | |
% 141.21/20.68 | | | End of split
% 141.21/20.68 | | |
% 141.21/20.68 | | Case 2:
% 141.21/20.68 | | |
% 141.21/20.68 | | | (107) all_57_3 = e1 & op(e2, e2) = e1
% 141.21/20.68 | | |
% 141.21/20.68 | | | ALPHA: (107) implies:
% 141.21/20.68 | | | (108) all_57_3 = e1
% 141.21/20.68 | | |
% 141.21/20.68 | | | COMBINE_EQS: (64), (108) imply:
% 141.21/20.68 | | | (109) e3 = e1
% 141.21/20.68 | | |
% 141.21/20.68 | | | COMBINE_EQS: (35), (109) imply:
% 141.21/20.68 | | | (110) all_57_14 = e1
% 141.21/20.68 | | |
% 141.21/20.68 | | | REF_CLOSE: (6), (13), (14), (25), (33), (34), (36), (44), (47), (48),
% 141.21/20.68 | | | (53), (55), (62), (110) are inconsistent by sub-proof #1038.
% 141.21/20.68 | | |
% 141.21/20.68 | | End of split
% 141.21/20.68 | |
% 141.21/20.68 | Case 2:
% 141.21/20.68 | |
% 141.21/20.68 | | (111) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 141.21/20.68 | | e1)
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (9), (11), (12), (55), (63), (111) are inconsistent by sub-proof
% 141.21/20.68 | | #165.
% 141.21/20.68 | |
% 141.21/20.68 | End of split
% 141.21/20.68 |
% 141.21/20.68 End of proof
% 141.21/20.68
% 141.21/20.68 Sub-proof #165 shows that the following formulas are inconsistent:
% 141.21/20.68 ----------------------------------------------------------------
% 141.21/20.68 (1) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.68 (2) ~ (all_52_7 = e1)
% 141.21/20.68 (3) op(e1, e2) = all_52_6
% 141.21/20.68 (4) ~ (all_52_6 = e1)
% 141.21/20.68 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.68 (6) op(e0, e2) = all_52_7
% 141.21/20.68
% 141.21/20.68 Begin of proof
% 141.21/20.68 |
% 141.21/20.68 | BETA: splitting (1) gives:
% 141.21/20.68 |
% 141.21/20.68 | Case 1:
% 141.21/20.68 | |
% 141.21/20.68 | | (7) all_57_7 = e1 & op(e1, e2) = e1
% 141.21/20.68 | |
% 141.21/20.68 | | ALPHA: (7) implies:
% 141.21/20.68 | | (8) op(e1, e2) = e1
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #341.
% 141.21/20.68 | |
% 141.21/20.68 | Case 2:
% 141.21/20.68 | |
% 141.21/20.68 | | (9) all_57_13 = e1 & op(e0, e2) = e1
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #366.
% 141.21/20.68 | |
% 141.21/20.68 | End of split
% 141.21/20.68 |
% 141.21/20.68 End of proof
% 141.21/20.68
% 141.21/20.68 Sub-proof #166 shows that the following formulas are inconsistent:
% 141.21/20.68 ----------------------------------------------------------------
% 141.21/20.68 (1) all_54_6 = e1 | all_54_6 = e0
% 141.21/20.68 (2) all_54_6 = all_52_9
% 141.21/20.68 (3) ~ (all_52_9 = e1)
% 141.21/20.68 (4) ~ (all_52_9 = e0)
% 141.21/20.68
% 141.21/20.68 Begin of proof
% 141.21/20.68 |
% 141.21/20.68 | BETA: splitting (1) gives:
% 141.21/20.68 |
% 141.21/20.68 | Case 1:
% 141.21/20.68 | |
% 141.21/20.68 | | (5) all_54_6 = e1
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #741.
% 141.21/20.68 | |
% 141.21/20.68 | Case 2:
% 141.21/20.68 | |
% 141.21/20.68 | | (6) all_54_6 = e0
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #759.
% 141.21/20.68 | |
% 141.21/20.68 | End of split
% 141.21/20.68 |
% 141.21/20.68 End of proof
% 141.21/20.68
% 141.21/20.68 Sub-proof #167 shows that the following formulas are inconsistent:
% 141.21/20.68 ----------------------------------------------------------------
% 141.21/20.68 (1) ~ (all_10_2 = e2)
% 141.21/20.68 (2) ~ (all_52_4 = all_52_7)
% 141.21/20.68 (3) ~ (all_52_1 = all_52_3)
% 141.21/20.68 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.21/20.68 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.68 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.21/20.68 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.21/20.68 (6) ~ (all_52_3 = all_52_7)
% 141.21/20.68 (7) op(e1, e3) = all_52_2
% 141.21/20.68 (8) all_57_6 = e3
% 141.21/20.68 (9) op(e1, e2) = all_52_6
% 141.21/20.68 (10) ~ (all_52_8 = e3)
% 141.21/20.68 (11) ~ (e2 = e1)
% 141.21/20.68 (12) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.21/20.68 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.21/20.68 (13) op(e2, e1) = e2
% 141.21/20.68 (14) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.68 (15) ~ (all_52_7 = e0)
% 141.21/20.68 (16) all_54_13 = all_52_7
% 141.21/20.68 (17) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.21/20.68 all_56_11 & $i(all_56_11))
% 141.21/20.68 (18) ~ (all_52_2 = all_52_6)
% 141.21/20.68 (19) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 141.21/20.68 all_26_1 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2,
% 141.21/20.68 e3) = all_26_1 & $i(all_26_1))
% 141.21/20.68 (20) op(e0, e3) = all_52_3
% 141.21/20.68 (21) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 141.21/20.68 all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3,
% 141.21/20.68 e2) = all_36_1 & $i(all_36_1))
% 141.21/20.68 (22) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.21/20.68 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.21/20.68 (23) ~ (all_10_2 = e1)
% 141.21/20.68 (24) ~ (all_52_7 = e3)
% 141.21/20.68 (25) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.68 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.21/20.68 e1)
% 141.21/20.68 (26) ~ (all_52_4 = all_52_6)
% 141.21/20.68 (27) all_54_12 = all_52_3
% 141.21/20.68 (28) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.21/20.68 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.21/20.68 (29) ~ (e3 = e0)
% 141.21/20.68 (30) op(e1, e1) = e1
% 141.21/20.68 (31) all_57_14 = e3
% 141.21/20.68 (32) op(e3, e1) = all_52_8
% 141.21/20.68 (33) all_54_9 = all_52_6
% 141.21/20.68 (34) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.21/20.68 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.21/20.68 (35) ~ (all_52_6 = all_52_7)
% 141.21/20.68 (36) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.21/20.68 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.21/20.68 e2)
% 141.21/20.68 (37) all_57_13 = e2
% 141.21/20.68 (38) op(e2, e3) = all_52_1
% 141.21/20.68 (39) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.21/20.68 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.21/20.68 (40) op(e0, e0) = all_10_2
% 141.21/20.68 (41) op(e3, e2) = e1
% 141.21/20.68 (42) ~ (e1 = e0)
% 141.21/20.68 (43) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.68 (44) op(e3, e2) = all_52_4
% 141.21/20.68 (45) ~ (e2 = e0)
% 141.21/20.68 (46) ~ (e3 = e2)
% 141.21/20.68 (47) ~ (all_52_2 = e1)
% 141.21/20.68 (48) ~ (all_52_1 = all_52_2)
% 141.21/20.68 (49) all_57_9 = e3
% 141.21/20.68 (50) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.21/20.68 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.21/20.68 (51) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.21/20.68 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.21/20.68 & $i(all_6_1))
% 141.21/20.68 (52) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.68 (53) ~ (all_52_3 = e0)
% 141.21/20.68 (54) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.21/20.68 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.21/20.68 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.68 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.21/20.68 (55) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.21/20.68 all_56_4 & $i(all_56_4))
% 141.21/20.68 (56) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.68 (57) ~ (all_52_13 = e2)
% 141.21/20.68 (58) ~ (e3 = e1)
% 141.21/20.68 (59) op(e0, e2) = all_52_7
% 141.21/20.68 (60) ~ (all_52_2 = all_52_3)
% 141.21/20.68 (61) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.68 (62) all_54_8 = all_52_2
% 141.21/20.68 (63) ~ (all_52_2 = e2)
% 141.21/20.68 (64) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.21/20.68 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.21/20.68 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.21/20.68 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.21/20.68 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.21/20.68 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.21/20.68 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.21/20.68 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.21/20.68 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.21/20.68 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.21/20.68 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.21/20.68 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.21/20.68 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.21/20.68 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.21/20.68 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.21/20.68 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.21/20.68 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.21/20.68 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.68 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.21/20.68 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.68 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.21/20.68 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.21/20.68 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.21/20.68 $i(all_56_14))))
% 141.21/20.68 (65) op(e3, e3) = all_14_2
% 141.21/20.68 (66) ~ (all_52_3 = e2)
% 141.21/20.68 (67) op(e2, e0) = all_52_13
% 141.21/20.68 (68) ~ (all_14_2 = e0)
% 141.21/20.68 (69) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.21/20.68 all_56_9 & $i(all_56_9))
% 141.21/20.68 (70) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 141.21/20.68 all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3,
% 141.21/20.68 e2) = all_44_1 & $i(all_44_1))
% 141.21/20.68
% 141.21/20.68 Begin of proof
% 141.21/20.68 |
% 141.21/20.68 | BETA: splitting (28) gives:
% 141.21/20.68 |
% 141.21/20.68 | Case 1:
% 141.21/20.68 | |
% 141.21/20.68 | | (71) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 141.21/20.68 | | e2)
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (46), (49), (52), (57), (67), (71) are inconsistent by sub-proof
% 141.21/20.68 | | #301.
% 141.21/20.68 | |
% 141.21/20.68 | Case 2:
% 141.21/20.68 | |
% 141.21/20.68 | | (72) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.21/20.68 | | e2)
% 141.21/20.68 | |
% 141.21/20.68 | | BETA: splitting (72) gives:
% 141.21/20.68 | |
% 141.21/20.68 | | Case 1:
% 141.21/20.68 | | |
% 141.21/20.68 | | | (73) all_57_11 = e2 & op(e1, e0) = e2
% 141.21/20.68 | | |
% 141.21/20.68 | | | ALPHA: (73) implies:
% 141.21/20.68 | | | (74) all_57_11 = e2
% 141.21/20.68 | | |
% 141.21/20.68 | | | BETA: splitting (39) gives:
% 141.21/20.68 | | |
% 141.21/20.68 | | | Case 1:
% 141.21/20.68 | | | |
% 141.21/20.68 | | | | (75) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 141.21/20.68 | | | | = e1)
% 141.21/20.68 | | | |
% 141.21/20.68 | | | | BETA: splitting (75) gives:
% 141.21/20.68 | | | |
% 141.21/20.68 | | | | Case 1:
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | (76) all_57_0 = e1 & op(e3, e3) = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | ALPHA: (76) implies:
% 141.21/20.68 | | | | | (77) op(e3, e3) = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | REF_CLOSE: (10), (32), (52), (69), (77) are inconsistent by sub-proof
% 141.21/20.68 | | | | | #295.
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | Case 2:
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | (78) all_57_2 = e1 & op(e2, e3) = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | REF_CLOSE: (2), (3), (6), (7), (9), (14), (16), (18), (19), (21),
% 141.21/20.68 | | | | | (24), (26), (27), (33), (35), (38), (41), (43), (44), (48),
% 141.21/20.68 | | | | | (51), (52), (56), (60), (61), (62), (63), (66), (70), (78)
% 141.21/20.68 | | | | | are inconsistent by sub-proof #169.
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | End of split
% 141.21/20.68 | | | |
% 141.21/20.68 | | | Case 2:
% 141.21/20.68 | | | |
% 141.21/20.68 | | | | (79) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 141.21/20.68 | | | | = e1)
% 141.21/20.68 | | | |
% 141.21/20.68 | | | | BETA: splitting (79) gives:
% 141.21/20.68 | | | |
% 141.21/20.68 | | | | Case 1:
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | (80) all_57_6 = e1 & op(e1, e3) = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | ALPHA: (80) implies:
% 141.21/20.68 | | | | | (81) op(e1, e3) = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | REF_CLOSE: (7), (47), (52), (81) are inconsistent by sub-proof #332.
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | Case 2:
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | (82) all_57_12 = e1 & op(e0, e3) = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | ALPHA: (82) implies:
% 141.21/20.68 | | | | | (83) all_57_12 = e1
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | BETA: splitting (55) gives:
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | | Case 1:
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | (84) all_56_11 = e1 & op(e2, e2) = e1
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | ALPHA: (84) implies:
% 141.21/20.68 | | | | | | (85) all_56_11 = e1
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | BETA: splitting (64) gives:
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | Case 1:
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | | (86) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 141.21/20.68 | | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) =
% 141.21/20.68 | | | | | | | e3 & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 &
% 141.21/20.68 | | | | | | | ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) =
% 141.21/20.68 | | | | | | | all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 =
% 141.21/20.68 | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 141.21/20.68 | | | | | | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 141.21/20.68 | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 & ~
% 141.21/20.68 | | | | | | | (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.21/20.68 | | | | | | | all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | | BETA: splitting (86) gives:
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | (87) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 141.21/20.68 | | | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) =
% 141.21/20.68 | | | | | | | | e3 & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 &
% 141.21/20.68 | | | | | | | | ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) =
% 141.21/20.68 | | | | | | | | all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | BETA: splitting (87) gives:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (88) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 141.21/20.68 | | | | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) =
% 141.21/20.68 | | | | | | | | | e3 & $i(all_56_0)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (88) implies:
% 141.21/20.68 | | | | | | | | | (89) all_56_11 = e3
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | COMBINE_EQS: (85), (89) imply:
% 141.21/20.68 | | | | | | | | | (90) e3 = e1
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (5), (10), (11), (22), (29), (30), (31), (32),
% 141.21/20.68 | | | | | | | | | (42), (45), (46), (50), (52), (58), (90) are
% 141.21/20.68 | | | | | | | | | inconsistent by sub-proof #1037.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (91) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 141.21/20.68 | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2, e2) =
% 141.21/20.68 | | | | | | | | | e3 & $i(all_56_3)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (91) implies:
% 141.21/20.68 | | | | | | | | | (92) all_56_11 = e3
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | COMBINE_EQS: (85), (92) imply:
% 141.21/20.68 | | | | | | | | | (93) e3 = e1
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (5), (10), (11), (22), (29), (30), (31), (32),
% 141.21/20.68 | | | | | | | | | (42), (45), (46), (50), (52), (58), (93) are
% 141.21/20.68 | | | | | | | | | inconsistent by sub-proof #1037.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | End of split
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | (94) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) &
% 141.21/20.68 | | | | | | | | op(e3, e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) =
% 141.21/20.68 | | | | | | | | e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 &
% 141.21/20.68 | | | | | | | | ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.21/20.68 | | | | | | | | all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | BETA: splitting (94) gives:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (95) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) &
% 141.21/20.68 | | | | | | | | | op(e3, e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) =
% 141.21/20.68 | | | | | | | | | e3 & $i(all_56_1)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (95) implies:
% 141.21/20.68 | | | | | | | | | (96) op(e1, e1) = e3
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (7), (8), (11), (12), (29), (34), (42), (45), (47),
% 141.21/20.68 | | | | | | | | | (52), (58), (74), (96) are inconsistent by
% 141.21/20.68 | | | | | | | | | sub-proof #303.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (97) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 141.21/20.68 | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1, e1) =
% 141.21/20.68 | | | | | | | | | e3 & $i(all_56_6)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (97) implies:
% 141.21/20.68 | | | | | | | | | (98) op(e1, e1) = e3
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (7), (8), (11), (12), (29), (34), (42), (45), (47),
% 141.21/20.68 | | | | | | | | | (52), (58), (74), (98) are inconsistent by
% 141.21/20.68 | | | | | | | | | sub-proof #303.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | End of split
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | End of split
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | Case 2:
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | | (99) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 141.21/20.68 | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) =
% 141.21/20.68 | | | | | | | e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 &
% 141.21/20.68 | | | | | | | ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.21/20.68 | | | | | | | all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11
% 141.21/20.68 | | | | | | | = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 141.21/20.68 | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 141.21/20.68 | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 141.21/20.68 | | | | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.21/20.68 | | | | | | | all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 141.21/20.68 | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.21/20.68 | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.21/20.68 | | | | | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.68 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0)
% 141.21/20.68 | | | | | | | & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.21/20.68 | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 141.21/20.68 | | | | | | | ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 141.21/20.68 | | | | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.21/20.68 | | | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 141.21/20.68 | | | | | | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | | BETA: splitting (99) gives:
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | (100) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 141.21/20.68 | | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 141.21/20.68 | | | | | | | | = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 =
% 141.21/20.68 | | | | | | | | e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2,
% 141.21/20.68 | | | | | | | | e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | BETA: splitting (100) gives:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (101) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 141.21/20.68 | | | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 141.21/20.68 | | | | | | | | | = e3 & $i(all_56_2)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (101) implies:
% 141.21/20.68 | | | | | | | | | (102) op(e0, e0) = e3
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (11), (15), (25), (29), (31), (36), (42), (45),
% 141.21/20.68 | | | | | | | | | (46), (52), (54), (58), (59), (102) are
% 141.21/20.68 | | | | | | | | | inconsistent by sub-proof #187.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (103) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2)
% 141.21/20.68 | | | | | | | | | & op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 141.21/20.68 | | | | | | | | | e1) = e2 & $i(all_56_4)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (103) implies:
% 141.21/20.68 | | | | | | | | | (104) ~ (all_56_4 = e2)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (17), (85), (104) are inconsistent by sub-proof
% 141.21/20.68 | | | | | | | | | #646.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | End of split
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | (105) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.21/20.68 | | | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1)
% 141.21/20.68 | | | | | | | | = e2 & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 =
% 141.21/20.68 | | | | | | | | e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 141.21/20.68 | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.21/20.68 | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 141.21/20.68 | | | | | | | | e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.21/20.68 | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.21/20.68 | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2
% 141.21/20.68 | | | | | | | | & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.21/20.68 | | | | | | | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 =
% 141.21/20.68 | | | | | | | | e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.21/20.68 | | | | | | | | e1) = e0 & op(e1, e0) = all_56_8 &
% 141.21/20.68 | | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1
% 141.21/20.68 | | | | | | | | & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.21/20.68 | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | BETA: splitting (105) gives:
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (106) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1)
% 141.21/20.68 | | | | | | | | | & op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1,
% 141.21/20.68 | | | | | | | | | e1) = e2 & $i(all_56_7)
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | ALPHA: (106) implies:
% 141.21/20.68 | | | | | | | | | (107) op(e1, e1) = e2
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | REF_CLOSE: (11), (30), (52), (107) are inconsistent by
% 141.21/20.68 | | | | | | | | | sub-proof #1085.
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | (108) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2)
% 141.21/20.68 | | | | | | | | | & op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 141.21/20.68 | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.21/20.68 | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.21/20.68 | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.21/20.68 | | | | | | | | | e3) = e0 & op(e0, e3) = all_56_10 &
% 141.21/20.68 | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.21/20.68 | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.21/20.68 | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.21/20.68 | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 141.21/20.68 | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 141.21/20.68 | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 141.21/20.68 | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.21/20.68 | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | BETA: splitting (108) gives:
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | | Case 1:
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | | (109) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 141.21/20.68 | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 141.21/20.68 | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | | ALPHA: (109) implies:
% 141.21/20.68 | | | | | | | | | | (110) op(e0, e0) = e2
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | | REF_CLOSE: (4), (11), (15), (25), (29), (37), (42), (45),
% 141.21/20.68 | | | | | | | | | | (46), (52), (54), (58), (59), (83), (110) are
% 141.21/20.68 | | | | | | | | | | inconsistent by sub-proof #835.
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | Case 2:
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | | (111) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9
% 141.21/20.68 | | | | | | | | | | = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.21/20.68 | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.21/20.68 | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.21/20.68 | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.21/20.68 | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.21/20.68 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 141.21/20.68 | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 141.21/20.68 | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 141.21/20.68 | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.21/20.68 | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | | ALPHA: (111) implies:
% 141.21/20.68 | | | | | | | | | | (112) op(e0, e0) = all_56_15
% 141.21/20.68 | | | | | | | | | | (113) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.21/20.68 | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 141.21/20.68 | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.21/20.68 | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.21/20.68 | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.21/20.68 | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 141.21/20.68 | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.21/20.68 | | | | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1
% 141.21/20.68 | | | | | | | | | | & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.21/20.68 | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | | REF_CLOSE: (1), (23), (40), (52), (65), (68), (112), (113)
% 141.21/20.68 | | | | | | | | | | are inconsistent by sub-proof #1114.
% 141.21/20.68 | | | | | | | | | |
% 141.21/20.68 | | | | | | | | | End of split
% 141.21/20.68 | | | | | | | | |
% 141.21/20.68 | | | | | | | | End of split
% 141.21/20.68 | | | | | | | |
% 141.21/20.68 | | | | | | | End of split
% 141.21/20.68 | | | | | | |
% 141.21/20.68 | | | | | | End of split
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | Case 2:
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | (114) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | ALPHA: (114) implies:
% 141.21/20.68 | | | | | | (115) ~ (all_56_4 = e2)
% 141.21/20.68 | | | | | | (116) op(e2, e1) = all_56_4
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | | REF_CLOSE: (13), (52), (115), (116) are inconsistent by sub-proof
% 141.21/20.68 | | | | | | #951.
% 141.21/20.68 | | | | | |
% 141.21/20.68 | | | | | End of split
% 141.21/20.68 | | | | |
% 141.21/20.68 | | | | End of split
% 141.21/20.68 | | | |
% 141.21/20.68 | | | End of split
% 141.21/20.68 | | |
% 141.21/20.68 | | Case 2:
% 141.21/20.68 | | |
% 141.21/20.68 | | | (117) all_57_15 = e2 & op(e0, e0) = e2
% 141.21/20.68 | | |
% 141.21/20.68 | | | REF_CLOSE: (4), (11), (15), (20), (25), (29), (37), (42), (45), (46),
% 141.21/20.68 | | | (52), (53), (54), (58), (59), (117) are inconsistent by
% 141.21/20.68 | | | sub-proof #168.
% 141.21/20.68 | | |
% 141.21/20.68 | | End of split
% 141.21/20.68 | |
% 141.21/20.68 | End of split
% 141.21/20.68 |
% 141.21/20.68 End of proof
% 141.21/20.68
% 141.21/20.68 Sub-proof #168 shows that the following formulas are inconsistent:
% 141.21/20.68 ----------------------------------------------------------------
% 141.21/20.68 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.21/20.68 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.68 (2) ~ (e2 = e1)
% 141.21/20.68 (3) ~ (all_52_7 = e0)
% 141.21/20.68 (4) all_57_15 = e2 & op(e0, e0) = e2
% 141.21/20.68 (5) op(e0, e3) = all_52_3
% 141.21/20.68 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.21/20.68 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.21/20.68 (7) ~ (e3 = e0)
% 141.21/20.68 (8) all_57_13 = e2
% 141.21/20.68 (9) ~ (e1 = e0)
% 141.21/20.68 (10) ~ (e2 = e0)
% 141.21/20.68 (11) ~ (e3 = e2)
% 141.21/20.68 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.68 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.68 (13) ~ (all_52_3 = e0)
% 141.21/20.68 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.21/20.68 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.21/20.68 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.68 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.21/20.68 (15) ~ (e3 = e1)
% 141.21/20.68 (16) op(e0, e2) = all_52_7
% 141.21/20.68
% 141.21/20.68 Begin of proof
% 141.21/20.68 |
% 141.21/20.68 | ALPHA: (4) implies:
% 141.21/20.68 | (17) op(e0, e0) = e2
% 141.21/20.68 |
% 141.21/20.68 | BETA: splitting (14) gives:
% 141.21/20.68 |
% 141.21/20.68 | Case 1:
% 141.21/20.68 | |
% 141.21/20.68 | | (18) all_57_15 = e0 & op(e0, e0) = e0
% 141.21/20.68 | |
% 141.21/20.68 | | ALPHA: (18) implies:
% 141.21/20.68 | | (19) op(e0, e0) = e0
% 141.21/20.68 | |
% 141.21/20.68 | | REF_CLOSE: (10), (12), (17), (19) are inconsistent by sub-proof #1094.
% 141.21/20.68 | |
% 141.21/20.68 | Case 2:
% 141.21/20.68 | |
% 141.21/20.68 | | (20) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.21/20.68 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 141.21/20.68 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.21/20.68 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.21/20.68 | |
% 141.21/20.68 | | ALPHA: (20) implies:
% 141.21/20.68 | | (21) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.21/20.68 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.21/20.68 | |
% 141.21/20.68 | | BETA: splitting (21) gives:
% 141.21/20.68 | |
% 141.21/20.68 | | Case 1:
% 141.21/20.68 | | |
% 141.21/20.68 | | | (22) all_57_12 = e0 & op(e0, e3) = e0
% 141.21/20.68 | | |
% 141.21/20.68 | | | ALPHA: (22) implies:
% 141.21/20.68 | | | (23) op(e0, e3) = e0
% 141.21/20.68 | | |
% 141.21/20.68 | | | REF_CLOSE: (5), (12), (13), (23) are inconsistent by sub-proof #986.
% 141.21/20.68 | | |
% 141.21/20.68 | | Case 2:
% 141.21/20.68 | | |
% 141.21/20.69 | | | (24) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 141.21/20.69 | | | = e0)
% 141.21/20.69 | | |
% 141.21/20.69 | | | BETA: splitting (24) gives:
% 141.21/20.69 | | |
% 141.21/20.69 | | | Case 1:
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | (25) all_57_13 = e0 & op(e0, e2) = e0
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | ALPHA: (25) implies:
% 141.21/20.69 | | | | (26) op(e0, e2) = e0
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | REF_CLOSE: (3), (12), (16), (26) are inconsistent by sub-proof #977.
% 141.21/20.69 | | | |
% 141.21/20.69 | | | Case 2:
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | (27) all_57_14 = e0 & op(e0, e1) = e0
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | ALPHA: (27) implies:
% 141.21/20.69 | | | | (28) all_57_14 = e0
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | REF_CLOSE: (1), (2), (6), (7), (8), (9), (11), (12), (15), (17), (28)
% 141.21/20.69 | | | | are inconsistent by sub-proof #1064.
% 141.21/20.69 | | | |
% 141.21/20.69 | | | End of split
% 141.21/20.69 | | |
% 141.21/20.69 | | End of split
% 141.21/20.69 | |
% 141.21/20.69 | End of split
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #169 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) ~ (all_52_4 = all_52_7)
% 141.21/20.69 (2) ~ (all_52_1 = all_52_3)
% 141.21/20.69 (3) ~ (all_52_3 = all_52_7)
% 141.21/20.69 (4) op(e1, e3) = all_52_2
% 141.21/20.69 (5) op(e1, e2) = all_52_6
% 141.21/20.69 (6) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.69 (7) all_54_13 = all_52_7
% 141.21/20.69 (8) ~ (all_52_2 = all_52_6)
% 141.21/20.69 (9) ( ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) = all_26_1
% 141.21/20.69 & $i(all_26_0) & $i(all_26_1)) | ( ~ (all_26_1 = e0) & op(e2, e3) =
% 141.21/20.69 all_26_1 & $i(all_26_1))
% 141.21/20.69 (10) all_57_2 = e1 & op(e2, e3) = e1
% 141.21/20.69 (11) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 141.21/20.69 all_36_1 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3,
% 141.21/20.69 e2) = all_36_1 & $i(all_36_1))
% 141.21/20.69 (12) ~ (all_52_7 = e3)
% 141.21/20.69 (13) ~ (all_52_4 = all_52_6)
% 141.21/20.69 (14) all_54_12 = all_52_3
% 141.21/20.69 (15) all_54_9 = all_52_6
% 141.21/20.69 (16) ~ (all_52_6 = all_52_7)
% 141.21/20.69 (17) op(e2, e3) = all_52_1
% 141.21/20.69 (18) op(e3, e2) = e1
% 141.21/20.69 (19) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.69 (20) op(e3, e2) = all_52_4
% 141.21/20.69 (21) ~ (all_52_1 = all_52_2)
% 141.21/20.69 (22) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.21/20.69 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.21/20.69 & $i(all_6_1))
% 141.21/20.69 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.69 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.69 (25) ~ (all_52_2 = all_52_3)
% 141.21/20.69 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69 (27) all_54_8 = all_52_2
% 141.21/20.69 (28) ~ (all_52_2 = e2)
% 141.21/20.69 (29) ~ (all_52_3 = e2)
% 141.21/20.69 (30) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 141.21/20.69 all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3,
% 141.21/20.69 e2) = all_44_1 & $i(all_44_1))
% 141.21/20.69
% 141.21/20.69 Begin of proof
% 141.21/20.69 |
% 141.21/20.69 | ALPHA: (10) implies:
% 141.21/20.69 | (31) op(e2, e3) = e1
% 141.21/20.69 |
% 141.21/20.69 | GROUND_INST: instantiating (23) with all_52_1, e1, e3, e2, simplifying with
% 141.21/20.69 | (17), (31) gives:
% 141.21/20.69 | (32) all_52_1 = e1
% 141.21/20.69 |
% 141.21/20.69 | GROUND_INST: instantiating (23) with all_52_4, e1, e2, e3, simplifying with
% 141.21/20.69 | (18), (20) gives:
% 141.21/20.69 | (33) all_52_4 = e1
% 141.21/20.69 |
% 141.21/20.69 | REDUCE: (21), (32) imply:
% 141.21/20.69 | (34) ~ (all_52_2 = e1)
% 141.21/20.69 |
% 141.21/20.69 | SIMP: (34) implies:
% 141.21/20.69 | (35) ~ (all_52_2 = e1)
% 141.21/20.69 |
% 141.21/20.69 | REDUCE: (2), (32) imply:
% 141.21/20.69 | (36) ~ (all_52_3 = e1)
% 141.21/20.69 |
% 141.21/20.69 | SIMP: (36) implies:
% 141.21/20.69 | (37) ~ (all_52_3 = e1)
% 141.21/20.69 |
% 141.21/20.69 | REDUCE: (13), (33) imply:
% 141.21/20.69 | (38) ~ (all_52_6 = e1)
% 141.21/20.69 |
% 141.21/20.69 | SIMP: (38) implies:
% 141.21/20.69 | (39) ~ (all_52_6 = e1)
% 141.21/20.69 |
% 141.21/20.69 | REDUCE: (1), (33) imply:
% 141.21/20.69 | (40) ~ (all_52_7 = e1)
% 141.21/20.69 |
% 141.21/20.69 | SIMP: (40) implies:
% 141.21/20.69 | (41) ~ (all_52_7 = e1)
% 141.21/20.69 |
% 141.21/20.69 | BETA: splitting (9) gives:
% 141.21/20.69 |
% 141.21/20.69 | Case 1:
% 141.21/20.69 | |
% 141.21/20.69 | | (42) ~ (all_26_0 = e1) & op(all_26_1, e2) = all_26_0 & op(e2, e3) =
% 141.21/20.69 | | all_26_1 & $i(all_26_0) & $i(all_26_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (42) implies:
% 141.21/20.69 | | (43) ~ (all_26_0 = e1)
% 141.21/20.69 | | (44) op(e2, e3) = all_26_1
% 141.21/20.69 | | (45) op(all_26_1, e2) = all_26_0
% 141.21/20.69 | |
% 141.21/20.69 | | BETA: splitting (11) gives:
% 141.21/20.69 | |
% 141.21/20.69 | | Case 1:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (46) ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 141.21/20.69 | | | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 141.21/20.69 | | |
% 141.21/20.69 | | | ALPHA: (46) implies:
% 141.21/20.69 | | | (47) ~ (all_36_0 = e0)
% 141.21/20.69 | | | (48) op(e3, e2) = all_36_1
% 141.21/20.69 | | | (49) op(all_36_1, e3) = all_36_0
% 141.21/20.69 | | |
% 141.21/20.69 | | | BETA: splitting (30) gives:
% 141.21/20.69 | | |
% 141.21/20.69 | | | Case 1:
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | (50) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 141.21/20.69 | | | | all_44_1 & $i(all_44_0) & $i(all_44_1)
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | ALPHA: (50) implies:
% 141.21/20.69 | | | | (51) op(e3, e2) = all_44_1
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (12), (14), (15), (16), (18),
% 141.21/20.69 | | | | (19), (22), (23), (24), (25), (26), (27), (28), (29), (31),
% 141.21/20.69 | | | | (35), (37), (41), (43), (44), (45), (47), (48), (49), (51)
% 141.21/20.69 | | | | are inconsistent by sub-proof #172.
% 141.21/20.69 | | | |
% 141.21/20.69 | | | Case 2:
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | (52) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | ALPHA: (52) implies:
% 141.21/20.69 | | | | (53) op(e3, e2) = all_44_1
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (12), (14), (15), (16), (18),
% 141.21/20.69 | | | | (19), (22), (23), (24), (25), (26), (27), (28), (29), (31),
% 141.21/20.69 | | | | (35), (37), (41), (43), (44), (45), (47), (48), (49), (53)
% 141.21/20.69 | | | | are inconsistent by sub-proof #172.
% 141.21/20.69 | | | |
% 141.21/20.69 | | | End of split
% 141.21/20.69 | | |
% 141.21/20.69 | | Case 2:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (54) ~ (all_36_1 = e1) & op(e3, e2) = all_36_1 & $i(all_36_1)
% 141.21/20.69 | | |
% 141.21/20.69 | | | ALPHA: (54) implies:
% 141.21/20.69 | | | (55) ~ (all_36_1 = e1)
% 141.21/20.69 | | | (56) op(e3, e2) = all_36_1
% 141.21/20.69 | | |
% 141.21/20.69 | | | REF_CLOSE: (18), (23), (30), (55), (56) are inconsistent by sub-proof
% 141.21/20.69 | | | #171.
% 141.21/20.69 | | |
% 141.21/20.69 | | End of split
% 141.21/20.69 | |
% 141.21/20.69 | Case 2:
% 141.21/20.69 | |
% 141.21/20.69 | | (57) ~ (all_26_1 = e0) & op(e2, e3) = all_26_1 & $i(all_26_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (57) implies:
% 141.21/20.69 | | (58) op(e2, e3) = all_26_1
% 141.21/20.69 | |
% 141.21/20.69 | | BETA: splitting (11) gives:
% 141.21/20.69 | |
% 141.21/20.69 | | Case 1:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (59) ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 141.21/20.69 | | | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 141.21/20.69 | | |
% 141.21/20.69 | | | ALPHA: (59) implies:
% 141.21/20.69 | | | (60) ~ (all_36_0 = e0)
% 141.21/20.69 | | | (61) op(e3, e2) = all_36_1
% 141.21/20.69 | | | (62) op(all_36_1, e3) = all_36_0
% 141.21/20.69 | | |
% 141.21/20.69 | | | BETA: splitting (30) gives:
% 141.21/20.69 | | |
% 141.21/20.69 | | | Case 1:
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | (63) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 141.21/20.69 | | | | all_44_1 & $i(all_44_0) & $i(all_44_1)
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | ALPHA: (63) implies:
% 141.21/20.69 | | | | (64) op(e3, e2) = all_44_1
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (12), (14), (15), (16), (18),
% 141.21/20.69 | | | | (19), (22), (23), (24), (25), (26), (27), (28), (29), (31),
% 141.21/20.69 | | | | (35), (37), (39), (41), (58), (60), (61), (62), (64) are
% 141.21/20.69 | | | | inconsistent by sub-proof #170.
% 141.21/20.69 | | | |
% 141.21/20.69 | | | Case 2:
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | (65) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | ALPHA: (65) implies:
% 141.21/20.69 | | | | (66) op(e3, e2) = all_44_1
% 141.21/20.69 | | | |
% 141.21/20.69 | | | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (12), (14), (15), (16), (18),
% 141.21/20.69 | | | | (19), (22), (23), (24), (25), (26), (27), (28), (29), (31),
% 141.21/20.69 | | | | (35), (37), (39), (41), (58), (60), (61), (62), (66) are
% 141.21/20.69 | | | | inconsistent by sub-proof #170.
% 141.21/20.69 | | | |
% 141.21/20.69 | | | End of split
% 141.21/20.69 | | |
% 141.21/20.69 | | Case 2:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (67) ~ (all_36_1 = e1) & op(e3, e2) = all_36_1 & $i(all_36_1)
% 141.21/20.69 | | |
% 141.21/20.69 | | | ALPHA: (67) implies:
% 141.21/20.69 | | | (68) ~ (all_36_1 = e1)
% 141.21/20.69 | | | (69) op(e3, e2) = all_36_1
% 141.21/20.69 | | |
% 141.21/20.69 | | | REF_CLOSE: (18), (23), (30), (68), (69) are inconsistent by sub-proof
% 141.21/20.69 | | | #171.
% 141.21/20.69 | | |
% 141.21/20.69 | | End of split
% 141.21/20.69 | |
% 141.21/20.69 | End of split
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #170 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) ~ (all_52_3 = all_52_7)
% 141.21/20.69 (2) op(e1, e3) = all_52_2
% 141.21/20.69 (3) ~ (all_52_7 = e1)
% 141.21/20.69 (4) op(e1, e2) = all_52_6
% 141.21/20.69 (5) ~ (all_52_6 = e1)
% 141.21/20.69 (6) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.69 (7) all_54_13 = all_52_7
% 141.21/20.69 (8) ~ (all_52_2 = all_52_6)
% 141.21/20.69 (9) ~ (all_36_0 = e0)
% 141.21/20.69 (10) ~ (all_52_7 = e3)
% 141.21/20.69 (11) op(e3, e2) = all_44_1
% 141.21/20.69 (12) all_54_12 = all_52_3
% 141.21/20.69 (13) all_54_9 = all_52_6
% 141.21/20.69 (14) op(e2, e3) = all_26_1
% 141.21/20.69 (15) ~ (all_52_6 = all_52_7)
% 141.21/20.69 (16) op(e2, e3) = e1
% 141.21/20.69 (17) op(e3, e2) = e1
% 141.21/20.69 (18) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.69 (19) ~ (all_52_3 = e1)
% 141.21/20.69 (20) ~ (all_52_2 = e1)
% 141.21/20.69 (21) op(all_36_1, e3) = all_36_0
% 141.21/20.69 (22) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.21/20.69 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.21/20.69 & $i(all_6_1))
% 141.21/20.69 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.69 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.69 (25) ~ (all_52_2 = all_52_3)
% 141.21/20.69 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69 (27) all_54_8 = all_52_2
% 141.21/20.69 (28) ~ (all_52_2 = e2)
% 141.21/20.69 (29) op(e3, e2) = all_36_1
% 141.21/20.69 (30) ~ (all_52_3 = e2)
% 141.21/20.69
% 141.21/20.69 Begin of proof
% 141.21/20.69 |
% 141.21/20.69 | BETA: splitting (22) gives:
% 141.21/20.69 |
% 141.21/20.69 | Case 1:
% 141.21/20.69 | |
% 141.21/20.69 | | (31) ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1
% 141.21/20.69 | | & $i(all_6_0) & $i(all_6_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (31) implies:
% 141.21/20.69 | | (32) ~ (all_6_0 = e0)
% 141.21/20.69 | | (33) op(e2, e3) = all_6_1
% 141.21/20.69 | | (34) op(all_6_1, e2) = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with e1, all_26_1, e3, e2, simplifying with
% 141.21/20.69 | | (14), (16) gives:
% 141.21/20.69 | | (35) all_26_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_6_1, all_26_1, e3, e2, simplifying
% 141.21/20.69 | | with (14), (33) gives:
% 141.21/20.69 | | (36) all_26_1 = all_6_1
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with e1, all_44_1, e2, e3, simplifying with
% 141.21/20.69 | | (11), (17) gives:
% 141.21/20.69 | | (37) all_44_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_36_1, all_44_1, e2, e3, simplifying
% 141.21/20.69 | | with (11), (29) gives:
% 141.21/20.69 | | (38) all_44_1 = all_36_1
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (37), (38) imply:
% 141.21/20.69 | | (39) all_36_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (35), (36) imply:
% 141.21/20.69 | | (40) all_6_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (40) implies:
% 141.21/20.69 | | (41) all_6_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (21), (39) imply:
% 141.21/20.69 | | (42) op(e1, e3) = all_36_0
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (34), (41) imply:
% 141.21/20.69 | | (43) op(e1, e2) = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_52_6, all_6_0, e2, e1, simplifying
% 141.21/20.69 | | with (4), (43) gives:
% 141.21/20.69 | | (44) all_52_6 = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_52_2, all_36_0, e3, e1, simplifying
% 141.21/20.69 | | with (2), (42) gives:
% 141.21/20.69 | | (45) all_52_2 = all_36_0
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (13), (44) imply:
% 141.21/20.69 | | (46) all_54_9 = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (27), (45) imply:
% 141.21/20.69 | | (47) all_54_8 = all_36_0
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (25), (45) imply:
% 141.21/20.69 | | (48) ~ (all_52_3 = all_36_0)
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (48) implies:
% 141.21/20.69 | | (49) ~ (all_52_3 = all_36_0)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (8), (44), (45) imply:
% 141.21/20.69 | | (50) ~ (all_36_0 = all_6_0)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (28), (45) imply:
% 141.21/20.69 | | (51) ~ (all_36_0 = e2)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (20), (45) imply:
% 141.21/20.69 | | (52) ~ (all_36_0 = e1)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (15), (44) imply:
% 141.21/20.69 | | (53) ~ (all_52_7 = all_6_0)
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (53) implies:
% 141.21/20.69 | | (54) ~ (all_52_7 = all_6_0)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (5), (44) imply:
% 141.21/20.69 | | (55) ~ (all_6_0 = e1)
% 141.21/20.69 | |
% 141.21/20.69 | | BETA: splitting (26) gives:
% 141.21/20.69 | |
% 141.21/20.69 | | Case 1:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (56) all_54_8 = e3
% 141.21/20.69 | | |
% 141.21/20.69 | | | COMBINE_EQS: (47), (56) imply:
% 141.21/20.69 | | | (57) all_36_0 = e3
% 141.21/20.69 | | |
% 141.21/20.69 | | | REDUCE: (49), (57) imply:
% 141.21/20.69 | | | (58) ~ (all_52_3 = e3)
% 141.21/20.69 | | |
% 141.21/20.69 | | | REDUCE: (50), (57) imply:
% 141.21/20.69 | | | (59) ~ (all_6_0 = e3)
% 141.21/20.69 | | |
% 141.21/20.69 | | | SIMP: (59) implies:
% 141.21/20.69 | | | (60) ~ (all_6_0 = e3)
% 141.21/20.69 | | |
% 141.21/20.69 | | | REF_CLOSE: (1), (3), (6), (7), (10), (12), (18), (19), (24), (30), (32),
% 141.21/20.69 | | | (46), (54), (55), (58), (60) are inconsistent by sub-proof
% 141.21/20.69 | | | #175.
% 141.21/20.69 | | |
% 141.21/20.69 | | Case 2:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (61) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69 | | |
% 141.21/20.69 | | | REF_CLOSE: (9), (47), (51), (52), (61) are inconsistent by sub-proof #174.
% 141.21/20.69 | | |
% 141.21/20.69 | | End of split
% 141.21/20.69 | |
% 141.21/20.69 | Case 2:
% 141.21/20.69 | |
% 141.21/20.69 | | (62) ~ (all_6_1 = e1) & op(e2, e3) = all_6_1 & $i(all_6_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (62) implies:
% 141.21/20.69 | | (63) ~ (all_6_1 = e1)
% 141.21/20.69 | | (64) op(e2, e3) = all_6_1
% 141.21/20.69 | |
% 141.21/20.69 | | REF_CLOSE: (14), (16), (23), (63), (64) are inconsistent by sub-proof #173.
% 141.21/20.69 | |
% 141.21/20.69 | End of split
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #171 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) ~ (all_36_1 = e1)
% 141.21/20.69 (2) op(e3, e2) = e1
% 141.21/20.69 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.69 (4) op(e3, e2) = all_36_1
% 141.21/20.69 (5) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) = all_44_1
% 141.21/20.69 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) & op(e3, e2) =
% 141.21/20.69 all_44_1 & $i(all_44_1))
% 141.21/20.69
% 141.21/20.69 Begin of proof
% 141.21/20.69 |
% 141.21/20.69 | BETA: splitting (5) gives:
% 141.21/20.69 |
% 141.21/20.69 | Case 1:
% 141.21/20.69 | |
% 141.21/20.69 | | (6) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 141.21/20.69 | | all_44_1 & $i(all_44_0) & $i(all_44_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (6) implies:
% 141.21/20.69 | | (7) op(e3, e2) = all_44_1
% 141.21/20.69 | |
% 141.21/20.69 | | REF_CLOSE: (1), (2), (3), (4), (7) are inconsistent by sub-proof #869.
% 141.21/20.69 | |
% 141.21/20.69 | Case 2:
% 141.21/20.69 | |
% 141.21/20.69 | | (8) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (8) implies:
% 141.21/20.69 | | (9) op(e3, e2) = all_44_1
% 141.21/20.69 | |
% 141.21/20.69 | | REF_CLOSE: (1), (2), (3), (4), (9) are inconsistent by sub-proof #869.
% 141.21/20.69 | |
% 141.21/20.69 | End of split
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #172 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) ~ (all_52_3 = all_52_7)
% 141.21/20.69 (2) op(e1, e3) = all_52_2
% 141.21/20.69 (3) ~ (all_52_7 = e1)
% 141.21/20.69 (4) op(all_26_1, e2) = all_26_0
% 141.21/20.69 (5) op(e1, e2) = all_52_6
% 141.21/20.69 (6) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.69 (7) all_54_13 = all_52_7
% 141.21/20.69 (8) ~ (all_52_2 = all_52_6)
% 141.21/20.69 (9) ~ (all_36_0 = e0)
% 141.21/20.69 (10) ~ (all_52_7 = e3)
% 141.21/20.69 (11) op(e3, e2) = all_44_1
% 141.21/20.69 (12) all_54_12 = all_52_3
% 141.21/20.69 (13) all_54_9 = all_52_6
% 141.21/20.69 (14) op(e2, e3) = all_26_1
% 141.21/20.69 (15) ~ (all_52_6 = all_52_7)
% 141.21/20.69 (16) op(e2, e3) = e1
% 141.21/20.69 (17) op(e3, e2) = e1
% 141.21/20.69 (18) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.69 (19) ~ (all_52_3 = e1)
% 141.21/20.69 (20) ~ (all_52_2 = e1)
% 141.21/20.69 (21) op(all_36_1, e3) = all_36_0
% 141.21/20.69 (22) ( ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1 &
% 141.21/20.69 $i(all_6_0) & $i(all_6_1)) | ( ~ (all_6_1 = e1) & op(e2, e3) = all_6_1
% 141.21/20.69 & $i(all_6_1))
% 141.21/20.69 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.69 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.69 (25) ~ (all_52_2 = all_52_3)
% 141.21/20.69 (26) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69 (27) all_54_8 = all_52_2
% 141.21/20.69 (28) ~ (all_52_2 = e2)
% 141.21/20.69 (29) op(e3, e2) = all_36_1
% 141.21/20.69 (30) ~ (all_26_0 = e1)
% 141.21/20.69 (31) ~ (all_52_3 = e2)
% 141.21/20.69
% 141.21/20.69 Begin of proof
% 141.21/20.69 |
% 141.21/20.69 | BETA: splitting (22) gives:
% 141.21/20.69 |
% 141.21/20.69 | Case 1:
% 141.21/20.69 | |
% 141.21/20.69 | | (32) ~ (all_6_0 = e0) & op(all_6_1, e2) = all_6_0 & op(e2, e3) = all_6_1
% 141.21/20.69 | | & $i(all_6_0) & $i(all_6_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (32) implies:
% 141.21/20.69 | | (33) ~ (all_6_0 = e0)
% 141.21/20.69 | | (34) op(e2, e3) = all_6_1
% 141.21/20.69 | | (35) op(all_6_1, e2) = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with e1, all_26_1, e3, e2, simplifying with
% 141.21/20.69 | | (14), (16) gives:
% 141.21/20.69 | | (36) all_26_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_6_1, all_26_1, e3, e2, simplifying
% 141.21/20.69 | | with (14), (34) gives:
% 141.21/20.69 | | (37) all_26_1 = all_6_1
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with e1, all_44_1, e2, e3, simplifying with
% 141.21/20.69 | | (11), (17) gives:
% 141.21/20.69 | | (38) all_44_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_36_1, all_44_1, e2, e3, simplifying
% 141.21/20.69 | | with (11), (29) gives:
% 141.21/20.69 | | (39) all_44_1 = all_36_1
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (38), (39) imply:
% 141.21/20.69 | | (40) all_36_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (36), (37) imply:
% 141.21/20.69 | | (41) all_6_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (41) implies:
% 141.21/20.69 | | (42) all_6_1 = e1
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (21), (40) imply:
% 141.21/20.69 | | (43) op(e1, e3) = all_36_0
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (4), (36) imply:
% 141.21/20.69 | | (44) op(e1, e2) = all_26_0
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (35), (42) imply:
% 141.21/20.69 | | (45) op(e1, e2) = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_52_6, all_6_0, e2, e1, simplifying
% 141.21/20.69 | | with (5), (45) gives:
% 141.21/20.69 | | (46) all_52_6 = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_52_6, all_26_0, e2, e1, simplifying
% 141.21/20.69 | | with (5), (44) gives:
% 141.21/20.69 | | (47) all_52_6 = all_26_0
% 141.21/20.69 | |
% 141.21/20.69 | | GROUND_INST: instantiating (23) with all_52_2, all_36_0, e3, e1, simplifying
% 141.21/20.69 | | with (2), (43) gives:
% 141.21/20.69 | | (48) all_52_2 = all_36_0
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (46), (47) imply:
% 141.21/20.69 | | (49) all_26_0 = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (49) implies:
% 141.21/20.69 | | (50) all_26_0 = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (13), (46) imply:
% 141.21/20.69 | | (51) all_54_9 = all_6_0
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (27), (48) imply:
% 141.21/20.69 | | (52) all_54_8 = all_36_0
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (25), (48) imply:
% 141.21/20.69 | | (53) ~ (all_52_3 = all_36_0)
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (53) implies:
% 141.21/20.69 | | (54) ~ (all_52_3 = all_36_0)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (8), (46), (48) imply:
% 141.21/20.69 | | (55) ~ (all_36_0 = all_6_0)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (28), (48) imply:
% 141.21/20.69 | | (56) ~ (all_36_0 = e2)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (20), (48) imply:
% 141.21/20.69 | | (57) ~ (all_36_0 = e1)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (15), (46) imply:
% 141.21/20.69 | | (58) ~ (all_52_7 = all_6_0)
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (58) implies:
% 141.21/20.69 | | (59) ~ (all_52_7 = all_6_0)
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (30), (50) imply:
% 141.21/20.69 | | (60) ~ (all_6_0 = e1)
% 141.21/20.69 | |
% 141.21/20.69 | | BETA: splitting (26) gives:
% 141.21/20.69 | |
% 141.21/20.69 | | Case 1:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (61) all_54_8 = e3
% 141.21/20.69 | | |
% 141.21/20.69 | | | COMBINE_EQS: (52), (61) imply:
% 141.21/20.69 | | | (62) all_36_0 = e3
% 141.21/20.69 | | |
% 141.21/20.69 | | | SIMP: (62) implies:
% 141.21/20.69 | | | (63) all_36_0 = e3
% 141.21/20.69 | | |
% 141.21/20.69 | | | REDUCE: (54), (63) imply:
% 141.21/20.69 | | | (64) ~ (all_52_3 = e3)
% 141.21/20.69 | | |
% 141.21/20.69 | | | REDUCE: (55), (63) imply:
% 141.21/20.69 | | | (65) ~ (all_6_0 = e3)
% 141.21/20.69 | | |
% 141.21/20.69 | | | SIMP: (65) implies:
% 141.21/20.69 | | | (66) ~ (all_6_0 = e3)
% 141.21/20.69 | | |
% 141.21/20.69 | | | REF_CLOSE: (1), (3), (6), (7), (10), (12), (18), (19), (24), (31), (33),
% 141.21/20.69 | | | (51), (59), (60), (64), (66) are inconsistent by sub-proof
% 141.21/20.69 | | | #175.
% 141.21/20.69 | | |
% 141.21/20.69 | | Case 2:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (67) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69 | | |
% 141.21/20.69 | | | REF_CLOSE: (9), (52), (56), (57), (67) are inconsistent by sub-proof #174.
% 141.21/20.69 | | |
% 141.21/20.69 | | End of split
% 141.21/20.69 | |
% 141.21/20.69 | Case 2:
% 141.21/20.69 | |
% 141.21/20.69 | | (68) ~ (all_6_1 = e1) & op(e2, e3) = all_6_1 & $i(all_6_1)
% 141.21/20.69 | |
% 141.21/20.69 | | ALPHA: (68) implies:
% 141.21/20.69 | | (69) ~ (all_6_1 = e1)
% 141.21/20.69 | | (70) op(e2, e3) = all_6_1
% 141.21/20.69 | |
% 141.21/20.69 | | REF_CLOSE: (14), (16), (23), (69), (70) are inconsistent by sub-proof #173.
% 141.21/20.69 | |
% 141.21/20.69 | End of split
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #173 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) op(e2, e3) = all_26_1
% 141.21/20.69 (2) op(e2, e3) = e1
% 141.21/20.69 (3) op(e2, e3) = all_6_1
% 141.21/20.69 (4) ~ (all_6_1 = e1)
% 141.21/20.69 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.69 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.69
% 141.21/20.69 Begin of proof
% 141.21/20.69 |
% 141.21/20.69 | GROUND_INST: instantiating (5) with e1, all_26_1, e3, e2, simplifying with
% 141.21/20.69 | (1), (2) gives:
% 141.21/20.69 | (6) all_26_1 = e1
% 141.21/20.69 |
% 141.21/20.69 | GROUND_INST: instantiating (5) with all_6_1, all_26_1, e3, e2, simplifying
% 141.21/20.69 | with (1), (3) gives:
% 141.21/20.69 | (7) all_26_1 = all_6_1
% 141.21/20.69 |
% 141.21/20.69 | COMBINE_EQS: (6), (7) imply:
% 141.21/20.69 | (8) all_6_1 = e1
% 141.21/20.69 |
% 141.21/20.69 | SIMP: (8) implies:
% 141.21/20.69 | (9) all_6_1 = e1
% 141.21/20.69 |
% 141.21/20.69 | REDUCE: (4), (9) imply:
% 141.21/20.69 | (10) $false
% 141.21/20.69 |
% 141.21/20.69 | CLOSE: (10) is inconsistent.
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #174 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) ~ (all_36_0 = e1)
% 141.21/20.69 (2) ~ (all_36_0 = e2)
% 141.21/20.69 (3) all_54_8 = all_36_0
% 141.21/20.69 (4) ~ (all_36_0 = e0)
% 141.21/20.69 (5) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69
% 141.21/20.69 Begin of proof
% 141.21/20.69 |
% 141.21/20.69 | BETA: splitting (5) gives:
% 141.21/20.69 |
% 141.21/20.69 | Case 1:
% 141.21/20.69 | |
% 141.21/20.69 | | (6) all_54_8 = e2
% 141.21/20.69 | |
% 141.21/20.69 | | COMBINE_EQS: (3), (6) imply:
% 141.21/20.69 | | (7) all_36_0 = e2
% 141.21/20.69 | |
% 141.21/20.69 | | SIMP: (7) implies:
% 141.21/20.69 | | (8) all_36_0 = e2
% 141.21/20.69 | |
% 141.21/20.69 | | REDUCE: (2), (8) imply:
% 141.21/20.69 | | (9) $false
% 141.21/20.69 | |
% 141.21/20.69 | | CLOSE: (9) is inconsistent.
% 141.21/20.69 | |
% 141.21/20.69 | Case 2:
% 141.21/20.69 | |
% 141.21/20.69 | | (10) all_54_8 = e1 | all_54_8 = e0
% 141.21/20.69 | |
% 141.21/20.69 | | BETA: splitting (10) gives:
% 141.21/20.69 | |
% 141.21/20.69 | | Case 1:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (11) all_54_8 = e1
% 141.21/20.69 | | |
% 141.21/20.69 | | | COMBINE_EQS: (3), (11) imply:
% 141.21/20.69 | | | (12) all_36_0 = e1
% 141.21/20.69 | | |
% 141.21/20.69 | | | REDUCE: (1), (12) imply:
% 141.21/20.69 | | | (13) $false
% 141.21/20.69 | | |
% 141.21/20.69 | | | CLOSE: (13) is inconsistent.
% 141.21/20.69 | | |
% 141.21/20.69 | | Case 2:
% 141.21/20.69 | | |
% 141.21/20.69 | | | (14) all_54_8 = e0
% 141.21/20.69 | | |
% 141.21/20.69 | | | COMBINE_EQS: (3), (14) imply:
% 141.21/20.69 | | | (15) all_36_0 = e0
% 141.21/20.69 | | |
% 141.21/20.69 | | | REDUCE: (4), (15) imply:
% 141.21/20.69 | | | (16) $false
% 141.21/20.69 | | |
% 141.21/20.69 | | | CLOSE: (16) is inconsistent.
% 141.21/20.69 | | |
% 141.21/20.69 | | End of split
% 141.21/20.69 | |
% 141.21/20.69 | End of split
% 141.21/20.69 |
% 141.21/20.69 End of proof
% 141.21/20.69
% 141.21/20.69 Sub-proof #175 shows that the following formulas are inconsistent:
% 141.21/20.69 ----------------------------------------------------------------
% 141.21/20.69 (1) ~ (all_52_3 = all_52_7)
% 141.21/20.69 (2) ~ (all_52_7 = e1)
% 141.21/20.69 (3) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.69 (4) all_54_13 = all_52_7
% 141.21/20.69 (5) ~ (all_52_7 = e3)
% 141.21/20.69 (6) ~ (all_6_0 = e3)
% 141.21/20.69 (7) all_54_12 = all_52_3
% 141.21/20.69 (8) ~ (all_6_0 = e0)
% 141.21/20.69 (9) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.69 (10) ~ (all_52_3 = e1)
% 141.21/20.69 (11) ~ (all_52_7 = all_6_0)
% 141.21/20.69 (12) ~ (all_6_0 = e1)
% 141.21/20.69 (13) all_54_9 = all_6_0
% 141.21/20.69 (14) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.69 (15) ~ (all_52_3 = e3)
% 141.21/20.70 (16) ~ (all_52_3 = e2)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (3) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (17) all_54_12 = e3
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (7), (15), (17) are inconsistent by sub-proof #232.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (18) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.21/20.70 | |
% 141.21/20.70 | | BETA: splitting (18) gives:
% 141.21/20.70 | |
% 141.21/20.70 | | Case 1:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (19) all_54_12 = e2
% 141.21/20.70 | | |
% 141.21/20.70 | | | REF_CLOSE: (7), (16), (19) are inconsistent by sub-proof #231.
% 141.21/20.70 | | |
% 141.21/20.70 | | Case 2:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (20) all_54_12 = e1 | all_54_12 = e0
% 141.21/20.70 | | |
% 141.21/20.70 | | | BETA: splitting (20) gives:
% 141.21/20.70 | | |
% 141.21/20.70 | | | Case 1:
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | (21) all_54_12 = e1
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | REF_CLOSE: (7), (10), (21) are inconsistent by sub-proof #662.
% 141.21/20.70 | | | |
% 141.21/20.70 | | | Case 2:
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | (22) all_54_12 = e0
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | COMBINE_EQS: (7), (22) imply:
% 141.21/20.70 | | | | (23) all_52_3 = e0
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | SIMP: (23) implies:
% 141.21/20.70 | | | | (24) all_52_3 = e0
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | REDUCE: (1), (24) imply:
% 141.21/20.70 | | | | (25) ~ (all_52_7 = e0)
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | SIMP: (25) implies:
% 141.21/20.70 | | | | (26) ~ (all_52_7 = e0)
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | BETA: splitting (14) gives:
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | Case 1:
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | (27) all_54_13 = e3
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | REF_CLOSE: (4), (5), (27) are inconsistent by sub-proof #364.
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | Case 2:
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | (28) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | BETA: splitting (28) gives:
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | Case 1:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | (29) all_54_13 = e2
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | COMBINE_EQS: (4), (29) imply:
% 141.21/20.70 | | | | | | (30) all_52_7 = e2
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | SIMP: (30) implies:
% 141.21/20.70 | | | | | | (31) all_52_7 = e2
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | REDUCE: (11), (31) imply:
% 141.21/20.70 | | | | | | (32) ~ (all_6_0 = e2)
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | SIMP: (32) implies:
% 141.21/20.70 | | | | | | (33) ~ (all_6_0 = e2)
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | BETA: splitting (9) gives:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | Case 1:
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | (34) all_54_9 = e3
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | COMBINE_EQS: (13), (34) imply:
% 141.21/20.70 | | | | | | | (35) all_6_0 = e3
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | SIMP: (35) implies:
% 141.21/20.70 | | | | | | | (36) all_6_0 = e3
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | REDUCE: (6), (36) imply:
% 141.21/20.70 | | | | | | | (37) $false
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | CLOSE: (37) is inconsistent.
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | Case 2:
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | (38) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | BETA: splitting (38) gives:
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | Case 1:
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | (39) all_54_9 = e2
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | COMBINE_EQS: (13), (39) imply:
% 141.21/20.70 | | | | | | | | (40) all_6_0 = e2
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | SIMP: (40) implies:
% 141.21/20.70 | | | | | | | | (41) all_6_0 = e2
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | REDUCE: (33), (41) imply:
% 141.21/20.70 | | | | | | | | (42) $false
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | CLOSE: (42) is inconsistent.
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | Case 2:
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | (43) all_54_9 = e1 | all_54_9 = e0
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | BETA: splitting (43) gives:
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | | Case 1:
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | (44) all_54_9 = e1
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | COMBINE_EQS: (13), (44) imply:
% 141.21/20.70 | | | | | | | | | (45) all_6_0 = e1
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | SIMP: (45) implies:
% 141.21/20.70 | | | | | | | | | (46) all_6_0 = e1
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | REDUCE: (12), (46) imply:
% 141.21/20.70 | | | | | | | | | (47) $false
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | CLOSE: (47) is inconsistent.
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | Case 2:
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | (48) all_54_9 = e0
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | COMBINE_EQS: (13), (48) imply:
% 141.21/20.70 | | | | | | | | | (49) all_6_0 = e0
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | SIMP: (49) implies:
% 141.21/20.70 | | | | | | | | | (50) all_6_0 = e0
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | REDUCE: (8), (50) imply:
% 141.21/20.70 | | | | | | | | | (51) $false
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | | CLOSE: (51) is inconsistent.
% 141.21/20.70 | | | | | | | | |
% 141.21/20.70 | | | | | | | | End of split
% 141.21/20.70 | | | | | | | |
% 141.21/20.70 | | | | | | | End of split
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | End of split
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | Case 2:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | (52) all_54_13 = e1 | all_54_13 = e0
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | REF_CLOSE: (2), (4), (26), (52) are inconsistent by sub-proof #362.
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | End of split
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | End of split
% 141.21/20.70 | | | |
% 141.21/20.70 | | | End of split
% 141.21/20.70 | | |
% 141.21/20.70 | | End of split
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #176 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_52_4 = e0)
% 141.21/20.70 (2) op(e2, e1) = e2
% 141.21/20.70 (3) ~ (e1 = e0)
% 141.21/20.70 (4) op(e3, e2) = all_52_4
% 141.21/20.70 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (6) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.21/20.70 all_56_4 & $i(all_56_4))
% 141.21/20.70 (7) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (7) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (8) all_57_1 = e0 & op(e3, e2) = e0
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1102.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (9) all_57_3 = e0 & op(e2, e2) = e0
% 141.21/20.70 | |
% 141.21/20.70 | | ALPHA: (9) implies:
% 141.21/20.70 | | (10) op(e2, e2) = e0
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (2), (3), (5), (6), (10) are inconsistent by sub-proof #950.
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #177 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_52_1 = e2)
% 141.21/20.70 (2) op(e3, e3) = e2
% 141.21/20.70 (3) ~ (all_52_4 = e3)
% 141.21/20.70 (4) op(e2, e3) = all_52_1
% 141.21/20.70 (5) op(e3, e2) = all_52_4
% 141.21/20.70 (6) op(e2, e2) = e3
% 141.21/20.70 (7) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.21/20.70 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.21/20.70 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.21/20.70 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.70 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.21/20.70 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.21/20.70 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.21/20.70 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.21/20.70 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.21/20.70 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.21/20.70 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.21/20.70 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.21/20.70 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.21/20.70 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.21/20.70 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.21/20.70 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.21/20.70 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.21/20.70 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.21/20.70 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.21/20.70 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12))))
% 141.21/20.70 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (7) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (9) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.21/20.70 | | e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.21/20.70 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.21/20.70 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.70 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.21/20.70 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.21/20.70 | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.21/20.70 | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.21/20.70 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.21/20.70 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.21/20.70 | | e3) = all_56_10 & $i(all_56_10)))
% 141.21/20.70 | |
% 141.21/20.70 | | ALPHA: (9) implies:
% 141.21/20.70 | | (10) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2,
% 141.21/20.70 | | e2) = all_56_11 & $i(all_56_11))
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (1), (4), (6), (8), (10) are inconsistent by sub-proof #178.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (11) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 141.21/20.70 | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.21/20.70 | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 141.21/20.70 | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.21/20.70 | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.21/20.70 | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.21/20.70 | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.21/20.70 | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.21/20.70 | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.21/20.70 | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 141.21/20.70 | | e2) = all_56_12 & $i(all_56_12)))
% 141.21/20.70 | |
% 141.21/20.70 | | ALPHA: (11) implies:
% 141.21/20.70 | | (12) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3)
% 141.21/20.70 | | = all_56_9 & $i(all_56_9))
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (2), (3), (5), (8), (12) are inconsistent by sub-proof #390.
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #178 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_52_1 = e2)
% 141.21/20.70 (2) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 141.21/20.70 all_56_11 & $i(all_56_11))
% 141.21/20.70 (3) op(e2, e3) = all_52_1
% 141.21/20.70 (4) op(e2, e2) = e3
% 141.21/20.70 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (2) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (6) all_56_3 = e2 & op(e2, e3) = e2
% 141.21/20.70 | |
% 141.21/20.70 | | ALPHA: (6) implies:
% 141.21/20.70 | | (7) op(e2, e3) = e2
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #882.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (8) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (4), (5), (8) are inconsistent by sub-proof #179.
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #179 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.21/20.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (3) op(e2, e2) = e3
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | ALPHA: (1) implies:
% 141.21/20.70 | (4) ~ (all_56_11 = e3)
% 141.21/20.70 | (5) op(e2, e2) = all_56_11
% 141.21/20.70 |
% 141.21/20.70 | GROUND_INST: instantiating (2) with e3, all_56_11, e2, e2, simplifying with
% 141.21/20.70 | (3), (5) gives:
% 141.21/20.70 | (6) all_56_11 = e3
% 141.21/20.70 |
% 141.21/20.70 | REDUCE: (4), (6) imply:
% 141.21/20.70 | (7) $false
% 141.21/20.70 |
% 141.21/20.70 | CLOSE: (7) is inconsistent.
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #180 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) op(e3, e3) = e2
% 141.21/20.70 (2) ~ (all_52_4 = e3)
% 141.21/20.70 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 141.21/20.70 (4) op(e3, e2) = all_52_4
% 141.21/20.70 (5) ~ (e3 = e2)
% 141.21/20.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (3) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 141.21/20.70 | |
% 141.21/20.70 | | ALPHA: (7) implies:
% 141.21/20.70 | | (8) op(e3, e3) = e3
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (1), (5), (6), (8) are inconsistent by sub-proof #450.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (9) all_57_1 = e3 & op(e3, e2) = e3
% 141.21/20.70 | |
% 141.21/20.70 | | ALPHA: (9) implies:
% 141.21/20.70 | | (10) op(e3, e2) = e3
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #1107.
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #181 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_10_2 = e2)
% 141.21/20.70 (2) ~ (all_10_2 = e1)
% 141.21/20.70 (3) op(e1, e1) = all_4_2
% 141.21/20.70 (4) op(e0, e0) = all_10_2
% 141.21/20.70 (5) ~ (all_4_2 = e2)
% 141.21/20.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (7) op(e3, e3) = all_14_2
% 141.21/20.70 (8) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.21/20.70 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.21/20.70 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.21/20.70 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.21/20.70 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.21/20.70 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.21/20.70 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.21/20.70 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.21/20.70 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.21/20.70 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.70 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.21/20.70 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.70 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.21/20.70 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.21/20.70 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.21/20.70 $i(all_56_14))))
% 141.21/20.70 (9) ~ (all_14_2 = e0)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (8) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.21/20.70 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.21/20.70 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.21/20.70 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (3), (5), (6), (7), (9), (10) are inconsistent by sub-proof
% 141.21/20.70 | | #1123.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (11) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.21/20.70 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.21/20.70 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.21/20.70 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.21/20.70 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.21/20.70 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.21/20.70 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.21/20.70 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.21/20.70 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.70 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.21/20.70 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.21/20.70 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.21/20.70 | | all_56_14 & $i(all_56_14))))
% 141.21/20.70 | |
% 141.21/20.70 | | BETA: splitting (11) gives:
% 141.21/20.70 | |
% 141.21/20.70 | | Case 1:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (12) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 141.21/20.70 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.21/20.70 | | |
% 141.21/20.70 | | | ALPHA: (12) implies:
% 141.21/20.70 | | | (13) op(e1, e1) = e2
% 141.21/20.70 | | |
% 141.21/20.70 | | | REF_CLOSE: (3), (5), (6), (13) are inconsistent by sub-proof #1124.
% 141.21/20.70 | | |
% 141.21/20.70 | | Case 2:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (14) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 141.21/20.70 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.21/20.70 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.21/20.70 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.21/20.70 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.21/20.70 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.21/20.70 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.70 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.21/20.70 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.21/20.70 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.21/20.70 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.21/20.70 | | |
% 141.21/20.70 | | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (14) are inconsistent by
% 141.21/20.70 | | | sub-proof #272.
% 141.21/20.70 | | |
% 141.21/20.70 | | End of split
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #182 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_14_2 = e2)
% 141.21/20.70 (2) all_54_0 = all_14_2
% 141.21/20.70 (3) all_54_0 = e3 | all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 141.21/20.70 (4) ~ (all_14_2 = e1)
% 141.21/20.70 (5) op(e3, e3) = e2
% 141.21/20.70 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (7) op(e3, e3) = all_14_2
% 141.21/20.70 (8) ~ (all_14_2 = e0)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (3) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (9) all_54_0 = e3
% 141.21/20.70 | |
% 141.21/20.70 | | COMBINE_EQS: (2), (9) imply:
% 141.21/20.70 | | (10) all_14_2 = e3
% 141.21/20.70 | |
% 141.21/20.70 | | REDUCE: (1), (10) imply:
% 141.21/20.70 | | (11) ~ (e3 = e2)
% 141.21/20.70 | |
% 141.21/20.70 | | REDUCE: (7), (10) imply:
% 141.21/20.70 | | (12) op(e3, e3) = e3
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (5), (6), (11), (12) are inconsistent by sub-proof #450.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (13) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (1), (2), (4), (8), (13) are inconsistent by sub-proof #883.
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #183 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) all_57_2 = e3 & op(e2, e3) = e3
% 141.21/20.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (3) op(e2, e3) = all_52_1
% 141.21/20.70 (4) ~ (all_52_1 = e3)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | ALPHA: (1) implies:
% 141.21/20.70 | (5) op(e2, e3) = e3
% 141.21/20.70 |
% 141.21/20.70 | GROUND_INST: instantiating (2) with all_52_1, e3, e3, e2, simplifying with
% 141.21/20.70 | (3), (5) gives:
% 141.21/20.70 | (6) all_52_1 = e3
% 141.21/20.70 |
% 141.21/20.70 | REDUCE: (4), (6) imply:
% 141.21/20.70 | (7) $false
% 141.21/20.70 |
% 141.21/20.70 | CLOSE: (7) is inconsistent.
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #184 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) all_57_14 = e3 & op(e0, e1) = e3
% 141.21/20.70 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (3) op(e0, e1) = all_52_11
% 141.21/20.70 (4) ~ (all_52_11 = e3)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | ALPHA: (1) implies:
% 141.21/20.70 | (5) op(e0, e1) = e3
% 141.21/20.70 |
% 141.21/20.70 | GROUND_INST: instantiating (2) with all_52_11, e3, e1, e0, simplifying with
% 141.21/20.70 | (3), (5) gives:
% 141.21/20.70 | (6) all_52_11 = e3
% 141.21/20.70 |
% 141.21/20.70 | REDUCE: (4), (6) imply:
% 141.21/20.70 | (7) $false
% 141.21/20.70 |
% 141.21/20.70 | CLOSE: (7) is inconsistent.
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #185 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) ~ (all_52_1 = e2)
% 141.21/20.70 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.21/20.70 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.21/20.70 (3) ~ (all_52_12 = e3)
% 141.21/20.70 (4) ~ (e2 = e1)
% 141.21/20.70 (5) all_57_5 = e1
% 141.21/20.70 (6) op(e0, e0) = e1
% 141.21/20.70 (7) op(e2, e3) = all_52_1
% 141.21/20.70 (8) all_57_11 = e2
% 141.21/20.70 (9) ~ (e2 = e0)
% 141.21/20.70 (10) ~ (e3 = e2)
% 141.21/20.70 (11) op(e3, e0) = all_52_12
% 141.21/20.70 (12) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.21/20.70 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.70 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (14) ~ (e3 = e1)
% 141.21/20.70 (15) op(e2, e2) = e0
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (2) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (16) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 141.21/20.70 | | e2)
% 141.21/20.70 | |
% 141.21/20.70 | | REF_CLOSE: (1), (7), (9), (13), (15), (16) are inconsistent by sub-proof
% 141.21/20.70 | | #881.
% 141.21/20.70 | |
% 141.21/20.70 | Case 2:
% 141.21/20.70 | |
% 141.21/20.70 | | (17) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 141.21/20.70 | | e2)
% 141.21/20.70 | |
% 141.21/20.70 | | BETA: splitting (17) gives:
% 141.21/20.70 | |
% 141.21/20.70 | | Case 1:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (18) all_57_5 = e2 & op(e2, e1) = e2
% 141.21/20.70 | | |
% 141.21/20.70 | | | ALPHA: (18) implies:
% 141.21/20.70 | | | (19) all_57_5 = e2
% 141.21/20.70 | | |
% 141.21/20.70 | | | REF_CLOSE: (4), (5), (19) are inconsistent by sub-proof #1031.
% 141.21/20.70 | | |
% 141.21/20.70 | | Case 2:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (20) all_57_10 = e2 & op(e2, e0) = e2
% 141.21/20.70 | | |
% 141.21/20.70 | | | ALPHA: (20) implies:
% 141.21/20.70 | | | (21) all_57_10 = e2
% 141.21/20.70 | | |
% 141.21/20.70 | | | REF_CLOSE: (3), (6), (8), (10), (11), (12), (13), (14), (21) are
% 141.21/20.70 | | | inconsistent by sub-proof #188.
% 141.21/20.70 | | |
% 141.21/20.70 | | End of split
% 141.21/20.70 | |
% 141.21/20.70 | End of split
% 141.21/20.70 |
% 141.21/20.70 End of proof
% 141.21/20.70
% 141.21/20.70 Sub-proof #186 shows that the following formulas are inconsistent:
% 141.21/20.70 ----------------------------------------------------------------
% 141.21/20.70 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.21/20.70 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.70 (2) all_57_10 = e2 & op(e2, e0) = e2
% 141.21/20.70 (3) op(e1, e1) = e3
% 141.21/20.70 (4) ~ (all_52_12 = e3)
% 141.21/20.70 (5) op(e1, e2) = all_52_6
% 141.21/20.70 (6) ~ (all_52_8 = e3)
% 141.21/20.70 (7) ~ (e2 = e1)
% 141.21/20.70 (8) all_57_5 = e1
% 141.21/20.70 (9) ~ (all_52_7 = e0)
% 141.21/20.70 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.21/20.70 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.21/20.70 (11) all_57_15 = e1
% 141.21/20.70 (12) all_57_7 = e1
% 141.21/20.70 (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.70 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.21/20.70 e1)
% 141.21/20.70 (14) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.21/20.70 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.21/20.70 (15) ~ (e3 = e0)
% 141.21/20.70 (16) op(e1, e1) = all_4_2
% 141.21/20.70 (17) op(e3, e1) = all_52_8
% 141.21/20.70 (18) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.21/20.70 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.21/20.70 (19) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.21/20.70 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.21/20.70 e2)
% 141.21/20.70 (20) op(e0, e0) = e1
% 141.21/20.70 (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.21/20.70 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.21/20.70 (22) ~ (e1 = e0)
% 141.21/20.70 (23) ~ (e2 = e0)
% 141.21/20.70 (24) ~ (e3 = e2)
% 141.21/20.70 (25) op(e3, e0) = all_52_12
% 141.21/20.70 (26) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.21/20.70 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.70 (27) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.21/20.70 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.21/20.70 (28) op(e3, e3) = e1
% 141.21/20.70 (29) ~ (all_4_2 = e2)
% 141.21/20.70 (30) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.21/20.70 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.21/20.70 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.70 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.70 (32) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.21/20.70 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.21/20.70 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.70 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.21/20.70 (33) ~ (e3 = e1)
% 141.21/20.70 (34) op(e0, e2) = all_52_7
% 141.21/20.70 (35) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.21/20.70 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.21/20.70 (36) op(e2, e2) = e0
% 141.21/20.70 (37) ~ (all_52_6 = e0)
% 141.21/20.70 (38) op(e2, e1) = all_52_9
% 141.21/20.70 (39) all_57_2 = e3
% 141.21/20.70 (40) ~ (all_52_9 = e0)
% 141.21/20.70
% 141.21/20.70 Begin of proof
% 141.21/20.70 |
% 141.21/20.70 | ALPHA: (2) implies:
% 141.21/20.70 | (41) all_57_10 = e2
% 141.21/20.70 |
% 141.21/20.70 | BETA: splitting (1) gives:
% 141.21/20.70 |
% 141.21/20.70 | Case 1:
% 141.21/20.70 | |
% 141.21/20.70 | | (42) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.21/20.70 | | e3)
% 141.21/20.70 | |
% 141.21/20.70 | | BETA: splitting (42) gives:
% 141.21/20.70 | |
% 141.21/20.70 | | Case 1:
% 141.21/20.70 | | |
% 141.21/20.70 | | | (43) all_57_12 = e3 & op(e0, e3) = e3
% 141.21/20.70 | | |
% 141.21/20.70 | | | ALPHA: (43) implies:
% 141.21/20.70 | | | (44) all_57_12 = e3
% 141.21/20.70 | | |
% 141.21/20.70 | | | BETA: splitting (18) gives:
% 141.21/20.70 | | |
% 141.21/20.70 | | | Case 1:
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | (45) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 141.21/20.70 | | | | = e0)
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | BETA: splitting (45) gives:
% 141.21/20.70 | | | |
% 141.21/20.70 | | | | Case 1:
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | (46) all_57_6 = e0 & op(e1, e3) = e0
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | ALPHA: (46) implies:
% 141.21/20.70 | | | | | (47) all_57_6 = e0
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | BETA: splitting (27) gives:
% 141.21/20.70 | | | | |
% 141.21/20.70 | | | | | Case 1:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | (48) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 141.21/20.70 | | | | | | e2) = e2)
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | BETA: splitting (48) gives:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | Case 1:
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | (49) all_57_6 = e2 & op(e1, e3) = e2
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | ALPHA: (49) implies:
% 141.21/20.70 | | | | | | | (50) all_57_6 = e2
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | REF_CLOSE: (23), (47), (50) are inconsistent by sub-proof #811.
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | Case 2:
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | (51) all_57_7 = e2 & op(e1, e2) = e2
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | REF_CLOSE: (7), (12), (51) are inconsistent by sub-proof #997.
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | End of split
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | Case 2:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | (52) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 141.21/20.70 | | | | | | e0) = e2)
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | BETA: splitting (52) gives:
% 141.21/20.70 | | | | | |
% 141.21/20.70 | | | | | | Case 1:
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | (53) all_57_8 = e2 & op(e1, e1) = e2
% 141.21/20.70 | | | | | | |
% 141.21/20.70 | | | | | | | ALPHA: (53) implies:
% 141.21/20.71 | | | | | | | (54) op(e1, e1) = e2
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | REF_CLOSE: (16), (29), (31), (54) are inconsistent by sub-proof
% 141.21/20.71 | | | | | | | #1124.
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | Case 2:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (55) all_57_11 = e2 & op(e1, e0) = e2
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | ALPHA: (55) implies:
% 141.21/20.71 | | | | | | | (56) all_57_11 = e2
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | BETA: splitting (26) gives:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (57) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 141.21/20.71 | | | | | | | | op(e2, e0) = e3)
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | BETA: splitting (57) gives:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (58) all_57_9 = e3 & op(e3, e0) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (58) implies:
% 141.21/20.71 | | | | | | | | | (59) op(e3, e0) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (4), (25), (31), (59) are inconsistent by sub-proof
% 141.21/20.71 | | | | | | | | | #1105.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (60) all_57_10 = e3 & op(e2, e0) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (60) implies:
% 141.21/20.71 | | | | | | | | | (61) all_57_10 = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | COMBINE_EQS: (41), (61) imply:
% 141.21/20.71 | | | | | | | | | (62) e3 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (15), (21), (24), (28), (31), (33), (39), (44),
% 141.21/20.71 | | | | | | | | | (47), (62) are inconsistent by sub-proof #190.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | End of split
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (63) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 141.21/20.71 | | | | | | | | op(e0, e0) = e3)
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | BETA: splitting (63) gives:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (64) all_57_11 = e3 & op(e1, e0) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (64) implies:
% 141.21/20.71 | | | | | | | | | (65) all_57_11 = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | COMBINE_EQS: (56), (65) imply:
% 141.21/20.71 | | | | | | | | | (66) e3 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (15), (21), (24), (28), (31), (33), (39), (44),
% 141.21/20.71 | | | | | | | | | (47), (66) are inconsistent by sub-proof #190.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (67) all_57_15 = e3 & op(e0, e0) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (7), (9), (13), (15), (19), (22), (23), (24), (31),
% 141.21/20.71 | | | | | | | | | (32), (33), (34), (44), (67) are inconsistent by
% 141.21/20.71 | | | | | | | | | sub-proof #467.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | End of split
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | End of split
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | End of split
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | End of split
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | Case 2:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (68) all_57_7 = e0 & op(e1, e2) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (68) implies:
% 141.21/20.71 | | | | | (69) op(e1, e2) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (5), (31), (37), (69) are inconsistent by sub-proof #999.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | End of split
% 141.21/20.71 | | | |
% 141.21/20.71 | | | Case 2:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | (70) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.21/20.71 | | | | = e0)
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | BETA: splitting (70) gives:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | Case 1:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (71) all_57_8 = e0 & op(e1, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (71) implies:
% 141.21/20.71 | | | | | (72) op(e1, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (3), (15), (31), (72) are inconsistent by sub-proof #308.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | Case 2:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (73) all_57_11 = e0 & op(e1, e0) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (73) implies:
% 141.21/20.71 | | | | | (74) all_57_11 = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | BETA: splitting (32) gives:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | Case 1:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | (75) all_57_15 = e0 & op(e0, e0) = e0
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | ALPHA: (75) implies:
% 141.21/20.71 | | | | | | (76) all_57_15 = e0
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | REF_CLOSE: (11), (22), (76) are inconsistent by sub-proof #291.
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | Case 2:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | (77) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 141.21/20.71 | | | | | | op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 141.21/20.71 | | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.71 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | ALPHA: (77) implies:
% 141.21/20.71 | | | | | | (78) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.71 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | BETA: splitting (26) gives:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | Case 1:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (79) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 141.21/20.71 | | | | | | | op(e2, e0) = e3)
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | REF_CLOSE: (4), (24), (25), (31), (41), (79) are inconsistent by
% 141.21/20.71 | | | | | | | sub-proof #189.
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | Case 2:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (80) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 141.21/20.71 | | | | | | | op(e0, e0) = e3)
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | BETA: splitting (80) gives:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (81) all_57_11 = e3 & op(e1, e0) = e3
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | ALPHA: (81) implies:
% 141.21/20.71 | | | | | | | | (82) all_57_11 = e3
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | REF_CLOSE: (15), (74), (82) are inconsistent by sub-proof #858.
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (83) all_57_15 = e3 & op(e0, e0) = e3
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | ALPHA: (83) implies:
% 141.21/20.71 | | | | | | | | (84) op(e0, e0) = e3
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | REF_CLOSE: (7), (9), (13), (15), (19), (22), (23), (24), (31),
% 141.21/20.71 | | | | | | | | (33), (34), (44), (78), (84) are inconsistent by
% 141.21/20.71 | | | | | | | | sub-proof #656.
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | End of split
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | End of split
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | End of split
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | End of split
% 141.21/20.71 | | | |
% 141.21/20.71 | | | End of split
% 141.21/20.71 | | |
% 141.21/20.71 | | Case 2:
% 141.21/20.71 | | |
% 141.21/20.71 | | | (85) all_57_13 = e3 & op(e0, e2) = e3
% 141.21/20.71 | | |
% 141.21/20.71 | | | ALPHA: (85) implies:
% 141.21/20.71 | | | (86) all_57_13 = e3
% 141.21/20.71 | | |
% 141.21/20.71 | | | BETA: splitting (14) gives:
% 141.21/20.71 | | |
% 141.21/20.71 | | | Case 1:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | (87) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2)
% 141.21/20.71 | | | | = e2)
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | BETA: splitting (87) gives:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | Case 1:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (88) all_57_1 = e2 & op(e3, e2) = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (88) implies:
% 141.21/20.71 | | | | | (89) all_57_1 = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | BETA: splitting (26) gives:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | Case 1:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | (90) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 141.21/20.71 | | | | | | e0) = e3)
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | REF_CLOSE: (4), (24), (25), (31), (41), (90) are inconsistent by
% 141.21/20.71 | | | | | | sub-proof #189.
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | Case 2:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | (91) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 141.21/20.71 | | | | | | op(e0, e0) = e3)
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | BETA: splitting (91) gives:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | Case 1:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (92) all_57_11 = e3 & op(e1, e0) = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | ALPHA: (92) implies:
% 141.21/20.71 | | | | | | | (93) all_57_11 = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | BETA: splitting (35) gives:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (94) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 141.21/20.71 | | | | | | | | op(e3, e2) = e3)
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | BETA: splitting (94) gives:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (95) all_57_0 = e3 & op(e3, e3) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (95) implies:
% 141.21/20.71 | | | | | | | | | (96) op(e3, e3) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (28), (31), (33), (96) are inconsistent by
% 141.21/20.71 | | | | | | | | | sub-proof #838.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (97) all_57_1 = e3 & op(e3, e2) = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (97) implies:
% 141.21/20.71 | | | | | | | | | (98) all_57_1 = e3
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | COMBINE_EQS: (89), (98) imply:
% 141.21/20.71 | | | | | | | | | (99) e3 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | SIMP: (99) implies:
% 141.21/20.71 | | | | | | | | | (100) e3 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | COMBINE_EQS: (93), (100) imply:
% 141.21/20.71 | | | | | | | | | (101) all_57_11 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (4), (20), (24), (25), (26), (31), (33), (41),
% 141.21/20.71 | | | | | | | | | (101) are inconsistent by sub-proof #188.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | End of split
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (102) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 141.21/20.71 | | | | | | | | op(e3, e0) = e3)
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | REF_CLOSE: (4), (6), (17), (25), (31), (102) are inconsistent by
% 141.21/20.71 | | | | | | | | sub-proof #1104.
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | End of split
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | Case 2:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (103) all_57_15 = e3 & op(e0, e0) = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | ALPHA: (103) implies:
% 141.21/20.71 | | | | | | | (104) op(e0, e0) = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | REF_CLOSE: (20), (31), (33), (104) are inconsistent by sub-proof
% 141.21/20.71 | | | | | | | #732.
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | End of split
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | End of split
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | Case 2:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (105) all_57_3 = e2 & op(e2, e2) = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (105) implies:
% 141.21/20.71 | | | | | (106) op(e2, e2) = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (23), (31), (36), (106) are inconsistent by sub-proof
% 141.21/20.71 | | | | | #1076.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | End of split
% 141.21/20.71 | | | |
% 141.21/20.71 | | | Case 2:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | (107) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 141.21/20.71 | | | | e2) = e2)
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | BETA: splitting (107) gives:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | Case 1:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (108) all_57_7 = e2 & op(e1, e2) = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (108) implies:
% 141.21/20.71 | | | | | (109) all_57_7 = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (7), (12), (109) are inconsistent by sub-proof #872.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | Case 2:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (110) all_57_13 = e2 & op(e0, e2) = e2
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (24), (86), (110) are inconsistent by sub-proof #969.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | End of split
% 141.21/20.71 | | | |
% 141.21/20.71 | | | End of split
% 141.21/20.71 | | |
% 141.21/20.71 | | End of split
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (111) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.21/20.71 | | e3)
% 141.21/20.71 | |
% 141.21/20.71 | | BETA: splitting (111) gives:
% 141.21/20.71 | |
% 141.21/20.71 | | Case 1:
% 141.21/20.71 | | |
% 141.21/20.71 | | | (112) all_57_14 = e3 & op(e0, e1) = e3
% 141.21/20.71 | | |
% 141.21/20.71 | | | ALPHA: (112) implies:
% 141.21/20.71 | | | (113) all_57_14 = e3
% 141.21/20.71 | | |
% 141.21/20.71 | | | BETA: splitting (10) gives:
% 141.21/20.71 | | |
% 141.21/20.71 | | | Case 1:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | (114) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 141.21/20.71 | | | | = e0)
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | BETA: splitting (114) gives:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | Case 1:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (115) all_57_4 = e0 & op(e3, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (115) implies:
% 141.21/20.71 | | | | | (116) all_57_4 = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | BETA: splitting (26) gives:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | Case 1:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | (117) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 141.21/20.71 | | | | | | op(e2, e0) = e3)
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | REF_CLOSE: (4), (24), (25), (31), (41), (117) are inconsistent by
% 141.21/20.71 | | | | | | sub-proof #189.
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | Case 2:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | (118) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 141.21/20.71 | | | | | | op(e0, e0) = e3)
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | BETA: splitting (118) gives:
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | | Case 1:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (119) all_57_11 = e3 & op(e1, e0) = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | ALPHA: (119) implies:
% 141.21/20.71 | | | | | | | (120) all_57_11 = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | BETA: splitting (30) gives:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (121) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 141.21/20.71 | | | | | | | | op(e2, e1) = e2)
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | BETA: splitting (121) gives:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (122) all_57_4 = e2 & op(e3, e1) = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (122) implies:
% 141.21/20.71 | | | | | | | | | (123) all_57_4 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (23), (116), (123) are inconsistent by sub-proof
% 141.21/20.71 | | | | | | | | | #1050.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (124) all_57_5 = e2 & op(e2, e1) = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (124) implies:
% 141.21/20.71 | | | | | | | | | (125) all_57_5 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (7), (8), (125) are inconsistent by sub-proof
% 141.21/20.71 | | | | | | | | | #1031.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | End of split
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | (126) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 141.21/20.71 | | | | | | | | op(e0, e1) = e2)
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | BETA: splitting (126) gives:
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 1:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (127) all_57_8 = e2 & op(e1, e1) = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (127) implies:
% 141.21/20.71 | | | | | | | | | (128) op(e1, e1) = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (16), (29), (31), (128) are inconsistent by
% 141.21/20.71 | | | | | | | | | sub-proof #1124.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | Case 2:
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | (129) all_57_14 = e2 & op(e0, e1) = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | ALPHA: (129) implies:
% 141.21/20.71 | | | | | | | | | (130) all_57_14 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | COMBINE_EQS: (113), (130) imply:
% 141.21/20.71 | | | | | | | | | (131) e3 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | COMBINE_EQS: (120), (131) imply:
% 141.21/20.71 | | | | | | | | | (132) all_57_11 = e2
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | | REF_CLOSE: (4), (20), (24), (25), (26), (31), (33), (41),
% 141.21/20.71 | | | | | | | | | (132) are inconsistent by sub-proof #188.
% 141.21/20.71 | | | | | | | | |
% 141.21/20.71 | | | | | | | | End of split
% 141.21/20.71 | | | | | | | |
% 141.21/20.71 | | | | | | | End of split
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | Case 2:
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | (133) all_57_15 = e3 & op(e0, e0) = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | ALPHA: (133) implies:
% 141.21/20.71 | | | | | | | (134) op(e0, e0) = e3
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | | REF_CLOSE: (7), (9), (13), (15), (19), (22), (23), (24), (31),
% 141.21/20.71 | | | | | | | (32), (33), (34), (113), (134) are inconsistent by
% 141.21/20.71 | | | | | | | sub-proof #187.
% 141.21/20.71 | | | | | | |
% 141.21/20.71 | | | | | | End of split
% 141.21/20.71 | | | | | |
% 141.21/20.71 | | | | | End of split
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | Case 2:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (135) all_57_5 = e0 & op(e2, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (135) implies:
% 141.21/20.71 | | | | | (136) op(e2, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (31), (38), (40), (136) are inconsistent by sub-proof
% 141.21/20.71 | | | | | #1091.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | End of split
% 141.21/20.71 | | | |
% 141.21/20.71 | | | Case 2:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | (137) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 141.21/20.71 | | | | e1) = e0)
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | BETA: splitting (137) gives:
% 141.21/20.71 | | | |
% 141.21/20.71 | | | | Case 1:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (138) all_57_8 = e0 & op(e1, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | ALPHA: (138) implies:
% 141.21/20.71 | | | | | (139) op(e1, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (3), (15), (31), (139) are inconsistent by sub-proof #308.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | Case 2:
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | (140) all_57_14 = e0 & op(e0, e1) = e0
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | | REF_CLOSE: (15), (113), (140) are inconsistent by sub-proof #626.
% 141.21/20.71 | | | | |
% 141.21/20.71 | | | | End of split
% 141.21/20.71 | | | |
% 141.21/20.71 | | | End of split
% 141.21/20.71 | | |
% 141.21/20.71 | | Case 2:
% 141.21/20.71 | | |
% 141.21/20.71 | | | (141) all_57_15 = e3 & op(e0, e0) = e3
% 141.21/20.71 | | |
% 141.21/20.71 | | | ALPHA: (141) implies:
% 141.21/20.71 | | | (142) op(e0, e0) = e3
% 141.21/20.71 | | |
% 141.21/20.71 | | | REF_CLOSE: (20), (31), (33), (142) are inconsistent by sub-proof #732.
% 141.21/20.71 | | |
% 141.21/20.71 | | End of split
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #187 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) ~ (e2 = e1)
% 141.21/20.71 (2) op(e0, e0) = e3
% 141.21/20.71 (3) ~ (all_52_7 = e0)
% 141.21/20.71 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.21/20.71 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.21/20.71 (5) ~ (e3 = e0)
% 141.21/20.71 (6) all_57_14 = e3
% 141.21/20.71 (7) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.21/20.71 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.21/20.71 (8) ~ (e1 = e0)
% 141.21/20.71 (9) ~ (e2 = e0)
% 141.21/20.71 (10) ~ (e3 = e2)
% 141.21/20.71 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.21/20.71 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.21/20.71 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.21/20.71 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.21/20.71 (13) ~ (e3 = e1)
% 141.21/20.71 (14) op(e0, e2) = all_52_7
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (12) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (15) all_57_15 = e0 & op(e0, e0) = e0
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (15) implies:
% 141.21/20.71 | | (16) op(e0, e0) = e0
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (2), (5), (11), (16) are inconsistent by sub-proof #751.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (17) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.21/20.71 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 141.21/20.71 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.21/20.71 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (17) implies:
% 141.21/20.71 | | (18) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.21/20.71 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 141.21/20.71 | | (14), (18) are inconsistent by sub-proof #509.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #188 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) all_57_10 = e2
% 141.21/20.71 (2) ~ (all_52_12 = e3)
% 141.21/20.71 (3) op(e0, e0) = e1
% 141.21/20.71 (4) all_57_11 = e2
% 141.21/20.71 (5) ~ (e3 = e2)
% 141.21/20.71 (6) op(e3, e0) = all_52_12
% 141.21/20.71 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.21/20.71 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.21/20.71 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71 (9) ~ (e3 = e1)
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (7) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 141.21/20.71 | | e3)
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (1), (2), (5), (6), (8), (10) are inconsistent by sub-proof #189.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (11) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.21/20.71 | | e3)
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (3), (4), (5), (8), (9), (11) are inconsistent by sub-proof #393.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #189 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) all_57_10 = e2
% 141.21/20.71 (2) ~ (all_52_12 = e3)
% 141.21/20.71 (3) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.21/20.71 (4) ~ (e3 = e2)
% 141.21/20.71 (5) op(e3, e0) = all_52_12
% 141.21/20.71 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (3) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (7) all_57_9 = e3 & op(e3, e0) = e3
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (7) implies:
% 141.21/20.71 | | (8) op(e3, e0) = e3
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #1105.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (9) all_57_10 = e3 & op(e2, e0) = e3
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (9) implies:
% 141.21/20.71 | | (10) all_57_10 = e3
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (1), (4), (10) are inconsistent by sub-proof #492.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #190 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) all_57_12 = e3
% 141.21/20.71 (2) ~ (e3 = e0)
% 141.21/20.71 (3) e3 = e2
% 141.21/20.71 (4) all_57_6 = e0
% 141.21/20.71 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.21/20.71 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.21/20.71 (6) ~ (e3 = e2)
% 141.21/20.71 (7) op(e3, e3) = e1
% 141.21/20.71 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71 (9) ~ (e3 = e1)
% 141.21/20.71 (10) all_57_2 = e3
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | SIMP: (3) implies:
% 141.21/20.71 | (11) e3 = e2
% 141.21/20.71 |
% 141.21/20.71 | COMBINE_EQS: (1), (11) imply:
% 141.21/20.71 | (12) all_57_12 = e2
% 141.21/20.71 |
% 141.21/20.71 | COMBINE_EQS: (10), (11) imply:
% 141.21/20.71 | (13) all_57_2 = e2
% 141.21/20.71 |
% 141.21/20.71 | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (12), (13) are inconsistent by
% 141.21/20.71 | sub-proof #779.
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #191 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) op(e1, e1) = e3
% 141.21/20.71 (2) ~ (e2 = e1)
% 141.21/20.71 (3) ~ (e3 = e0)
% 141.21/20.71 (4) op(e0, e0) = e1
% 141.21/20.71 (5) ~ (e1 = e0)
% 141.21/20.71 (6) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 141.21/20.71 op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 141.21/20.71 e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 141.21/20.71 = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 141.21/20.71 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.21/20.71 e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.21/20.71 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.21/20.71 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.71 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.21/20.71 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.21/20.71 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.21/20.71 $i(all_56_14))))
% 141.21/20.71 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71 (8) ~ (e3 = e1)
% 141.21/20.71 (9) op(e2, e2) = e0
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (6) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (10) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.21/20.71 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (10) implies:
% 141.21/20.71 | | (11) op(e2, e2) = e1
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (5), (7), (9), (11) are inconsistent by sub-proof #1117.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (12) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.21/20.71 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.21/20.71 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.21/20.71 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.21/20.71 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.21/20.71 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.21/20.71 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.21/20.71 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.21/20.71 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.21/20.71 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.21/20.71 | | all_56_14 & $i(all_56_14))))
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (12) are inconsistent by sub-proof
% 141.21/20.71 | | #277.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #192 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) op(e0, e0) = e1
% 141.21/20.71 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.21/20.71 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.21/20.71 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.21/20.71 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.21/20.71 (3) ~ (e1 = e0)
% 141.21/20.71 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71 (5) ~ (e3 = e1)
% 141.21/20.71 (6) op(e2, e2) = e0
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (2) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (7) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 141.21/20.71 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (7) implies:
% 141.21/20.71 | | (8) op(e0, e0) = e3
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #732.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (9) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.21/20.71 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (9) implies:
% 141.21/20.71 | | (10) op(e2, e2) = e1
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1117.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #193 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) op(e1, e1) = e3
% 141.21/20.71 (2) ~ (all_52_11 = e1)
% 141.21/20.71 (3) op(e0, e1) = all_52_11
% 141.21/20.71 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71 (5) ~ (e3 = e1)
% 141.21/20.71 (6) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (6) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (7) implies:
% 141.21/20.71 | | (8) op(e1, e1) = e1
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1096.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (9) all_57_14 = e1 & op(e0, e1) = e1
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #347.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #194 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 & op(e0, e1) = all_30_1
% 141.21/20.71 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1) =
% 141.21/20.71 all_30_1 & $i(all_30_1))
% 141.21/20.71 (2) op(e2, e0) = e3
% 141.21/20.71 (3) op(e0, e1) = all_10_1
% 141.21/20.71 (4) op(e0, e1) = e2
% 141.21/20.71 (5) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0, e1) = all_10_1
% 141.21/20.71 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e3) & op(e0, e1) =
% 141.21/20.71 all_10_1 & $i(all_10_1))
% 141.21/20.71 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.71 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.71
% 141.21/20.71 Begin of proof
% 141.21/20.71 |
% 141.21/20.71 | GROUND_INST: instantiating (6) with e2, all_10_1, e1, e0, simplifying with
% 141.21/20.71 | (3), (4) gives:
% 141.21/20.71 | (7) all_10_1 = e2
% 141.21/20.71 |
% 141.21/20.71 | BETA: splitting (1) gives:
% 141.21/20.71 |
% 141.21/20.71 | Case 1:
% 141.21/20.71 | |
% 141.21/20.71 | | (8) ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 141.21/20.71 | | all_30_1 & $i(all_30_0) & $i(all_30_1)
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (8) implies:
% 141.21/20.71 | | (9) ~ (all_30_0 = e3)
% 141.21/20.71 | | (10) op(e0, e1) = all_30_1
% 141.21/20.71 | | (11) op(all_30_1, e0) = all_30_0
% 141.21/20.71 | |
% 141.21/20.71 | | GROUND_INST: instantiating (6) with e2, all_30_1, e1, e0, simplifying with
% 141.21/20.71 | | (4), (10) gives:
% 141.21/20.71 | | (12) all_30_1 = e2
% 141.21/20.71 | |
% 141.21/20.71 | | REDUCE: (11), (12) imply:
% 141.21/20.71 | | (13) op(e2, e0) = all_30_0
% 141.21/20.71 | |
% 141.21/20.71 | | GROUND_INST: instantiating (6) with e3, all_30_0, e0, e2, simplifying with
% 141.21/20.71 | | (2), (13) gives:
% 141.21/20.71 | | (14) all_30_0 = e3
% 141.21/20.71 | |
% 141.21/20.71 | | REDUCE: (9), (14) imply:
% 141.21/20.71 | | (15) $false
% 141.21/20.71 | |
% 141.21/20.71 | | CLOSE: (15) is inconsistent.
% 141.21/20.71 | |
% 141.21/20.71 | Case 2:
% 141.21/20.71 | |
% 141.21/20.71 | | (16) ~ (all_30_1 = e2) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 141.21/20.71 | |
% 141.21/20.71 | | ALPHA: (16) implies:
% 141.21/20.71 | | (17) ~ (all_30_1 = e2)
% 141.21/20.71 | | (18) op(e0, e1) = all_30_1
% 141.21/20.71 | |
% 141.21/20.71 | | REF_CLOSE: (4), (5), (6), (17), (18) are inconsistent by sub-proof #380.
% 141.21/20.71 | |
% 141.21/20.71 | End of split
% 141.21/20.71 |
% 141.21/20.71 End of proof
% 141.21/20.71
% 141.21/20.71 Sub-proof #195 shows that the following formulas are inconsistent:
% 141.21/20.71 ----------------------------------------------------------------
% 141.21/20.71 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.21/20.71 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.21/20.71 (2) op(e1, e1) = e3
% 141.21/20.71 (3) ~ (all_52_14 = e1)
% 141.21/20.71 (4) ~ (all_52_7 = e1)
% 141.21/20.71 (5) ~ (e2 = e1)
% 141.21/20.72 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.21/20.72 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.21/20.72 (7) ~ (e3 = e0)
% 141.21/20.72 (8) op(e1, e1) = all_4_2
% 141.21/20.72 (9) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.21/20.72 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.21/20.72 (10) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.21/20.72 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.21/20.72 (11) ~ (e1 = e0)
% 141.21/20.72 (12) op(e2, e2) = e2
% 141.21/20.72 (13) ~ (e2 = e0)
% 141.21/20.72 (14) ~ (e3 = e2)
% 141.21/20.72 (15) e3 = e2
% 141.21/20.72 (16) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.21/20.72 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.21/20.72 (17) ~ (all_4_2 = e2)
% 141.21/20.72 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.21/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.21/20.72 (19) all_57_1 = e3
% 141.21/20.72 (20) ~ (e3 = e1)
% 141.21/20.72 (21) op(e0, e2) = all_52_7
% 141.21/20.72 (22) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.21/20.72 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.21/20.72 (23) op(e1, e0) = all_52_14
% 141.21/20.72
% 141.21/20.72 Begin of proof
% 141.21/20.72 |
% 141.21/20.72 | COMBINE_EQS: (15), (19) imply:
% 141.21/20.72 | (24) all_57_1 = e2
% 141.21/20.72 |
% 141.21/20.72 | BETA: splitting (22) gives:
% 141.21/20.72 |
% 141.21/20.72 | Case 1:
% 141.21/20.72 | |
% 141.34/20.72 | | (25) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.34/20.72 | | e3)
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (12), (14), (18), (24), (25) are inconsistent by sub-proof #207.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (26) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.34/20.72 | | e3)
% 141.34/20.72 | |
% 141.34/20.72 | | BETA: splitting (26) gives:
% 141.34/20.72 | |
% 141.34/20.72 | | Case 1:
% 141.34/20.72 | | |
% 141.34/20.72 | | | (27) all_57_7 = e3 & op(e1, e2) = e3
% 141.34/20.72 | | |
% 141.34/20.72 | | | ALPHA: (27) implies:
% 141.34/20.72 | | | (28) all_57_7 = e3
% 141.34/20.72 | | |
% 141.34/20.72 | | | BETA: splitting (6) gives:
% 141.34/20.72 | | |
% 141.34/20.72 | | | Case 1:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | (29) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2)
% 141.34/20.72 | | | | = e1)
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | BETA: splitting (29) gives:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | Case 1:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | (30) all_57_6 = e1 & op(e1, e3) = e1
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | ALPHA: (30) implies:
% 141.34/20.72 | | | | | (31) all_57_6 = e1
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | REF_CLOSE: (2), (5), (7), (8), (9), (11), (13), (14), (16), (17),
% 141.34/20.72 | | | | | (18), (28), (31) are inconsistent by sub-proof #234.
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | Case 2:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | (32) all_57_7 = e1 & op(e1, e2) = e1
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | REF_CLOSE: (20), (28), (32) are inconsistent by sub-proof #1058.
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | End of split
% 141.34/20.72 | | | |
% 141.34/20.72 | | | Case 2:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | (33) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0)
% 141.34/20.72 | | | | = e1)
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | REF_CLOSE: (2), (3), (18), (20), (23), (33) are inconsistent by
% 141.34/20.72 | | | | sub-proof #268.
% 141.34/20.72 | | | |
% 141.34/20.72 | | | End of split
% 141.34/20.72 | | |
% 141.34/20.72 | | Case 2:
% 141.34/20.72 | | |
% 141.34/20.72 | | | (34) all_57_13 = e3 & op(e0, e2) = e3
% 141.34/20.72 | | |
% 141.34/20.72 | | | ALPHA: (34) implies:
% 141.34/20.72 | | | (35) all_57_13 = e3
% 141.34/20.72 | | |
% 141.34/20.72 | | | BETA: splitting (10) gives:
% 141.34/20.72 | | |
% 141.34/20.72 | | | Case 1:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | (36) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2)
% 141.34/20.72 | | | | = e0)
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | BETA: splitting (36) gives:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | Case 1:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | (37) all_57_1 = e0 & op(e3, e2) = e0
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | REF_CLOSE: (13), (24), (37) are inconsistent by sub-proof #267.
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | Case 2:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | (38) all_57_3 = e0 & op(e2, e2) = e0
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | ALPHA: (38) implies:
% 141.34/20.72 | | | | | (39) op(e2, e2) = e0
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | REF_CLOSE: (12), (13), (18), (39) are inconsistent by sub-proof #1076.
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | End of split
% 141.34/20.72 | | | |
% 141.34/20.72 | | | Case 2:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | (40) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2)
% 141.34/20.72 | | | | = e0)
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | BETA: splitting (40) gives:
% 141.34/20.72 | | | |
% 141.34/20.72 | | | | Case 1:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | (41) all_57_7 = e0 & op(e1, e2) = e0
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | ALPHA: (41) implies:
% 141.34/20.72 | | | | | (42) all_57_7 = e0
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | BETA: splitting (1) gives:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | Case 1:
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | | (43) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 141.34/20.72 | | | | | | e2) = e1)
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | | BETA: splitting (43) gives:
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | | Case 1:
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | (44) all_57_1 = e1 & op(e3, e2) = e1
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | REF_CLOSE: (5), (24), (44) are inconsistent by sub-proof #1092.
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | Case 2:
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | (45) all_57_3 = e1 & op(e2, e2) = e1
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | ALPHA: (45) implies:
% 141.34/20.72 | | | | | | | (46) op(e2, e2) = e1
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | REF_CLOSE: (5), (12), (18), (46) are inconsistent by sub-proof
% 141.34/20.72 | | | | | | | #749.
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | End of split
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | Case 2:
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | | (47) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 141.34/20.72 | | | | | | e2) = e1)
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | | BETA: splitting (47) gives:
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | | Case 1:
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | (48) all_57_7 = e1 & op(e1, e2) = e1
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | ALPHA: (48) implies:
% 141.34/20.72 | | | | | | | (49) all_57_7 = e1
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | REF_CLOSE: (11), (42), (49) are inconsistent by sub-proof #712.
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | Case 2:
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | (50) all_57_13 = e1 & op(e0, e2) = e1
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | | REF_CLOSE: (4), (18), (21), (50) are inconsistent by sub-proof
% 141.34/20.72 | | | | | | | #366.
% 141.34/20.72 | | | | | | |
% 141.34/20.72 | | | | | | End of split
% 141.34/20.72 | | | | | |
% 141.34/20.72 | | | | | End of split
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | Case 2:
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | (51) all_57_13 = e0 & op(e0, e2) = e0
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | | REF_CLOSE: (7), (35), (51) are inconsistent by sub-proof #1016.
% 141.34/20.72 | | | | |
% 141.34/20.72 | | | | End of split
% 141.34/20.72 | | | |
% 141.34/20.72 | | | End of split
% 141.34/20.72 | | |
% 141.34/20.72 | | End of split
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #196 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) op(e1, e3) = all_52_2
% 141.34/20.72 (2) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.34/20.72 (3) op(e0, e3) = all_52_3
% 141.34/20.72 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72 (5) ~ (all_52_3 = e0)
% 141.34/20.72 (6) ~ (all_52_2 = e0)
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (2) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (7) all_57_6 = e0 & op(e1, e3) = e0
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (1), (4), (6), (7) are inconsistent by sub-proof #206.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (8) all_57_12 = e0 & op(e0, e3) = e0
% 141.34/20.72 | |
% 141.34/20.72 | | ALPHA: (8) implies:
% 141.34/20.72 | | (9) op(e0, e3) = e0
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #986.
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #197 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.34/20.72 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.34/20.72 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.34/20.72 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.34/20.72 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.34/20.72 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.34/20.72 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.34/20.72 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.34/20.72 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.34/20.72 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.34/20.72 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.34/20.72 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.34/20.72 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.34/20.72 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.34/20.72 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.34/20.72 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.34/20.72 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.34/20.72 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.34/20.72 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.34/20.72 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.34/20.72 (2) ~ (e2 = e1)
% 141.34/20.72 (3) op(e0, e1) = e0
% 141.34/20.72 (4) op(e0, e0) = e2
% 141.34/20.72 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72 (6) ~ (all_52_13 = e2)
% 141.34/20.72 (7) op(e2, e2) = e0
% 141.34/20.72 (8) op(e2, e0) = all_52_13
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (1) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (9) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1)
% 141.34/20.72 | | = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.34/20.72 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.34/20.72 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.34/20.72 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1)
% 141.34/20.72 | | = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1)
% 141.34/20.72 | | | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.34/20.72 | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.34/20.72 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.34/20.72 | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.34/20.72 | | $i(all_56_14)))
% 141.34/20.72 | |
% 141.34/20.72 | | ALPHA: (9) implies:
% 141.34/20.72 | | (10) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 141.34/20.72 | | e1) = all_56_14 & $i(all_56_14))
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (2), (3), (4), (5), (10) are inconsistent by sub-proof #972.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (11) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.34/20.72 | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.34/20.72 | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.34/20.72 | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.34/20.72 | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.34/20.72 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.34/20.72 | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.34/20.72 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.34/20.72 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.34/20.72 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.34/20.72 | | e0) = all_56_8 & $i(all_56_8)))
% 141.34/20.72 | |
% 141.34/20.72 | | ALPHA: (11) implies:
% 141.34/20.72 | | (12) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.34/20.72 | | e2) = all_56_11 & $i(all_56_11))
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (5), (6), (7), (8), (12) are inconsistent by sub-proof #856.
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #198 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) ~ (all_10_2 = e2)
% 141.34/20.72 (2) ~ (all_10_2 = e1)
% 141.34/20.72 (3) ~ (all_10_2 = e0)
% 141.34/20.72 (4) all_54_15 = all_10_2
% 141.34/20.72 (5) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (5) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (6) all_54_15 = e2
% 141.34/20.72 | |
% 141.34/20.72 | | COMBINE_EQS: (4), (6) imply:
% 141.34/20.72 | | (7) all_10_2 = e2
% 141.34/20.72 | |
% 141.34/20.72 | | REDUCE: (1), (7) imply:
% 141.34/20.72 | | (8) $false
% 141.34/20.72 | |
% 141.34/20.72 | | CLOSE: (8) is inconsistent.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (9) all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72 | |
% 141.34/20.72 | | BETA: splitting (9) gives:
% 141.34/20.72 | |
% 141.34/20.72 | | Case 1:
% 141.34/20.72 | | |
% 141.34/20.72 | | | (10) all_54_15 = e1
% 141.34/20.72 | | |
% 141.34/20.72 | | | COMBINE_EQS: (4), (10) imply:
% 141.34/20.72 | | | (11) all_10_2 = e1
% 141.34/20.72 | | |
% 141.34/20.72 | | | REDUCE: (2), (11) imply:
% 141.34/20.72 | | | (12) $false
% 141.34/20.72 | | |
% 141.34/20.72 | | | CLOSE: (12) is inconsistent.
% 141.34/20.72 | | |
% 141.34/20.72 | | Case 2:
% 141.34/20.72 | | |
% 141.34/20.72 | | | (13) all_54_15 = e0
% 141.34/20.72 | | |
% 141.34/20.72 | | | COMBINE_EQS: (4), (13) imply:
% 141.34/20.72 | | | (14) all_10_2 = e0
% 141.34/20.72 | | |
% 141.34/20.72 | | | REDUCE: (3), (14) imply:
% 141.34/20.72 | | | (15) $false
% 141.34/20.72 | | |
% 141.34/20.72 | | | CLOSE: (15) is inconsistent.
% 141.34/20.72 | | |
% 141.34/20.72 | | End of split
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #199 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) op(e1, e3) = all_52_2
% 141.34/20.72 (2) op(e1, e2) = all_52_6
% 141.34/20.72 (3) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 141.34/20.72 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72 (5) ~ (all_52_2 = e0)
% 141.34/20.72 (6) ~ (all_52_6 = e0)
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (3) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (7) all_57_6 = e0 & op(e1, e3) = e0
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #206.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (8) all_57_7 = e0 & op(e1, e2) = e0
% 141.34/20.72 | |
% 141.34/20.72 | | ALPHA: (8) implies:
% 141.34/20.72 | | (9) op(e1, e2) = e0
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #999.
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #200 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) ~ (all_10_2 = e2)
% 141.34/20.72 (2) op(e1, e1) = e3
% 141.34/20.72 (3) ~ (all_10_2 = e3)
% 141.34/20.72 (4) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.34/20.72 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.34/20.72 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.34/20.72 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.34/20.72 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.34/20.72 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.34/20.72 e1) = all_56_14 & $i(all_56_14))
% 141.34/20.72 (5) ~ (all_10_2 = e1)
% 141.34/20.72 (6) op(e2, e2) = e1
% 141.34/20.72 (7) ~ (e3 = e0)
% 141.34/20.72 (8) op(e0, e0) = all_10_2
% 141.34/20.72 (9) ~ (e1 = e0)
% 141.34/20.72 (10) all_54_15 = all_10_2
% 141.34/20.72 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72 (12) op(e0, e0) = all_56_15
% 141.34/20.72 (13) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (4) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (14) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.34/20.72 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.34/20.72 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.34/20.72 | | e2) = all_56_12 & $i(all_56_12))
% 141.34/20.72 | |
% 141.34/20.72 | | BETA: splitting (14) gives:
% 141.34/20.72 | |
% 141.34/20.72 | | Case 1:
% 141.34/20.72 | | |
% 141.34/20.72 | | | (15) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 141.34/20.72 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.34/20.72 | | |
% 141.34/20.72 | | | ALPHA: (15) implies:
% 141.34/20.72 | | | (16) all_56_15 = e3
% 141.34/20.72 | | |
% 141.34/20.72 | | | REDUCE: (12), (16) imply:
% 141.34/20.72 | | | (17) op(e0, e0) = e3
% 141.34/20.72 | | |
% 141.34/20.72 | | | REF_CLOSE: (1), (3), (5), (8), (10), (11), (13), (17) are inconsistent by
% 141.34/20.72 | | | sub-proof #202.
% 141.34/20.72 | | |
% 141.34/20.72 | | Case 2:
% 141.34/20.72 | | |
% 141.34/20.72 | | | (18) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.34/20.72 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.34/20.72 | | |
% 141.34/20.72 | | | ALPHA: (18) implies:
% 141.34/20.72 | | | (19) op(e2, e2) = e0
% 141.34/20.72 | | |
% 141.34/20.72 | | | REF_CLOSE: (6), (9), (11), (19) are inconsistent by sub-proof #1117.
% 141.34/20.72 | | |
% 141.34/20.72 | | End of split
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (20) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.34/20.72 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.34/20.72 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.34/20.72 | | e1) = all_56_14 & $i(all_56_14))
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (2), (7), (11), (20) are inconsistent by sub-proof #279.
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #201 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) ~ (all_10_2 = e2)
% 141.34/20.72 (2) op(e0, e0) = e3
% 141.34/20.72 (3) ~ (all_10_2 = e3)
% 141.34/20.72 (4) ~ (all_10_2 = e1)
% 141.34/20.72 (5) op(e0, e0) = all_10_2
% 141.34/20.72 (6) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72 (7) all_54_15 = all_10_2
% 141.34/20.72 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (6) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (9) all_54_15 = e3
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (3), (7), (9) are inconsistent by sub-proof #755.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (10) ~ (all_54_15 = e3)
% 141.34/20.72 | | (11) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11) are inconsistent by
% 141.34/20.72 | | sub-proof #202.
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #202 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) ~ (all_10_2 = e2)
% 141.34/20.72 (2) op(e0, e0) = e3
% 141.34/20.72 (3) ~ (all_10_2 = e3)
% 141.34/20.72 (4) ~ (all_10_2 = e1)
% 141.34/20.72 (5) op(e0, e0) = all_10_2
% 141.34/20.72 (6) all_54_15 = all_10_2
% 141.34/20.72 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72 (8) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72
% 141.34/20.72 Begin of proof
% 141.34/20.72 |
% 141.34/20.72 | BETA: splitting (8) gives:
% 141.34/20.72 |
% 141.34/20.72 | Case 1:
% 141.34/20.72 | |
% 141.34/20.72 | | (9) all_54_15 = e2
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (1), (6), (9) are inconsistent by sub-proof #754.
% 141.34/20.72 | |
% 141.34/20.72 | Case 2:
% 141.34/20.72 | |
% 141.34/20.72 | | (10) all_54_15 = e1 | all_54_15 = e0
% 141.34/20.72 | |
% 141.34/20.72 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 141.34/20.72 | | #750.
% 141.34/20.72 | |
% 141.34/20.72 | End of split
% 141.34/20.72 |
% 141.34/20.72 End of proof
% 141.34/20.72
% 141.34/20.72 Sub-proof #203 shows that the following formulas are inconsistent:
% 141.34/20.72 ----------------------------------------------------------------
% 141.34/20.72 (1) ~ (all_52_1 = e2)
% 141.34/20.72 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.34/20.72 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.34/20.72 (3) ~ (all_52_8 = all_52_11)
% 141.34/20.72 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.34/20.72 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.34/20.72 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.34/20.72 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.34/20.72 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.34/20.72 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.34/20.72 (7) op(e1, e3) = all_52_2
% 141.34/20.72 (8) op(e1, e1) = e3
% 141.34/20.72 (9) ~ (all_52_8 = all_52_9)
% 141.34/20.72 (10) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.34/20.72 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.34/20.72 (11) ~ (all_52_8 = e3)
% 141.34/20.72 (12) ~ (all_52_4 = e0)
% 141.34/20.72 (13) ~ (e2 = e1)
% 141.34/20.72 (14) ~ (all_52_4 = all_52_8)
% 141.34/20.72 (15) op(e0, e0) = e3
% 141.34/20.72 (16) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.34/20.72 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.34/20.72 (17) ~ (all_52_11 = e3)
% 141.34/20.72 (18) op(e0, e3) = all_52_3
% 141.34/20.72 (19) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.34/20.72 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.34/20.72 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.34/20.72 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.34/20.72 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.34/20.72 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.34/20.72 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.34/20.72 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.34/20.72 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.34/20.72 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.34/20.72 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.34/20.72 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.34/20.72 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.34/20.72 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.34/20.72 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.34/20.72 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.34/20.72 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.34/20.72 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.34/20.72 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.34/20.72 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.34/20.72 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.34/20.72 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.34/20.72 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.34/20.72 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.34/20.72 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.34/20.72 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.34/20.72 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.34/20.72 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.34/20.72 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.34/20.72 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.34/20.72 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.34/20.72 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.34/20.72 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.34/20.72 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.34/20.72 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.34/20.72 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.34/20.72 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.34/20.72 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.34/20.72 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.34/20.72 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.34/20.72 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.34/20.72 (20) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.34/20.72 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.34/20.72 (21) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 141.34/20.72 (22) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.34/20.72 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.34/20.72 e1)
% 141.34/20.72 (23) ~ (all_52_9 = e2)
% 141.34/20.72 (24) ~ (all_52_9 = all_52_11)
% 141.34/20.72 (25) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.34/20.72 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.34/20.72 (26) all_54_2 = all_52_8
% 141.34/20.72 (27) ~ (all_52_1 = e0)
% 141.34/20.72 (28) ~ (e3 = e0)
% 141.34/20.72 (29) op(e1, e1) = all_4_2
% 141.34/20.72 (30) op(e3, e1) = all_52_8
% 141.34/20.72 (31) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.34/20.72 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.34/20.72 (32) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.34/20.72 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.34/20.72 e2)
% 141.34/20.72 (33) op(e2, e3) = all_52_1
% 141.34/20.72 (34) ~ (all_52_12 = e0)
% 141.34/20.72 (35) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 141.34/20.72 (36) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.34/20.72 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.34/20.72 (37) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.34/20.72 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.34/20.72 (38) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.34/20.72 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.34/20.72 (39) ( ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 & op(e1, e3) = all_8_1 &
% 141.34/20.72 $i(all_8_0) & $i(all_8_1)) | ( ~ (all_8_1 = e2) & op(e1, e3) = all_8_1
% 141.34/20.72 & $i(all_8_1))
% 141.34/20.72 (40) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.34/20.72 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.34/20.72 (41) ~ (e1 = e0)
% 141.34/20.72 (42) op(e2, e2) = e2
% 141.34/20.72 (43) ~ (all_52_4 = e2)
% 141.34/20.72 (44) op(e3, e2) = all_52_4
% 141.34/20.72 (45) ~ (e2 = e0)
% 141.34/20.72 (46) ~ (all_52_8 = all_14_2)
% 141.34/20.72 (47) ~ (e3 = e2)
% 141.34/20.72 (48) op(e0, e1) = all_52_11
% 141.34/20.72 (49) op(e3, e0) = all_52_12
% 141.34/20.72 (50) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.34/20.72 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.34/20.72 (51) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.34/20.72 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.34/20.72 (52) ~ (all_4_2 = e2)
% 141.34/20.72 (53) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.34/20.72 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.34/20.72 (54) all_54_14 = all_52_11
% 141.34/20.72 (55) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.72 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.72 (56) ~ (all_52_3 = e0)
% 141.34/20.73 (57) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.34/20.73 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.34/20.73 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.34/20.73 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.34/20.73 (58) ~ (all_52_2 = e0)
% 141.34/20.73 (59) ~ (all_52_8 = e0)
% 141.34/20.73 (60) ~ (all_52_13 = e2)
% 141.34/20.73 (61) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.34/20.73 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.34/20.73 (62) ~ (e3 = e1)
% 141.34/20.73 (63) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.34/20.73 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.34/20.73 (64) ~ (all_6_2 = e3)
% 141.34/20.73 (65) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.34/20.73 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.34/20.73 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.34/20.73 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.34/20.73 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.34/20.73 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.34/20.73 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.34/20.73 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.34/20.73 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.34/20.73 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.34/20.73 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.34/20.73 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.34/20.73 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.34/20.73 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.34/20.73 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.34/20.73 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.34/20.73 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.34/20.73 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.34/20.73 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.34/20.73 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.73 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.34/20.73 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.34/20.73 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.34/20.73 $i(all_56_14))))
% 141.34/20.73 (66) all_57_0 = e0
% 141.34/20.73 (67) ( ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 & op(e1, e3) =
% 141.34/20.73 all_12_1 & $i(all_12_0) & $i(all_12_1)) | ( ~ (all_12_1 = e0) & op(e1,
% 141.34/20.73 e3) = all_12_1 & $i(all_12_1))
% 141.34/20.73 (68) op(e2, e2) = all_6_2
% 141.34/20.73 (69) all_57_8 = e3
% 141.34/20.73 (70) op(e3, e3) = e0
% 141.34/20.73 (71) op(e2, e1) = all_52_9
% 141.34/20.73 (72) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.34/20.73 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.34/20.73 (73) op(e3, e3) = all_14_2
% 141.34/20.73 (74) ~ (all_52_4 = all_52_12)
% 141.34/20.73 (75) op(e2, e0) = all_52_13
% 141.34/20.73 (76) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.34/20.73 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.34/20.73 (77) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.34/20.73 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.34/20.73
% 141.34/20.73 Begin of proof
% 141.34/20.73 |
% 141.34/20.73 | BETA: splitting (2) gives:
% 141.34/20.73 |
% 141.34/20.73 | Case 1:
% 141.34/20.73 | |
% 141.34/20.73 | | (78) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.34/20.73 | | e3)
% 141.34/20.73 | |
% 141.34/20.73 | | BETA: splitting (78) gives:
% 141.34/20.73 | |
% 141.34/20.73 | | Case 1:
% 141.34/20.73 | | |
% 141.34/20.73 | | | (79) all_57_2 = e3 & op(e2, e3) = e3
% 141.34/20.73 | | |
% 141.34/20.73 | | | ALPHA: (79) implies:
% 141.34/20.73 | | | (80) all_57_2 = e3
% 141.34/20.73 | | |
% 141.34/20.73 | | | BETA: splitting (76) gives:
% 141.34/20.73 | | |
% 141.34/20.73 | | | Case 1:
% 141.34/20.73 | | | |
% 141.34/20.73 | | | | (81) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 141.34/20.73 | | | | = e3)
% 141.34/20.73 | | | |
% 141.34/20.73 | | | | BETA: splitting (81) gives:
% 141.34/20.73 | | | |
% 141.34/20.73 | | | | Case 1:
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | (82) all_57_1 = e3 & op(e3, e2) = e3
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | ALPHA: (82) implies:
% 141.34/20.73 | | | | | (83) all_57_1 = e3
% 141.34/20.73 | | | | | (84) op(e3, e2) = e3
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | GROUND_INST: instantiating (55) with all_52_4, e3, e2, e3, simplifying
% 141.34/20.73 | | | | | with (44), (84) gives:
% 141.34/20.73 | | | | | (85) all_52_4 = e3
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | REDUCE: (14), (85) imply:
% 141.34/20.73 | | | | | (86) ~ (all_52_8 = e3)
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | REDUCE: (74), (85) imply:
% 141.34/20.73 | | | | | (87) ~ (all_52_12 = e3)
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | SIMP: (87) implies:
% 141.34/20.73 | | | | | (88) ~ (all_52_12 = e3)
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | BETA: splitting (19) gives:
% 141.34/20.73 | | | | |
% 141.34/20.73 | | | | | Case 1:
% 141.34/20.73 | | | | | |
% 141.34/20.73 | | | | | | (89) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 141.34/20.73 | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 141.34/20.73 | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 141.34/20.73 | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.34/20.73 | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 141.34/20.73 | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.34/20.73 | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.34/20.73 | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.34/20.73 | | | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1,
% 141.34/20.73 | | | | | | e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.34/20.73 | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 141.34/20.73 | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.34/20.73 | | | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11
% 141.34/20.73 | | | | | | & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 141.34/20.73 | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.34/20.73 | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) |
% 141.34/20.73 | | | | | | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.34/20.73 | | | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) |
% 141.34/20.73 | | | | | | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.34/20.73 | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) |
% 141.34/20.73 | | | | | | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.34/20.73 | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2)
% 141.34/20.73 | | | | | | | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.34/20.73 | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.34/20.73 | | | | | | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.34/20.73 | | | | | | $i(all_56_12))))
% 141.34/20.73 | | | | | |
% 141.34/20.73 | | | | | | REF_CLOSE: (15), (18), (45), (55), (56), (70), (84), (89) are
% 141.34/20.73 | | | | | | inconsistent by sub-proof #212.
% 141.34/20.73 | | | | | |
% 141.34/20.73 | | | | | Case 2:
% 141.34/20.73 | | | | | |
% 141.34/20.73 | | | | | | (90) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.34/20.73 | | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.34/20.73 | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 141.34/20.73 | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.34/20.73 | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3,
% 141.34/20.73 | | | | | | e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 141.34/20.73 | | | | | | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.34/20.73 | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.34/20.73 | | | | | | all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 141.34/20.73 | | | | | | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.34/20.73 | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 &
% 141.34/20.73 | | | | | | op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 141.34/20.73 | | | | | | all_56_14 & $i(all_56_14)))) | (op(e0, e0) = all_56_15
% 141.34/20.73 | | | | | | & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 141.34/20.73 | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.34/20.73 | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.34/20.73 | | | | | | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 141.34/20.73 | | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) |
% 141.34/20.73 | | | | | | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.34/20.73 | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) |
% 141.34/20.73 | | | | | | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.34/20.73 | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) |
% 141.34/20.73 | | | | | | ( ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.34/20.73 | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.34/20.73 | | | | | | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.34/20.73 | | | | | | $i(all_56_8))))
% 141.34/20.73 | | | | | |
% 141.34/20.73 | | | | | | BETA: splitting (90) gives:
% 141.34/20.73 | | | | | |
% 141.34/20.73 | | | | | | Case 1:
% 141.34/20.73 | | | | | | |
% 141.34/20.73 | | | | | | | (91) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.34/20.73 | | | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.34/20.73 | | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 141.34/20.73 | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.34/20.73 | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3,
% 141.34/20.73 | | | | | | | e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 141.34/20.73 | | | | | | | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.34/20.73 | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.34/20.73 | | | | | | | all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 141.34/20.73 | | | | | | | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.34/20.73 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 &
% 141.34/20.73 | | | | | | | op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 141.34/20.73 | | | | | | | all_56_14 & $i(all_56_14)))
% 141.34/20.73 | | | | | | |
% 141.34/20.73 | | | | | | | ALPHA: (91) implies:
% 141.34/20.73 | | | | | | | (92) op(e1, e1) = all_56_13
% 141.34/20.73 | | | | | | | (93) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0)
% 141.34/20.73 | | | | | | | & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.34/20.73 | | | | | | | (94) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1)
% 141.34/20.73 | | | | | | | & op(e0, e0) = all_56_15 & $i(all_56_15))
% 141.34/20.73 | | | | | | | (95) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 141.34/20.73 | | | | | | | op(e2, e1) = all_56_4 & $i(all_56_4))
% 141.34/20.73 | | | | | | | (96) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 141.34/20.73 | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))
% 141.34/20.73 | | | | | | | (97) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) &
% 141.34/20.73 | | | | | | | op(e2, e2) = all_56_11 & $i(all_56_11))
% 141.34/20.73 | | | | | | | (98) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) &
% 141.34/20.73 | | | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.34/20.73 | | | | | | |
% 141.34/20.73 | | | | | | | BETA: splitting (93) gives:
% 141.34/20.73 | | | | | | |
% 141.34/20.73 | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | (99) all_56_15 = e1 & op(e0, e0) = e1
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | ALPHA: (99) implies:
% 141.34/20.73 | | | | | | | | (100) op(e0, e0) = e1
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | REF_CLOSE: (8), (13), (28), (29), (41), (45), (52), (55), (62),
% 141.34/20.73 | | | | | | | | (65), (70), (100) are inconsistent by sub-proof #210.
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | (101) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.34/20.73 | | | | | | | | $i(all_56_14)
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | ALPHA: (101) implies:
% 141.34/20.73 | | | | | | | | (102) ~ (all_56_14 = e0)
% 141.34/20.73 | | | | | | | | (103) op(e0, e1) = all_56_14
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | BETA: splitting (95) gives:
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | (104) all_56_11 = e1 & op(e2, e2) = e1
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | ALPHA: (104) implies:
% 141.34/20.73 | | | | | | | | | (105) op(e2, e2) = e1
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | REF_CLOSE: (3), (9), (15), (17), (21), (24), (26), (30), (35),
% 141.34/20.73 | | | | | | | | | (41), (48), (54), (55), (59), (62), (70), (71),
% 141.34/20.73 | | | | | | | | | (93), (94), (95), (96), (97), (105) are
% 141.34/20.73 | | | | | | | | | inconsistent by sub-proof #532.
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | (106) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.34/20.73 | | | | | | | | | $i(all_56_4)
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | ALPHA: (106) implies:
% 141.34/20.73 | | | | | | | | | (107) ~ (all_56_4 = e2)
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | BETA: splitting (96) gives:
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | (108) all_56_9 = e1 & op(e3, e3) = e1
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | ALPHA: (108) implies:
% 141.34/20.73 | | | | | | | | | | (109) all_56_9 = e1
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | REF_CLOSE: (11), (30), (55), (98), (109) are inconsistent by
% 141.34/20.73 | | | | | | | | | | sub-proof #898.
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | (110) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.34/20.73 | | | | | | | | | | $i(all_56_1)
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | ALPHA: (110) implies:
% 141.34/20.73 | | | | | | | | | | (111) ~ (all_56_1 = e3)
% 141.34/20.73 | | | | | | | | | | (112) op(e3, e1) = all_56_1
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | BETA: splitting (94) gives:
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | (113) all_56_14 = e0 & op(e0, e1) = e0
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | ALPHA: (113) implies:
% 141.34/20.73 | | | | | | | | | | | (114) op(e0, e1) = e0
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | REF_CLOSE: (55), (102), (103), (114) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | sub-proof #973.
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | (115) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 141.34/20.73 | | | | | | | | | | | $i(all_56_15)
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | ALPHA: (115) implies:
% 141.34/20.73 | | | | | | | | | | | (116) ~ (all_56_15 = e1)
% 141.34/20.73 | | | | | | | | | | | (117) op(e0, e0) = all_56_15
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | BETA: splitting (97) gives:
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | (118) all_56_4 = e2 & op(e2, e1) = e2
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | ALPHA: (118) implies:
% 141.34/20.73 | | | | | | | | | | | | (119) op(e2, e1) = e2
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | REF_CLOSE: (3), (9), (15), (17), (21), (24), (26), (30),
% 141.34/20.73 | | | | | | | | | | | | (35), (48), (54), (55), (59), (62), (71), (93),
% 141.34/20.73 | | | | | | | | | | | | (111), (112), (119) are inconsistent by sub-proof
% 141.34/20.73 | | | | | | | | | | | | #535.
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | (120) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.34/20.73 | | | | | | | | | | | | $i(all_56_11)
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | ALPHA: (120) implies:
% 141.34/20.73 | | | | | | | | | | | | (121) ~ (all_56_11 = e1)
% 141.34/20.73 | | | | | | | | | | | | (122) op(e2, e2) = all_56_11
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | BETA: splitting (98) gives:
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | (123) all_56_1 = e3 & op(e3, e1) = e3
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | ALPHA: (123) implies:
% 141.34/20.73 | | | | | | | | | | | | | (124) op(e3, e1) = e3
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | REF_CLOSE: (55), (111), (112), (124) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | | | sub-proof #734.
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | (125) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.34/20.73 | | | | | | | | | | | | | $i(all_56_9)
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | ALPHA: (125) implies:
% 141.34/20.73 | | | | | | | | | | | | | (126) ~ (all_56_9 = e1)
% 141.34/20.73 | | | | | | | | | | | | | (127) op(e3, e3) = all_56_9
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e3, all_56_15, e0, e0,
% 141.34/20.73 | | | | | | | | | | | | | simplifying with (15), (117) gives:
% 141.34/20.73 | | | | | | | | | | | | | (128) all_56_15 = e3
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_52_11, all_56_14, e1,
% 141.34/20.73 | | | | | | | | | | | | | e0, simplifying with (48), (103) gives:
% 141.34/20.73 | | | | | | | | | | | | | (129) all_56_14 = all_52_11
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e3, all_56_13, e1, e1,
% 141.34/20.73 | | | | | | | | | | | | | simplifying with (8), (92) gives:
% 141.34/20.73 | | | | | | | | | | | | | (130) all_56_13 = e3
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e2, all_56_11, e2, e2,
% 141.34/20.73 | | | | | | | | | | | | | simplifying with (42), (122) gives:
% 141.34/20.73 | | | | | | | | | | | | | (131) all_56_11 = e2
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_52_8, all_56_1, e1,
% 141.34/20.73 | | | | | | | | | | | | | e3, simplifying with (30), (112) gives:
% 141.34/20.73 | | | | | | | | | | | | | (132) all_56_1 = all_52_8
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e0, all_56_9, e3, e3,
% 141.34/20.73 | | | | | | | | | | | | | simplifying with (70), (127) gives:
% 141.34/20.73 | | | | | | | | | | | | | (133) all_56_9 = e0
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | REDUCE: (126), (133) imply:
% 141.34/20.73 | | | | | | | | | | | | | (134) ~ (e1 = e0)
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | REDUCE: (102), (129) imply:
% 141.34/20.73 | | | | | | | | | | | | | (135) ~ (all_52_11 = e0)
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | BETA: splitting (57) gives:
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | (136) all_57_15 = e0 & op(e0, e0) = e0
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | ALPHA: (136) implies:
% 141.34/20.73 | | | | | | | | | | | | | | (137) op(e0, e0) = e0
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | REF_CLOSE: (15), (28), (55), (137) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | | | | sub-proof #751.
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | (138) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 141.34/20.73 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 141.34/20.73 | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 141.34/20.73 | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.34/20.73 | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | ALPHA: (138) implies:
% 141.34/20.73 | | | | | | | | | | | | | | (139) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 141.34/20.73 | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 141.34/20.73 | | | | | | | | | | | | | | e0) = e0)
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | (140) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 141.34/20.73 | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | (141) all_57_4 = e0 & op(e3, e1) = e0
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | REF_CLOSE: (30), (55), (59), (141) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | | | | | | sub-proof #981.
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | (142) all_57_5 = e0 & op(e2, e1) = e0
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | ALPHA: (142) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | (143) all_57_5 = e0
% 141.34/20.73 | | | | | | | | | | | | | | | | (144) op(e2, e1) = e0
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | (145) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | BETA: splitting (145) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (146) all_57_2 = e1 & op(e2, e3) = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | ALPHA: (146) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (147) all_57_2 = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (80), (147) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (148) e3 = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | SIMP: (148) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (149) e3 = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (149) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (150) all_56_15 = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | REF_CLOSE: (48), (55), (94), (135), (150) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | | | | | | | | sub-proof #432.
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (151) all_57_3 = e1 & op(e2, e2) = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | ALPHA: (151) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (152) op(e2, e2) = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (94), (97), (102), (103), (107), (122),
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (152) are inconsistent by sub-proof #534.
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | (153) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 =
% 141.34/20.73 | | | | | | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | BETA: splitting (153) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (154) all_57_5 = e1 & op(e2, e1) = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (143), (154) are inconsistent by sub-proof
% 141.34/20.73 | | | | | | | | | | | | | | | | | | #258.
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (155) all_57_10 = e1 & op(e2, e0) = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | (156) all_57_10 = e1
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | BETA: splitting (51) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | (157) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (157) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (158) all_57_6 = e2 & op(e1, e3) = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (159) op(e1, e3) = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | BETA: splitting (39) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (160) ~ (all_8_0 = e0) & op(all_8_1, e1) = all_8_0 &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_8_1 & $i(all_8_0) & $i(all_8_1)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (160) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (161) ~ (all_8_0 = e0)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (162) op(e1, e3) = all_8_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (163) op(all_8_1, e1) = all_8_0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (164) ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_12_1 & $i(all_12_0) &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (165) op(e1, e3) = all_12_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (166) op(all_12_1, e1) = all_12_0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e2, all_12_1, e3, e1,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (159), (165) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (167) all_12_1 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_8_1, all_12_1, e3, e1,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (162), (165) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (168) all_12_1 = all_8_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (167), (168) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (169) all_8_1 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (166), (167) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (170) op(e2, e1) = all_12_0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (169) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (171) op(e2, e1) = all_8_0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e0, all_12_0, e1, e2,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (144), (170) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (172) all_12_0 = e0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_8_0, all_12_0, e1, e2,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (170), (171) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (173) all_12_0 = all_8_0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (172), (173) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (174) all_8_0 = e0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | SIMP: (174) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (175) all_8_0 = e0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (175) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (176) $false
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (176) is inconsistent.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (177) ~ (all_12_1 = e0) & op(e1, e3) = all_12_1 &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (178) op(e1, e3) = all_12_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e2, all_12_1, e3, e1,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (159), (178) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (179) all_12_1 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with all_8_1, all_12_1, e3, e1,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (162), (178) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (180) all_12_1 = all_8_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (179), (180) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (181) all_8_1 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (163), (181) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (182) op(e2, e1) = all_8_0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (55) with e0, all_8_0, e1, e2,
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | simplifying with (144), (182) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (183) all_8_0 = e0
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REDUCE: (161), (183) imply:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (184) $false
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | CLOSE: (184) is inconsistent.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (185) ~ (all_8_1 = e2) & op(e1, e3) = all_8_1 &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | $i(all_8_1)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | ALPHA: (185) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (186) ~ (all_8_1 = e2)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | (187) op(e1, e3) = all_8_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (67) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (188) ~ (all_12_0 = e2) & op(all_12_1, e1) = all_12_0 &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | op(e1, e3) = all_12_1 & $i(all_12_0) &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (188) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (189) op(e1, e3) = all_12_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (159), (186), (187), (189) are inconsistent
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #209.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (190) ~ (all_12_1 = e0) & op(e1, e3) = all_12_1 &
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | $i(all_12_1)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (190) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | (191) op(e1, e3) = all_12_1
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (159), (186), (187), (191) are inconsistent
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | | by sub-proof #209.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (192) all_57_7 = e2 & op(e1, e2) = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (193) all_57_7 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (28), (40), (41), (42), (45), (47),
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (55), (62), (76), (83), (193) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | sub-proof #310.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | (194) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | BETA: splitting (194) gives:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (195) all_57_8 = e2 & op(e1, e1) = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | ALPHA: (195) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (196) op(e1, e1) = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (52), (55), (196) are inconsistent by
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | sub-proof #1124.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (197) all_57_11 = e2 & op(e1, e0) = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | ALPHA: (197) implies:
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | (198) all_57_11 = e2
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (41), (45), (49), (55), (139), (156), (198)
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #716.
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | Case 2:
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | (199) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 141.34/20.73 | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (48), (55), (135), (199) are
% 141.34/20.73 | | | | | | | | | | | | | | | inconsistent by sub-proof #263.
% 141.34/20.73 | | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | | |
% 141.34/20.73 | | | | | | | | | End of split
% 141.34/20.73 | | | | | | | | |
% 141.34/20.73 | | | | | | | | End of split
% 141.34/20.73 | | | | | | | |
% 141.34/20.73 | | | | | | | End of split
% 141.34/20.73 | | | | | | |
% 141.34/20.73 | | | | | | Case 2:
% 141.34/20.73 | | | | | | |
% 141.34/20.73 | | | | | | | (200) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3
% 141.34/20.73 | | | | | | | & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.34/20.73 | | | | | | | = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 &
% 141.34/20.73 | | | | | | | op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2)
% 141.34/20.73 | | | | | | | = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 &
% 141.34/20.73 | | | | | | | op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.34/20.73 | | | | | | | = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 &
% 141.34/20.73 | | | | | | | op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.34/20.73 | | | | | | | all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2,
% 141.34/20.73 | | | | | | | e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 141.34/20.73 | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.34/20.74 | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.34/20.74 | | | | | | | all_56_8 & $i(all_56_8)))
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | REF_CLOSE: (13), (15), (41), (42), (45), (47), (49), (55), (62),
% 141.34/20.74 | | | | | | | (65), (70), (88), (200) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | #644.
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | End of split
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | End of split
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | Case 2:
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | (201) all_57_3 = e3 & op(e2, e2) = e3
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | ALPHA: (201) implies:
% 141.34/20.74 | | | | | (202) op(e2, e2) = e3
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | REF_CLOSE: (42), (47), (55), (202) are inconsistent by sub-proof #728.
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | End of split
% 141.34/20.74 | | | |
% 141.34/20.74 | | | Case 2:
% 141.34/20.74 | | | |
% 141.34/20.74 | | | | (203) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 141.34/20.74 | | | | e2) = e3)
% 141.34/20.74 | | | |
% 141.34/20.74 | | | | REF_CLOSE: (8), (13), (15), (16), (22), (28), (29), (31), (32), (41),
% 141.34/20.74 | | | | (45), (47), (51), (52), (55), (57), (62), (203) are
% 141.34/20.74 | | | | inconsistent by sub-proof #208.
% 141.34/20.74 | | | |
% 141.34/20.74 | | | End of split
% 141.34/20.74 | | |
% 141.34/20.74 | | Case 2:
% 141.34/20.74 | | |
% 141.34/20.74 | | | (204) all_57_3 = e3 & op(e2, e2) = e3
% 141.34/20.74 | | |
% 141.34/20.74 | | | ALPHA: (204) implies:
% 141.34/20.74 | | | (205) op(e2, e2) = e3
% 141.34/20.74 | | |
% 141.34/20.74 | | | REF_CLOSE: (42), (47), (55), (205) are inconsistent by sub-proof #728.
% 141.34/20.74 | | |
% 141.34/20.74 | | End of split
% 141.34/20.74 | |
% 141.34/20.74 | Case 2:
% 141.34/20.74 | |
% 141.34/20.74 | | (206) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 141.34/20.74 | | e3)
% 141.34/20.74 | |
% 141.34/20.74 | | BETA: splitting (206) gives:
% 141.34/20.74 | |
% 141.34/20.74 | | Case 1:
% 141.34/20.74 | | |
% 141.34/20.74 | | | (207) all_57_5 = e3 & op(e2, e1) = e3
% 141.34/20.74 | | |
% 141.34/20.74 | | | ALPHA: (207) implies:
% 141.34/20.74 | | | (208) all_57_5 = e3
% 141.34/20.74 | | |
% 141.34/20.74 | | | BETA: splitting (76) gives:
% 141.34/20.74 | | |
% 141.34/20.74 | | | Case 1:
% 141.34/20.74 | | | |
% 141.34/20.74 | | | | (209) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 141.34/20.74 | | | | = e3)
% 141.34/20.74 | | | |
% 141.34/20.74 | | | | BETA: splitting (209) gives:
% 141.34/20.74 | | | |
% 141.34/20.74 | | | | Case 1:
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | (210) all_57_1 = e3 & op(e3, e2) = e3
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | ALPHA: (210) implies:
% 141.34/20.74 | | | | | (211) all_57_1 = e3
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | BETA: splitting (77) gives:
% 141.34/20.74 | | | | |
% 141.34/20.74 | | | | | Case 1:
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | | (212) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 141.34/20.74 | | | | | | e2) = e0)
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | | REF_CLOSE: (27), (33), (42), (45), (55), (212) are inconsistent by
% 141.34/20.74 | | | | | | sub-proof #394.
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | Case 2:
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | | (213) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 141.34/20.74 | | | | | | op(e2, e0) = e0)
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | | BETA: splitting (213) gives:
% 141.34/20.74 | | | | | |
% 141.34/20.74 | | | | | | Case 1:
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | (214) all_57_5 = e0 & op(e2, e1) = e0
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | REF_CLOSE: (28), (208), (214) are inconsistent by sub-proof #729.
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | Case 2:
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | (215) all_57_10 = e0 & op(e2, e0) = e0
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | ALPHA: (215) implies:
% 141.34/20.74 | | | | | | | (216) all_57_10 = e0
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | BETA: splitting (10) gives:
% 141.34/20.74 | | | | | | |
% 141.34/20.74 | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | |
% 141.34/20.74 | | | | | | | | (217) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 141.34/20.74 | | | | | | | | op(e2, e2) = e1)
% 141.34/20.74 | | | | | | | |
% 141.34/20.74 | | | | | | | | BETA: splitting (217) gives:
% 141.34/20.74 | | | | | | | |
% 141.34/20.74 | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | |
% 141.34/20.74 | | | | | | | | | (218) all_57_2 = e1 & op(e2, e3) = e1
% 141.34/20.74 | | | | | | | | |
% 141.34/20.74 | | | | | | | | | ALPHA: (218) implies:
% 141.34/20.74 | | | | | | | | | (219) all_57_2 = e1
% 141.34/20.74 | | | | | | | | |
% 141.34/20.74 | | | | | | | | | BETA: splitting (37) gives:
% 141.34/20.74 | | | | | | | | |
% 141.34/20.74 | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | (220) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 141.34/20.74 | | | | | | | | | | & op(e2, e3) = e3)
% 141.34/20.74 | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | REF_CLOSE: (28), (62), (66), (219), (220) are inconsistent by
% 141.34/20.74 | | | | | | | | | | sub-proof #649.
% 141.34/20.74 | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | (221) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3
% 141.34/20.74 | | | | | | | | | | & op(e0, e3) = e3)
% 141.34/20.74 | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | BETA: splitting (221) gives:
% 141.34/20.74 | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | (222) all_57_6 = e3 & op(e1, e3) = e3
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | ALPHA: (222) implies:
% 141.34/20.74 | | | | | | | | | | | (223) all_57_6 = e3
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | BETA: splitting (20) gives:
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | (224) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 141.34/20.74 | | | | | | | | | | | | & op(e2, e1) = e0)
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | BETA: splitting (224) gives:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (225) all_57_4 = e0 & op(e3, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (30), (55), (59), (225) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | sub-proof #981.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (226) all_57_5 = e0 & op(e2, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | ALPHA: (226) implies:
% 141.34/20.74 | | | | | | | | | | | | | (227) all_57_5 = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | COMBINE_EQS: (208), (227) imply:
% 141.34/20.74 | | | | | | | | | | | | | (228) e3 = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | COMBINE_EQS: (223), (228) imply:
% 141.34/20.74 | | | | | | | | | | | | | (229) all_57_6 = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (13), (28), (37), (38), (41), (45), (47), (55),
% 141.34/20.74 | | | | | | | | | | | | | (62), (66), (70), (72), (219), (229) are
% 141.34/20.74 | | | | | | | | | | | | | inconsistent by sub-proof #323.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | (230) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 141.34/20.74 | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | BETA: splitting (230) gives:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (231) all_57_8 = e0 & op(e1, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | ALPHA: (231) implies:
% 141.34/20.74 | | | | | | | | | | | | | (232) op(e1, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (8), (28), (55), (232) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | sub-proof #308.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (233) all_57_14 = e0 & op(e0, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | ALPHA: (233) implies:
% 141.34/20.74 | | | | | | | | | | | | | (234) all_57_14 = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | BETA: splitting (51) gives:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | (235) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 141.34/20.74 | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | BETA: splitting (235) gives:
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | (236) all_57_6 = e2 & op(e1, e3) = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | ALPHA: (236) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | (237) all_57_6 = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | COMBINE_EQS: (223), (237) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | (238) e3 = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | COMBINE_EQS: (211), (238) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | (239) all_57_1 = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | BETA: splitting (63) gives:
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | (240) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | BETA: splitting (240) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | (241) all_57_0 = e3 & op(e3, e3) = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (66), (241) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | #1108.
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (47), (210), (239) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | #842.
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | (242) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | BETA: splitting (242) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | (243) all_57_4 = e3 & op(e3, e1) = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | ALPHA: (243) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (244) op(e3, e1) = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (30), (55), (244) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | sub-proof #1106.
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | (245) all_57_9 = e3 & op(e3, e0) = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | ALPHA: (245) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (246) all_57_9 = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | REF_CLOSE: (42), (47), (55), (209), (239) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | sub-proof #207.
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | (247) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | BETA: splitting (247) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | (248) all_57_7 = e3 & op(e1, e2) = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (16), (28), (29), (31), (41), (45),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | (47), (51), (52), (55), (62), (248) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #233.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | (249) all_57_13 = e3 & op(e0, e2) = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | ALPHA: (249) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | (250) all_57_13 = e3
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | (251) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (252) all_57_0 = e1 & op(e3, e3) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (253) op(e3, e3) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (55), (70), (253) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | sub-proof #840.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (254) all_57_1 = e1 & op(e3, e2) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (239), (254) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | #1092.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | (255) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | BETA: splitting (255) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (256) all_57_4 = e1 & op(e3, e1) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | ALPHA: (256) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (257) all_57_4 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (258) op(e3, e1) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (53) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | (259) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (23), (55), (71), (257), (259) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #331.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | (260) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (260) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | (261) all_57_8 = e2 & op(e1, e1) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | (262) op(e1, e1) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (52), (55), (262) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1124.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | (263) all_57_14 = e2 & op(e0, e1) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (263) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | (264) all_57_14 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (57) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | (265) all_57_15 = e0 & op(e0, e0) = e0
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | (266) op(e0, e0) = e0
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | (267) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_57_9 = e2 & op(e3, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_57_9 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (246), (269) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (270) e3 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (238), (250) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_57_13 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (12), (13), (28), (40), (41), (42), (44),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (47), (55), (62), (76), (271) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #710.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (272) all_57_10 = e2 & op(e2, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (272) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (273) op(e2, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (55), (60), (75), (273) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1030.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | (274) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (274) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_57_11 = e2 & op(e1, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_57_11 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (31) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e0)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_57_6 = e0 & op(e1, e3) = e0
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (55), (58), (278) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #206.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_57_7 = e0 & op(e1, e2) = e0
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (279) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) all_57_7 = e0
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (281) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_57_12 = e1 & op(e0, e3) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (282) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) all_57_12 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (72) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (33), (45), (55), (70), (284) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #707.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (285) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (286) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_57_6 = e1 & op(e1, e3) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (28), (37), (45), (47), (55), (62), (66),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (70), (72), (283), (287) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #205.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (288) all_57_7 = e1 & op(e1, e2) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (288) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (289) all_57_7 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (41), (280), (289) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #712.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (290) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (290) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (291) all_57_8 = e1 & op(e1, e1) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (291) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (292) op(e1, e1) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (28), (31), (33), (37), (38), (41),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (45), (47), (50), (55), (62), (66), (70), (72),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (237), (276), (292) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #651.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_57_11 = e1 & op(e1, e0) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_57_11 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (22), (25), (28), (41), (45), (47),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (60), (62), (75), (246), (264), (294)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #300.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) all_57_12 = e2 & op(e0, e3) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (295) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_57_12 = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (283), (296) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) e2 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (297) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_57_11 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (22), (25), (28), (41), (45), (47),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (60), (62), (75), (246), (264), (298)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #300.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_57_13 = e1 & op(e0, e2) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (299) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) all_57_13 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (250), (300) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1001.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_57_14 = e1 & op(e0, e1) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (302) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_57_14 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (264), (303) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) e2 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (304) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e2 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (276), (305) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) all_57_11 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (5), (13), (22), (25), (28), (41), (45), (47),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (57), (60), (62), (75), (246), (264), (306)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #300.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_57_15 = e1 & op(e0, e0) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (307) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) op(e0, e0) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (13), (28), (29), (30), (46), (52),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (64), (65), (68), (73), (258), (308) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | (309) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (45), (55), (276), (309) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #307.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_57_15 = e2 & op(e0, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (310) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (311) op(e0, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (45), (55), (266), (311) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #1094.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | (312) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | (313) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | e1) = e0)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (22) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | (314) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (314) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (315) all_57_12 = e1 & op(e0, e3) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (315) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (316) all_57_12 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (41), (45), (250), (264), (313), (316) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #400.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (317) all_57_13 = e1 & op(e0, e2) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (317) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (318) all_57_13 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (18), (41), (45), (55), (56), (264), (313), (318)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #551.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | (319) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (319) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (320) all_57_14 = e1 & op(e0, e1) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (320) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (321) all_57_14 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (264), (321) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | #1048.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (322) all_57_15 = e1 & op(e0, e0) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (322) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (323) op(e0, e0) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (11), (13), (28), (29), (30), (46), (52),
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | (55), (64), (65), (68), (73), (258), (323) are
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #204.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | (324) all_57_9 = e1 & op(e3, e0) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (62), (246), (324) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | | #599.
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | (325) all_57_7 = e2 & op(e1, e2) = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | ALPHA: (325) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | (326) all_57_7 = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | REF_CLOSE: (4), (13), (28), (40), (41), (42), (45), (47),
% 141.34/20.74 | | | | | | | | | | | | | | | (55), (62), (76), (211), (326) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | sub-proof #310.
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | (327) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 141.34/20.74 | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | BETA: splitting (327) gives:
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | (328) all_57_8 = e2 & op(e1, e1) = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | ALPHA: (328) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | (329) op(e1, e1) = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | REF_CLOSE: (29), (52), (55), (329) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | | | sub-proof #1124.
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | (330) all_57_11 = e2 & op(e1, e0) = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | ALPHA: (330) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | (331) all_57_11 = e2
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | BETA: splitting (16) gives:
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | (332) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | & op(e1, e2) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | BETA: splitting (332) gives:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | (333) all_57_6 = e1 & op(e1, e3) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | ALPHA: (333) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (334) all_57_6 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | COMBINE_EQS: (223), (334) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (335) e3 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | COMBINE_EQS: (69), (335) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (336) all_57_8 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | COMBINE_EQS: (208), (335) imply:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (337) all_57_5 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (13), (28), (45), (47), (53), (62), (234),
% 141.34/20.74 | | | | | | | | | | | | | | | | | (336), (337) are inconsistent by sub-proof #494.
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | (338) all_57_7 = e1 & op(e1, e2) = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | ALPHA: (338) implies:
% 141.34/20.74 | | | | | | | | | | | | | | | | | (339) all_57_7 = e1
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (28), (31), (41), (45), (55), (223), (331),
% 141.34/20.74 | | | | | | | | | | | | | | | | | (339) are inconsistent by sub-proof #306.
% 141.34/20.74 | | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | (340) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 141.34/20.74 | | | | | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (13), (55), (62), (331), (340) are
% 141.34/20.74 | | | | | | | | | | | | | | | | inconsistent by sub-proof #304.
% 141.34/20.74 | | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | (341) all_57_12 = e3 & op(e0, e3) = e3
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | ALPHA: (341) implies:
% 141.34/20.74 | | | | | | | | | | | (342) all_57_12 = e3
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | BETA: splitting (20) gives:
% 141.34/20.74 | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | (343) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 141.34/20.74 | | | | | | | | | | | | & op(e2, e1) = e0)
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | BETA: splitting (343) gives:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (344) all_57_4 = e0 & op(e3, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (30), (55), (59), (344) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | sub-proof #981.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (345) all_57_5 = e0 & op(e2, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (28), (208), (345) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | #729.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | End of split
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | (346) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 141.34/20.74 | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | BETA: splitting (346) gives:
% 141.34/20.74 | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 1:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (347) all_57_8 = e0 & op(e1, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | ALPHA: (347) implies:
% 141.34/20.74 | | | | | | | | | | | | | (348) op(e1, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (8), (28), (55), (348) are inconsistent by
% 141.34/20.74 | | | | | | | | | | | | | sub-proof #308.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | Case 2:
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | (349) all_57_14 = e0 & op(e0, e1) = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | ALPHA: (349) implies:
% 141.34/20.74 | | | | | | | | | | | | | (350) all_57_14 = e0
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.74 | | | | | | | | | | | | | REF_CLOSE: (13), (15), (22), (32), (41), (45), (47), (55),
% 141.34/20.74 | | | | | | | | | | | | | (62), (342), (350) are inconsistent by sub-proof
% 141.34/20.74 | | | | | | | | | | | | | #657.
% 141.34/20.74 | | | | | | | | | | | | |
% 141.34/20.75 | | | | | | | | | | | | End of split
% 141.34/20.75 | | | | | | | | | | | |
% 141.34/20.75 | | | | | | | | | | | End of split
% 141.34/20.75 | | | | | | | | | | |
% 141.34/20.75 | | | | | | | | | | End of split
% 141.34/20.75 | | | | | | | | | |
% 141.34/20.75 | | | | | | | | | End of split
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | Case 2:
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | (351) all_57_3 = e1 & op(e2, e2) = e1
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | ALPHA: (351) implies:
% 141.34/20.75 | | | | | | | | | (352) op(e2, e2) = e1
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | REF_CLOSE: (13), (42), (55), (352) are inconsistent by
% 141.34/20.75 | | | | | | | | | sub-proof #749.
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | End of split
% 141.34/20.75 | | | | | | | |
% 141.34/20.75 | | | | | | | Case 2:
% 141.34/20.75 | | | | | | | |
% 141.34/20.75 | | | | | | | | (353) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 141.34/20.75 | | | | | | | | op(e2, e0) = e1)
% 141.34/20.75 | | | | | | | |
% 141.34/20.75 | | | | | | | | BETA: splitting (353) gives:
% 141.34/20.75 | | | | | | | |
% 141.34/20.75 | | | | | | | | Case 1:
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | (354) all_57_5 = e1 & op(e2, e1) = e1
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | REF_CLOSE: (62), (208), (354) are inconsistent by sub-proof
% 141.34/20.75 | | | | | | | | | #726.
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | Case 2:
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | (355) all_57_10 = e1 & op(e2, e0) = e1
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | ALPHA: (355) implies:
% 141.34/20.75 | | | | | | | | | (356) all_57_10 = e1
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | | REF_CLOSE: (41), (216), (356) are inconsistent by sub-proof
% 141.34/20.75 | | | | | | | | | #590.
% 141.34/20.75 | | | | | | | | |
% 141.34/20.75 | | | | | | | | End of split
% 141.34/20.75 | | | | | | | |
% 141.34/20.75 | | | | | | | End of split
% 141.34/20.75 | | | | | | |
% 141.34/20.75 | | | | | | End of split
% 141.34/20.75 | | | | | |
% 141.34/20.75 | | | | | End of split
% 141.34/20.75 | | | | |
% 141.34/20.75 | | | | Case 2:
% 141.34/20.75 | | | | |
% 141.34/20.75 | | | | | (357) all_57_3 = e3 & op(e2, e2) = e3
% 141.34/20.75 | | | | |
% 141.34/20.75 | | | | | ALPHA: (357) implies:
% 141.34/20.75 | | | | | (358) op(e2, e2) = e3
% 141.34/20.75 | | | | |
% 141.34/20.75 | | | | | REF_CLOSE: (42), (47), (55), (358) are inconsistent by sub-proof #728.
% 141.34/20.75 | | | | |
% 141.34/20.75 | | | | End of split
% 141.34/20.75 | | | |
% 141.34/20.75 | | | Case 2:
% 141.34/20.75 | | | |
% 141.34/20.75 | | | | (359) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 141.34/20.75 | | | | e2) = e3)
% 141.34/20.75 | | | |
% 141.34/20.75 | | | | REF_CLOSE: (8), (13), (15), (16), (22), (28), (29), (31), (32), (41),
% 141.34/20.75 | | | | (45), (47), (51), (52), (55), (57), (62), (359) are
% 141.34/20.75 | | | | inconsistent by sub-proof #208.
% 141.34/20.75 | | | |
% 141.34/20.75 | | | End of split
% 141.34/20.75 | | |
% 141.34/20.75 | | Case 2:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (360) all_57_10 = e3 & op(e2, e0) = e3
% 141.34/20.75 | | |
% 141.34/20.75 | | | ALPHA: (360) implies:
% 141.34/20.75 | | | (361) all_57_10 = e3
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (13), (15), (25), (28), (41), (45), (47), (55), (57), (61),
% 141.34/20.75 | | | (62), (361) are inconsistent by sub-proof #650.
% 141.34/20.75 | | |
% 141.34/20.75 | | End of split
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #204 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) op(e1, e1) = e3
% 141.34/20.75 (2) ~ (all_52_8 = e3)
% 141.34/20.75 (3) ~ (e2 = e1)
% 141.34/20.75 (4) ~ (e3 = e0)
% 141.34/20.75 (5) op(e1, e1) = all_4_2
% 141.34/20.75 (6) op(e3, e1) = all_52_8
% 141.34/20.75 (7) op(e0, e0) = e1
% 141.34/20.75 (8) ~ (all_52_8 = all_14_2)
% 141.34/20.75 (9) ~ (all_4_2 = e2)
% 141.34/20.75 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (11) op(e3, e1) = e1
% 141.34/20.75 (12) ~ (all_6_2 = e3)
% 141.34/20.75 (13) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.34/20.75 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.34/20.75 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.34/20.75 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.34/20.75 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.34/20.75 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.34/20.75 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.34/20.75 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.34/20.75 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.34/20.75 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.34/20.75 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.34/20.75 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.34/20.75 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.34/20.75 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.34/20.75 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.34/20.75 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.34/20.75 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.34/20.75 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.34/20.75 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.34/20.75 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.34/20.75 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.34/20.75 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.34/20.75 $i(all_56_14))))
% 141.34/20.75 (14) op(e2, e2) = all_6_2
% 141.34/20.75 (15) op(e3, e3) = all_14_2
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | GROUND_INST: instantiating (10) with all_52_8, e1, e1, e3, simplifying with
% 141.34/20.75 | (6), (11) gives:
% 141.34/20.75 | (16) all_52_8 = e1
% 141.34/20.75 |
% 141.34/20.75 | REDUCE: (8), (16) imply:
% 141.34/20.75 | (17) ~ (all_14_2 = e1)
% 141.34/20.75 |
% 141.34/20.75 | SIMP: (17) implies:
% 141.34/20.75 | (18) ~ (all_14_2 = e1)
% 141.34/20.75 |
% 141.34/20.75 | REDUCE: (2), (16) imply:
% 141.34/20.75 | (19) ~ (e3 = e1)
% 141.34/20.75 |
% 141.34/20.75 | SIMP: (19) implies:
% 141.34/20.75 | (20) ~ (e3 = e1)
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (13) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (21) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 141.34/20.75 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.34/20.75 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 141.34/20.75 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 141.34/20.75 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 141.34/20.75 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.34/20.75 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 141.34/20.75 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.34/20.75 | |
% 141.34/20.75 | | BETA: splitting (21) gives:
% 141.34/20.75 | |
% 141.34/20.75 | | Case 1:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (22) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 141.34/20.75 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.34/20.75 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 141.34/20.75 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (10), (12), (14), (22) are inconsistent by sub-proof #1128.
% 141.34/20.75 | | |
% 141.34/20.75 | | Case 2:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (23) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 141.34/20.75 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.34/20.75 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 141.34/20.75 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (10), (15), (18), (23) are inconsistent by sub-proof #316.
% 141.34/20.75 | | |
% 141.34/20.75 | | End of split
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (24) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.34/20.75 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.34/20.75 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.34/20.75 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 141.34/20.75 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.34/20.75 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.34/20.75 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.34/20.75 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.34/20.75 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.34/20.75 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.34/20.75 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.34/20.75 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.34/20.75 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.34/20.75 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.34/20.75 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.34/20.75 | | all_56_14 & $i(all_56_14))))
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (1), (3), (4), (5), (7), (9), (10), (20), (24) are inconsistent
% 141.34/20.75 | | by sub-proof #211.
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #205 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) ~ (e2 = e1)
% 141.34/20.75 (2) ~ (e3 = e0)
% 141.34/20.75 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.34/20.75 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.34/20.75 (4) ~ (e2 = e0)
% 141.34/20.75 (5) ~ (e3 = e2)
% 141.34/20.75 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (7) ~ (e3 = e1)
% 141.34/20.75 (8) all_57_0 = e0
% 141.34/20.75 (9) op(e3, e3) = e0
% 141.34/20.75 (10) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.34/20.75 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.34/20.75 (11) all_57_6 = e1 & op(e1, e3) = e1
% 141.34/20.75 (12) all_57_12 = e1
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | ALPHA: (11) implies:
% 141.34/20.75 | (13) all_57_6 = e1
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (10) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 141.34/20.75 | | e2)
% 141.34/20.75 | |
% 141.34/20.75 | | BETA: splitting (14) gives:
% 141.34/20.75 | |
% 141.34/20.75 | | Case 1:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (15) all_57_0 = e2 & op(e3, e3) = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | ALPHA: (15) implies:
% 141.34/20.75 | | | (16) op(e3, e3) = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (4), (6), (9), (16) are inconsistent by sub-proof #880.
% 141.34/20.75 | | |
% 141.34/20.75 | | Case 2:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (17) all_57_2 = e2 & op(e2, e3) = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | ALPHA: (17) implies:
% 141.34/20.75 | | | (18) all_57_2 = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (2), (3), (5), (7), (8), (12), (13), (18) are inconsistent by
% 141.34/20.75 | | | sub-proof #541.
% 141.34/20.75 | | |
% 141.34/20.75 | | End of split
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (19) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 141.34/20.75 | | e2)
% 141.34/20.75 | |
% 141.34/20.75 | | BETA: splitting (19) gives:
% 141.34/20.75 | |
% 141.34/20.75 | | Case 1:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (20) all_57_6 = e2 & op(e1, e3) = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | ALPHA: (20) implies:
% 141.34/20.75 | | | (21) all_57_6 = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (1), (13), (21) are inconsistent by sub-proof #700.
% 141.34/20.75 | | |
% 141.34/20.75 | | Case 2:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (22) all_57_12 = e2 & op(e0, e3) = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | ALPHA: (22) implies:
% 141.34/20.75 | | | (23) all_57_12 = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (1), (12), (23) are inconsistent by sub-proof #970.
% 141.34/20.75 | | |
% 141.34/20.75 | | End of split
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #206 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) all_57_6 = e0 & op(e1, e3) = e0
% 141.34/20.75 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (3) op(e1, e3) = all_52_2
% 141.34/20.75 (4) ~ (all_52_2 = e0)
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | ALPHA: (1) implies:
% 141.34/20.75 | (5) op(e1, e3) = e0
% 141.34/20.75 |
% 141.34/20.75 | GROUND_INST: instantiating (2) with all_52_2, e0, e3, e1, simplifying with
% 141.34/20.75 | (3), (5) gives:
% 141.34/20.75 | (6) all_52_2 = e0
% 141.34/20.75 |
% 141.34/20.75 | REDUCE: (4), (6) imply:
% 141.34/20.75 | (7) $false
% 141.34/20.75 |
% 141.34/20.75 | CLOSE: (7) is inconsistent.
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #207 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 141.34/20.75 (2) op(e2, e2) = e2
% 141.34/20.75 (3) ~ (e3 = e2)
% 141.34/20.75 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (5) all_57_1 = e2
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (1) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (6) all_57_1 = e3 & op(e3, e2) = e3
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #842.
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (7) all_57_3 = e3 & op(e2, e2) = e3
% 141.34/20.75 | |
% 141.34/20.75 | | ALPHA: (7) implies:
% 141.34/20.75 | | (8) op(e2, e2) = e3
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #728.
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #208 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) op(e1, e1) = e3
% 141.34/20.75 (2) ~ (e2 = e1)
% 141.34/20.75 (3) op(e0, e0) = e3
% 141.34/20.75 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.34/20.75 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.34/20.75 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.34/20.75 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.34/20.75 (6) ~ (e3 = e0)
% 141.34/20.75 (7) op(e1, e1) = all_4_2
% 141.34/20.75 (8) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.34/20.75 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.34/20.75 (9) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.34/20.75 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.34/20.75 (10) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.34/20.75 (11) ~ (e1 = e0)
% 141.34/20.75 (12) ~ (e2 = e0)
% 141.34/20.75 (13) ~ (e3 = e2)
% 141.34/20.75 (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.34/20.75 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.34/20.75 (15) ~ (all_4_2 = e2)
% 141.34/20.75 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (17) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.34/20.75 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.34/20.75 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.34/20.75 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.34/20.75 (18) ~ (e3 = e1)
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (10) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (19) all_57_7 = e3 & op(e1, e2) = e3
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 141.34/20.75 | | (18), (19) are inconsistent by sub-proof #233.
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (20) all_57_13 = e3 & op(e0, e2) = e3
% 141.34/20.75 | |
% 141.34/20.75 | | ALPHA: (20) implies:
% 141.34/20.75 | | (21) all_57_13 = e3
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (2), (3), (5), (6), (9), (11), (12), (13), (16), (17), (18), (21)
% 141.34/20.75 | | are inconsistent by sub-proof #252.
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #209 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) op(e1, e3) = all_8_1
% 141.34/20.75 (2) op(e1, e3) = e2
% 141.34/20.75 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (4) op(e1, e3) = all_12_1
% 141.34/20.75 (5) ~ (all_8_1 = e2)
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | GROUND_INST: instantiating (3) with e2, all_12_1, e3, e1, simplifying with
% 141.34/20.75 | (2), (4) gives:
% 141.34/20.75 | (6) all_12_1 = e2
% 141.34/20.75 |
% 141.34/20.75 | GROUND_INST: instantiating (3) with all_8_1, all_12_1, e3, e1, simplifying
% 141.34/20.75 | with (1), (4) gives:
% 141.34/20.75 | (7) all_12_1 = all_8_1
% 141.34/20.75 |
% 141.34/20.75 | COMBINE_EQS: (6), (7) imply:
% 141.34/20.75 | (8) all_8_1 = e2
% 141.34/20.75 |
% 141.34/20.75 | REDUCE: (5), (8) imply:
% 141.34/20.75 | (9) $false
% 141.34/20.75 |
% 141.34/20.75 | CLOSE: (9) is inconsistent.
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #210 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) op(e1, e1) = e3
% 141.34/20.75 (2) ~ (e2 = e1)
% 141.34/20.75 (3) ~ (e3 = e0)
% 141.34/20.75 (4) op(e1, e1) = all_4_2
% 141.34/20.75 (5) op(e0, e0) = e1
% 141.34/20.75 (6) ~ (e1 = e0)
% 141.34/20.75 (7) ~ (e2 = e0)
% 141.34/20.75 (8) ~ (all_4_2 = e2)
% 141.34/20.75 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (10) ~ (e3 = e1)
% 141.34/20.75 (11) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.34/20.75 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.34/20.75 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.34/20.75 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.34/20.75 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.34/20.75 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.34/20.75 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.34/20.75 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.34/20.75 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.34/20.75 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.34/20.75 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.34/20.75 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.34/20.75 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.34/20.75 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.34/20.75 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.34/20.75 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.34/20.75 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.34/20.75 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.34/20.75 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.34/20.75 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.34/20.75 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.34/20.75 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.34/20.75 $i(all_56_14))))
% 141.34/20.75 (12) op(e3, e3) = e0
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (11) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (13) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 141.34/20.75 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.34/20.75 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 141.34/20.75 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 141.34/20.75 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 141.34/20.75 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.34/20.75 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 141.34/20.75 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (6), (7), (9), (12), (13) are inconsistent by sub-proof #752.
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (14) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.34/20.75 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.34/20.75 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.34/20.75 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 141.34/20.75 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.34/20.75 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.34/20.75 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.34/20.75 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.34/20.75 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.34/20.75 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.34/20.75 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.34/20.75 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.34/20.75 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.34/20.75 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.34/20.75 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.34/20.75 | | all_56_14 & $i(all_56_14))))
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (14) are inconsistent by
% 141.34/20.75 | | sub-proof #211.
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #211 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) op(e1, e1) = e3
% 141.34/20.75 (2) ~ (e2 = e1)
% 141.34/20.75 (3) ~ (e3 = e0)
% 141.34/20.75 (4) op(e1, e1) = all_4_2
% 141.34/20.75 (5) op(e0, e0) = e1
% 141.34/20.75 (6) ~ (all_4_2 = e2)
% 141.34/20.75 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (8) ~ (e3 = e1)
% 141.34/20.75 (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.34/20.75 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.34/20.75 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.34/20.75 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.34/20.75 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.34/20.75 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.34/20.75 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.34/20.75 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.34/20.75 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.34/20.75 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.34/20.75 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.34/20.75 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.34/20.75 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.34/20.75 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.34/20.75 $i(all_56_14))))
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (9) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.34/20.75 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.34/20.75 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.34/20.75 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (4), (5), (6), (7), (8), (10) are inconsistent by sub-proof #462.
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (11) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.34/20.75 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.34/20.75 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.34/20.75 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.34/20.75 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.34/20.75 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.34/20.75 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.34/20.75 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.34/20.75 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.34/20.75 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.34/20.75 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.34/20.75 | | all_56_14 & $i(all_56_14))))
% 141.34/20.75 | |
% 141.34/20.75 | | BETA: splitting (11) gives:
% 141.34/20.75 | |
% 141.34/20.75 | | Case 1:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (12) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 141.34/20.75 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.34/20.75 | | |
% 141.34/20.75 | | | ALPHA: (12) implies:
% 141.34/20.75 | | | (13) op(e1, e1) = e2
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (4), (6), (7), (13) are inconsistent by sub-proof #1124.
% 141.34/20.75 | | |
% 141.34/20.75 | | Case 2:
% 141.34/20.75 | | |
% 141.34/20.75 | | | (14) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 141.34/20.75 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.34/20.75 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.34/20.75 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.34/20.75 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.34/20.75 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.34/20.75 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.34/20.75 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.34/20.75 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.34/20.75 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.34/20.75 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.34/20.75 | | |
% 141.34/20.75 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (14) are inconsistent by
% 141.34/20.75 | | | sub-proof #277.
% 141.34/20.75 | | |
% 141.34/20.75 | | End of split
% 141.34/20.75 | |
% 141.34/20.75 | End of split
% 141.34/20.75 |
% 141.34/20.75 End of proof
% 141.34/20.75
% 141.34/20.75 Sub-proof #212 shows that the following formulas are inconsistent:
% 141.34/20.75 ----------------------------------------------------------------
% 141.34/20.75 (1) op(e0, e0) = e3
% 141.34/20.75 (2) op(e0, e3) = all_52_3
% 141.34/20.75 (3) ~ (e2 = e0)
% 141.34/20.75 (4) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.34/20.75 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.34/20.75 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.34/20.75 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.34/20.75 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.34/20.75 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.34/20.75 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.34/20.75 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.34/20.75 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.34/20.75 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.34/20.75 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.34/20.75 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.34/20.75 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.34/20.75 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.34/20.75 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.34/20.75 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.34/20.75 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.34/20.75 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.34/20.75 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.34/20.75 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12))))
% 141.34/20.75 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.75 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.75 (6) ~ (all_52_3 = e0)
% 141.34/20.75 (7) op(e3, e2) = e3
% 141.34/20.75 (8) op(e3, e3) = e0
% 141.34/20.75
% 141.34/20.75 Begin of proof
% 141.34/20.75 |
% 141.34/20.75 | BETA: splitting (4) gives:
% 141.34/20.75 |
% 141.34/20.75 | Case 1:
% 141.34/20.75 | |
% 141.34/20.75 | | (9) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.34/20.75 | | e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.34/20.75 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.34/20.75 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.34/20.75 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.34/20.75 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.34/20.75 | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.34/20.75 | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.34/20.75 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.34/20.75 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.34/20.75 | | e3) = all_56_10 & $i(all_56_10)))
% 141.34/20.75 | |
% 141.34/20.75 | | ALPHA: (9) implies:
% 141.34/20.75 | | (10) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.34/20.75 | | e0) = all_56_15 & $i(all_56_15))
% 141.34/20.75 | |
% 141.34/20.75 | | REF_CLOSE: (1), (2), (5), (6), (10) are inconsistent by sub-proof #739.
% 141.34/20.75 | |
% 141.34/20.75 | Case 2:
% 141.34/20.75 | |
% 141.34/20.75 | | (11) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 141.34/20.75 | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.34/20.75 | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 141.34/20.75 | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.34/20.75 | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.34/20.75 | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.34/20.76 | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.34/20.76 | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.34/20.76 | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.34/20.76 | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 141.34/20.76 | | e2) = all_56_12 & $i(all_56_12)))
% 141.34/20.76 | |
% 141.34/20.76 | | ALPHA: (11) implies:
% 141.34/20.76 | | (12) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2)
% 141.34/20.76 | | = all_56_0 & $i(all_56_0))
% 141.34/20.76 | |
% 141.34/20.76 | | BETA: splitting (12) gives:
% 141.34/20.76 | |
% 141.34/20.76 | | Case 1:
% 141.34/20.76 | | |
% 141.34/20.76 | | | (13) all_56_9 = e2 & op(e3, e3) = e2
% 141.34/20.76 | | |
% 141.34/20.76 | | | ALPHA: (13) implies:
% 141.34/20.76 | | | (14) op(e3, e3) = e2
% 141.34/20.76 | | |
% 141.34/20.76 | | | REF_CLOSE: (3), (5), (8), (14) are inconsistent by sub-proof #880.
% 141.34/20.76 | | |
% 141.34/20.76 | | Case 2:
% 141.34/20.76 | | |
% 141.34/20.76 | | | (15) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0)
% 141.34/20.76 | | |
% 141.34/20.76 | | | ALPHA: (15) implies:
% 141.34/20.76 | | | (16) ~ (all_56_0 = e3)
% 141.34/20.76 | | | (17) op(e3, e2) = all_56_0
% 141.34/20.76 | | |
% 141.34/20.76 | | | REF_CLOSE: (5), (7), (16), (17) are inconsistent by sub-proof #670.
% 141.34/20.76 | | |
% 141.34/20.76 | | End of split
% 141.34/20.76 | |
% 141.34/20.76 | End of split
% 141.34/20.76 |
% 141.34/20.76 End of proof
% 141.34/20.76
% 141.34/20.76 Sub-proof #213 shows that the following formulas are inconsistent:
% 141.34/20.76 ----------------------------------------------------------------
% 141.34/20.76 (1) ~ (all_52_8 = all_52_11)
% 141.34/20.76 (2) ~ (all_52_8 = all_52_9)
% 141.34/20.76 (3) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.34/20.76 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.34/20.76 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.34/20.76 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.34/20.76 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.34/20.76 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.34/20.76 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.34/20.76 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.34/20.76 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.34/20.76 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.34/20.76 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.34/20.76 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.34/20.76 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.34/20.76 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.34/20.76 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.34/20.76 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.34/20.76 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.34/20.76 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.34/20.76 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.34/20.76 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.34/20.76 (4) ~ (e2 = e1)
% 141.34/20.76 (5) ~ (all_52_11 = e2)
% 141.34/20.76 (6) ~ (all_52_9 = all_52_11)
% 141.34/20.76 (7) op(e3, e1) = all_52_8
% 141.34/20.76 (8) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 141.34/20.76 (9) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 141.34/20.76 (10) ~ (e1 = e0)
% 141.34/20.76 (11) op(e0, e1) = all_52_11
% 141.34/20.76 (12) op(e3, e3) = e1
% 141.34/20.76 (13) op(e0, e0) = e2
% 141.34/20.76 (14) all_54_14 = all_52_11
% 141.34/20.76 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.76 (16) ~ (all_52_13 = e2)
% 141.34/20.76 (17) op(e2, e2) = e0
% 141.34/20.76 (18) op(e2, e1) = all_52_9
% 141.34/20.76 (19) all_54_6 = all_52_9
% 141.34/20.76 (20) op(e2, e0) = all_52_13
% 141.34/20.76 (21) ~ (all_52_9 = e0)
% 141.34/20.76
% 141.34/20.76 Begin of proof
% 141.34/20.76 |
% 141.34/20.76 | BETA: splitting (3) gives:
% 141.34/20.76 |
% 141.34/20.76 | Case 1:
% 141.34/20.76 | |
% 141.34/20.76 | | (22) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.34/20.76 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.34/20.76 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.34/20.76 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.34/20.76 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.34/20.76 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.34/20.76 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.34/20.76 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.34/20.76 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.34/20.76 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 141.34/20.76 | | e1) = all_56_14 & $i(all_56_14)))
% 141.34/20.76 | |
% 141.34/20.76 | | ALPHA: (22) implies:
% 141.34/20.76 | | (23) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 141.34/20.76 | | e1) = all_56_14 & $i(all_56_14))
% 141.34/20.76 | | (24) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 141.34/20.76 | | e1) = all_56_4 & $i(all_56_4))
% 141.34/20.76 | | (25) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3)
% 141.34/20.76 | | = all_56_9 & $i(all_56_9))
% 141.34/20.76 | |
% 141.34/20.76 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.34/20.76 | | (14), (15), (17), (18), (19), (21), (23), (24), (25) are
% 141.34/20.76 | | inconsistent by sub-proof #756.
% 141.34/20.76 | |
% 141.34/20.76 | Case 2:
% 141.34/20.76 | |
% 141.34/20.76 | | (26) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.34/20.76 | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.34/20.76 | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.34/20.76 | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.34/20.76 | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.34/20.76 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.34/20.76 | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.34/20.76 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.34/20.76 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.34/20.76 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.34/20.76 | | e0) = all_56_8 & $i(all_56_8)))
% 141.34/20.76 | |
% 141.34/20.76 | | ALPHA: (26) implies:
% 141.34/20.76 | | (27) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.34/20.76 | | e2) = all_56_11 & $i(all_56_11))
% 141.34/20.76 | |
% 141.34/20.76 | | REF_CLOSE: (15), (16), (17), (20), (27) are inconsistent by sub-proof #856.
% 141.34/20.76 | |
% 141.34/20.76 | End of split
% 141.34/20.76 |
% 141.34/20.76 End of proof
% 141.34/20.76
% 141.34/20.76 Sub-proof #214 shows that the following formulas are inconsistent:
% 141.34/20.76 ----------------------------------------------------------------
% 141.34/20.76 (1) op(e1, e3) = all_52_2
% 141.34/20.76 (2) op(e1, e1) = e3
% 141.34/20.76 (3) ~ (all_52_2 = e1)
% 141.34/20.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.34/20.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.34/20.76 (5) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) = e2)
% 141.34/20.76 | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.34/20.76 ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.34/20.76 all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 141.34/20.76 ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.34/20.76 ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.34/20.76 all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.34/20.76 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.34/20.76 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.34/20.76 all_56_10 & $i(all_56_10)))
% 141.34/20.76
% 141.34/20.76 Begin of proof
% 141.34/20.76 |
% 141.34/20.76 | ALPHA: (5) implies:
% 141.34/20.76 | (6) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.34/20.76 | all_56_13 & $i(all_56_13))
% 141.34/20.76 |
% 141.34/20.76 | BETA: splitting (6) gives:
% 141.34/20.76 |
% 141.34/20.76 | Case 1:
% 141.34/20.76 | |
% 141.34/20.76 | | (7) all_56_6 = e1 & op(e1, e3) = e1
% 141.34/20.76 | |
% 141.34/20.76 | | ALPHA: (7) implies:
% 141.34/20.76 | | (8) op(e1, e3) = e1
% 141.34/20.76 | |
% 141.34/20.76 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #332.
% 141.34/20.76 | |
% 141.34/20.76 | Case 2:
% 141.34/20.76 | |
% 141.34/20.76 | | (9) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.34/20.76 | |
% 141.34/20.76 | | ALPHA: (9) implies:
% 141.34/20.76 | | (10) ~ (all_56_13 = e3)
% 141.34/20.76 | | (11) op(e1, e1) = all_56_13
% 141.34/20.76 | |
% 141.34/20.76 | | REF_CLOSE: (2), (4), (10), (11) are inconsistent by sub-proof #230.
% 141.34/20.76 | |
% 141.34/20.76 | End of split
% 141.34/20.76 |
% 141.34/20.76 End of proof
% 141.34/20.76
% 141.34/20.76 Sub-proof #215 shows that the following formulas are inconsistent:
% 141.34/20.76 ----------------------------------------------------------------
% 141.34/20.76 (1) all_54_11 = all_52_14
% 141.34/20.76 (2) all_54_11 = e2
% 141.34/20.76 (3) ~ (all_52_14 = e2)
% 141.34/20.76
% 141.34/20.76 Begin of proof
% 141.34/20.76 |
% 141.34/20.76 | COMBINE_EQS: (1), (2) imply:
% 141.34/20.76 | (4) all_52_14 = e2
% 141.34/20.76 |
% 141.34/20.76 | SIMP: (4) implies:
% 141.34/20.76 | (5) all_52_14 = e2
% 141.34/20.76 |
% 141.34/20.76 | REDUCE: (3), (5) imply:
% 141.34/20.76 | (6) $false
% 141.34/20.76 |
% 141.34/20.76 | CLOSE: (6) is inconsistent.
% 141.34/20.76 |
% 141.34/20.76 End of proof
% 141.34/20.76
% 141.34/20.76 Sub-proof #216 shows that the following formulas are inconsistent:
% 141.34/20.76 ----------------------------------------------------------------
% 141.34/20.76 (1) all_54_11 = all_52_14
% 141.34/20.76 (2) all_54_11 = e3
% 141.34/20.76 (3) ~ (all_52_14 = e3)
% 141.34/20.76
% 141.34/20.76 Begin of proof
% 141.34/20.76 |
% 141.34/20.76 | COMBINE_EQS: (1), (2) imply:
% 141.34/20.76 | (4) all_52_14 = e3
% 141.34/20.76 |
% 141.34/20.76 | SIMP: (4) implies:
% 141.34/20.76 | (5) all_52_14 = e3
% 141.34/20.76 |
% 141.34/20.76 | REDUCE: (3), (5) imply:
% 141.34/20.76 | (6) $false
% 141.34/20.76 |
% 141.34/20.76 | CLOSE: (6) is inconsistent.
% 141.34/20.76 |
% 141.34/20.76 End of proof
% 141.34/20.76
% 141.34/20.76 Sub-proof #217 shows that the following formulas are inconsistent:
% 141.34/20.76 ----------------------------------------------------------------
% 141.43/20.76 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.43/20.76 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.43/20.76 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.43/20.76 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.43/20.76 (2) ~ (e1 = e0)
% 141.43/20.76 (3) op(e3, e3) = e1
% 141.43/20.76 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.76 (5) op(e2, e2) = e0
% 141.43/20.76
% 141.43/20.76 Begin of proof
% 141.43/20.76 |
% 141.43/20.76 | BETA: splitting (1) gives:
% 141.43/20.76 |
% 141.43/20.76 | Case 1:
% 141.43/20.76 | |
% 141.43/20.76 | | (6) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 141.43/20.76 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.43/20.76 | |
% 141.43/20.76 | | ALPHA: (6) implies:
% 141.43/20.76 | | (7) op(e3, e3) = e0
% 141.43/20.76 | |
% 141.43/20.76 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #840.
% 141.43/20.76 | |
% 141.43/20.76 | Case 2:
% 141.43/20.76 | |
% 141.43/20.76 | | (8) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.43/20.76 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 141.43/20.76 | |
% 141.43/20.76 | | ALPHA: (8) implies:
% 141.43/20.76 | | (9) op(e2, e2) = e1
% 141.43/20.76 | |
% 141.43/20.76 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1117.
% 141.43/20.76 | |
% 141.43/20.76 | End of split
% 141.43/20.76 |
% 141.43/20.76 End of proof
% 141.43/20.76
% 141.43/20.76 Sub-proof #218 shows that the following formulas are inconsistent:
% 141.43/20.76 ----------------------------------------------------------------
% 141.43/20.76 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.43/20.76 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.43/20.76 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.43/20.76 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.76 (3) ~ (all_52_8 = e3)
% 141.43/20.76 (4) ~ (all_52_4 = e0)
% 141.43/20.76 (5) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.76 (6) ~ (all_52_9 = all_52_13)
% 141.43/20.76 (7) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.76 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.76 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.76 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.76 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.43/20.76 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.43/20.76 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.43/20.76 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.43/20.76 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.43/20.76 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.43/20.76 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.43/20.76 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.76 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.43/20.76 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.43/20.76 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.76 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.43/20.76 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.43/20.76 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.43/20.76 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.43/20.76 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.76 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.76 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.76 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.76 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.76 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.76 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.76 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.76 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.43/20.76 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.43/20.76 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.43/20.76 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.43/20.76 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.76 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.43/20.76 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.43/20.76 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.76 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.43/20.76 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.76 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.76 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.43/20.76 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.76 (8) ~ (all_52_1 = e3)
% 141.43/20.76 (9) ~ (all_10_2 = e1)
% 141.43/20.76 (10) all_57_4 = e0
% 141.43/20.76 (11) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.76 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.43/20.76 e1)
% 141.43/20.76 (12) ~ (all_52_1 = e1)
% 141.43/20.76 (13) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.43/20.76 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.43/20.76 (14) ~ (all_52_1 = e0)
% 141.43/20.76 (15) ~ (e3 = e0)
% 141.43/20.76 (16) op(e1, e1) = all_4_2
% 141.43/20.76 (17) op(e3, e1) = all_52_8
% 141.43/20.76 (18) ~ (all_52_1 = all_52_13)
% 141.43/20.76 (19) op(e2, e3) = all_52_1
% 141.43/20.76 (20) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 141.43/20.76 (21) op(e0, e0) = all_10_2
% 141.43/20.76 (22) op(e3, e2) = all_52_4
% 141.43/20.76 (23) ~ (all_52_1 = all_52_9)
% 141.43/20.76 (24) op(e3, e3) = e1
% 141.43/20.76 (25) ~ (all_4_2 = e2)
% 141.43/20.76 (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.76 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.76 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.76 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.76 (28) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.76 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.76 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.76 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.76 (29) ~ (all_52_9 = e3)
% 141.43/20.76 (30) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.43/20.76 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.43/20.76 (31) all_54_4 = all_52_1
% 141.43/20.76 (32) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.76 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.76 (33) op(e2, e2) = e0
% 141.43/20.76 (34) op(e2, e1) = all_52_9
% 141.43/20.76 (35) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.76 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.76 (36) all_54_6 = all_52_9
% 141.43/20.76 (37) op(e2, e0) = all_52_13
% 141.43/20.76 (38) ~ (all_52_9 = e0)
% 141.43/20.76
% 141.43/20.76 Begin of proof
% 141.43/20.76 |
% 141.43/20.76 | BETA: splitting (5) gives:
% 141.43/20.76 |
% 141.43/20.76 | Case 1:
% 141.43/20.76 | |
% 141.43/20.76 | | (39) all_54_4 = e3
% 141.43/20.76 | |
% 141.43/20.76 | | REF_CLOSE: (8), (31), (39) are inconsistent by sub-proof #796.
% 141.43/20.76 | |
% 141.43/20.76 | Case 2:
% 141.43/20.76 | |
% 141.43/20.76 | | (40) ~ (all_54_4 = e3)
% 141.43/20.76 | | (41) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.76 | |
% 141.43/20.76 | | BETA: splitting (41) gives:
% 141.43/20.76 | |
% 141.43/20.76 | | Case 1:
% 141.43/20.76 | | |
% 141.43/20.76 | | | (42) all_54_4 = e2
% 141.43/20.76 | | |
% 141.43/20.76 | | | COMBINE_EQS: (31), (42) imply:
% 141.43/20.76 | | | (43) all_52_1 = e2
% 141.43/20.76 | | |
% 141.43/20.76 | | | SIMP: (43) implies:
% 141.43/20.76 | | | (44) all_52_1 = e2
% 141.43/20.76 | | |
% 141.43/20.76 | | | REDUCE: (23), (44) imply:
% 141.43/20.76 | | | (45) ~ (all_52_9 = e2)
% 141.43/20.76 | | |
% 141.43/20.76 | | | SIMP: (45) implies:
% 141.43/20.76 | | | (46) ~ (all_52_9 = e2)
% 141.43/20.76 | | |
% 141.43/20.76 | | | REDUCE: (18), (44) imply:
% 141.43/20.76 | | | (47) ~ (all_52_13 = e2)
% 141.43/20.76 | | |
% 141.43/20.76 | | | SIMP: (47) implies:
% 141.43/20.76 | | | (48) ~ (all_52_13 = e2)
% 141.43/20.76 | | |
% 141.43/20.76 | | | REDUCE: (8), (44) imply:
% 141.43/20.76 | | | (49) ~ (e3 = e2)
% 141.43/20.76 | | |
% 141.43/20.76 | | | SIMP: (49) implies:
% 141.43/20.76 | | | (50) ~ (e3 = e2)
% 141.43/20.76 | | |
% 141.43/20.76 | | | REDUCE: (14), (44) imply:
% 141.43/20.76 | | | (51) ~ (e2 = e0)
% 141.43/20.76 | | |
% 141.43/20.76 | | | REDUCE: (19), (44) imply:
% 141.43/20.76 | | | (52) op(e2, e3) = e2
% 141.43/20.76 | | |
% 141.43/20.76 | | | BETA: splitting (20) gives:
% 141.43/20.76 | | |
% 141.43/20.76 | | | Case 1:
% 141.43/20.76 | | | |
% 141.43/20.76 | | | | (53) all_54_6 = e3
% 141.43/20.76 | | | |
% 141.43/20.76 | | | | REF_CLOSE: (29), (36), (53) are inconsistent by sub-proof #763.
% 141.43/20.76 | | | |
% 141.43/20.76 | | | Case 2:
% 141.43/20.76 | | | |
% 141.43/20.76 | | | | (54) ~ (all_54_6 = e3)
% 141.43/20.76 | | | | (55) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 141.43/20.76 | | | |
% 141.43/20.76 | | | | BETA: splitting (55) gives:
% 141.43/20.76 | | | |
% 141.43/20.76 | | | | Case 1:
% 141.43/20.76 | | | | |
% 141.43/20.76 | | | | | (56) all_54_6 = e2
% 141.43/20.76 | | | | |
% 141.43/20.76 | | | | | REF_CLOSE: (36), (46), (56) are inconsistent by sub-proof #762.
% 141.43/20.76 | | | | |
% 141.43/20.76 | | | | Case 2:
% 141.43/20.76 | | | | |
% 141.43/20.76 | | | | | (57) ~ (all_54_6 = e2)
% 141.43/20.76 | | | | | (58) all_54_6 = e1 | all_54_6 = e0
% 141.43/20.76 | | | | |
% 141.43/20.76 | | | | | BETA: splitting (7) gives:
% 141.43/20.76 | | | | |
% 141.43/20.76 | | | | | Case 1:
% 141.43/20.76 | | | | | |
% 141.43/20.76 | | | | | | (59) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 141.43/20.76 | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 141.43/20.76 | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 141.43/20.76 | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.43/20.76 | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 141.43/20.76 | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.43/20.76 | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.43/20.76 | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.43/20.76 | | | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1,
% 141.43/20.76 | | | | | | e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.43/20.76 | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 141.43/20.76 | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.43/20.76 | | | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11
% 141.43/20.76 | | | | | | & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 141.43/20.76 | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.43/20.76 | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) |
% 141.43/20.76 | | | | | | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.76 | | | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) |
% 141.43/20.76 | | | | | | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.76 | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) |
% 141.43/20.76 | | | | | | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.43/20.76 | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2)
% 141.43/20.76 | | | | | | | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.76 | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.43/20.76 | | | | | | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.43/20.76 | | | | | | $i(all_56_12))))
% 141.43/20.76 | | | | | |
% 141.43/20.76 | | | | | | BETA: splitting (59) gives:
% 141.43/20.76 | | | | | |
% 141.43/20.76 | | | | | | Case 1:
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | (60) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 141.43/20.76 | | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 141.43/20.76 | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 141.43/20.76 | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.43/20.76 | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 141.43/20.76 | | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.43/20.76 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.43/20.76 | | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.43/20.76 | | | | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1,
% 141.43/20.76 | | | | | | | e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.43/20.76 | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 141.43/20.76 | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.43/20.76 | | | | | | | all_56_10 & $i(all_56_10)))
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | ALPHA: (60) implies:
% 141.43/20.76 | | | | | | | (61) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) &
% 141.43/20.76 | | | | | | | op(e2, e3) = all_56_3 & $i(all_56_3))
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | REF_CLOSE: (15), (27), (33), (52), (61) are inconsistent by
% 141.43/20.76 | | | | | | | sub-proof #978.
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | Case 2:
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | (62) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 141.43/20.76 | | | | | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.43/20.76 | | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 141.43/20.76 | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 141.43/20.76 | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.43/20.76 | | | | | | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 141.43/20.76 | | | | | | | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.43/20.76 | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 141.43/20.76 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 &
% 141.43/20.76 | | | | | | | op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 141.43/20.76 | | | | | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.43/20.76 | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 141.43/20.76 | | | | | | | all_56_12 & $i(all_56_12)))
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | ALPHA: (62) implies:
% 141.43/20.76 | | | | | | | (63) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 141.43/20.76 | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | BETA: splitting (26) gives:
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | | (64) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 141.43/20.76 | | | | | | | | op(e2, e1) = e2)
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | | BETA: splitting (64) gives:
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | (65) all_57_4 = e2 & op(e3, e1) = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | ALPHA: (65) implies:
% 141.43/20.76 | | | | | | | | | (66) all_57_4 = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | COMBINE_EQS: (10), (66) imply:
% 141.43/20.76 | | | | | | | | | (67) e2 = e0
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | REDUCE: (51), (67) imply:
% 141.43/20.76 | | | | | | | | | (68) $false
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | CLOSE: (68) is inconsistent.
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | (69) all_57_5 = e2 & op(e2, e1) = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | ALPHA: (69) implies:
% 141.43/20.76 | | | | | | | | | (70) op(e2, e1) = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | REF_CLOSE: (27), (34), (46), (70) are inconsistent by
% 141.43/20.76 | | | | | | | | | sub-proof #890.
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | End of split
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | | (71) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 141.43/20.76 | | | | | | | | op(e0, e1) = e2)
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | | BETA: splitting (71) gives:
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | (72) all_57_8 = e2 & op(e1, e1) = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | ALPHA: (72) implies:
% 141.43/20.76 | | | | | | | | | (73) op(e1, e1) = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | REF_CLOSE: (16), (25), (27), (73) are inconsistent by
% 141.43/20.76 | | | | | | | | | sub-proof #1124.
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | (74) all_57_14 = e2 & op(e0, e1) = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | ALPHA: (74) implies:
% 141.43/20.76 | | | | | | | | | (75) all_57_14 = e2
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | BETA: splitting (58) gives:
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | (76) all_54_6 = e1
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | COMBINE_EQS: (36), (76) imply:
% 141.43/20.76 | | | | | | | | | | (77) all_52_9 = e1
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | SIMP: (77) implies:
% 141.43/20.76 | | | | | | | | | | (78) all_52_9 = e1
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | REDUCE: (6), (78) imply:
% 141.43/20.76 | | | | | | | | | | (79) ~ (all_52_13 = e1)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | SIMP: (79) implies:
% 141.43/20.76 | | | | | | | | | | (80) ~ (all_52_13 = e1)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | REDUCE: (29), (78) imply:
% 141.43/20.76 | | | | | | | | | | (81) ~ (e3 = e1)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | SIMP: (81) implies:
% 141.43/20.76 | | | | | | | | | | (82) ~ (e3 = e1)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | REDUCE: (46), (78) imply:
% 141.43/20.76 | | | | | | | | | | (83) ~ (e2 = e1)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | SIMP: (83) implies:
% 141.43/20.76 | | | | | | | | | | (84) ~ (e2 = e1)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | REDUCE: (38), (78) imply:
% 141.43/20.76 | | | | | | | | | | (85) ~ (e1 = e0)
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | BETA: splitting (30) gives:
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | (86) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 141.43/20.76 | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | BETA: splitting (86) gives:
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | (87) all_57_9 = e1 & op(e3, e0) = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | ALPHA: (87) implies:
% 141.43/20.76 | | | | | | | | | | | | (88) all_57_9 = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | REF_CLOSE: (1), (4), (15), (22), (24), (27), (32), (35),
% 141.43/20.76 | | | | | | | | | | | | (50), (51), (82), (84), (85), (88) are
% 141.43/20.76 | | | | | | | | | | | | inconsistent by sub-proof #812.
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | (89) all_57_10 = e1 & op(e2, e0) = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | REF_CLOSE: (27), (37), (80), (89) are inconsistent by
% 141.43/20.76 | | | | | | | | | | | | sub-proof #460.
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | End of split
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | (90) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 141.43/20.76 | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | BETA: splitting (90) gives:
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | (91) all_57_11 = e1 & op(e1, e0) = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | ALPHA: (91) implies:
% 141.43/20.76 | | | | | | | | | | | | (92) all_57_11 = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | BETA: splitting (32) gives:
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | (93) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 141.43/20.76 | | | | | | | | | | | | | & op(e3, e2) = e3)
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | Case 1:
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | | (94) all_57_0 = e3 & op(e3, e3) = e3
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | | ALPHA: (94) implies:
% 141.43/20.76 | | | | | | | | | | | | | | (95) op(e3, e3) = e3
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (82), (95) are inconsistent by
% 141.43/20.76 | | | | | | | | | | | | | | sub-proof #838.
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | | (96) all_57_1 = e3 & op(e3, e2) = e3
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | | ALPHA: (96) implies:
% 141.43/20.76 | | | | | | | | | | | | | | (97) op(e3, e2) = e3
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | | REF_CLOSE: (24), (27), (63), (84), (97) are inconsistent by
% 141.43/20.76 | | | | | | | | | | | | | | sub-proof #296.
% 141.43/20.76 | | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | End of split
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | (98) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 141.43/20.76 | | | | | | | | | | | | | & op(e3, e0) = e3)
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | | REF_CLOSE: (2), (3), (11), (13), (15), (17), (27), (28),
% 141.43/20.76 | | | | | | | | | | | | | (37), (48), (50), (51), (75), (82), (84), (85),
% 141.43/20.76 | | | | | | | | | | | | | (92), (98) are inconsistent by sub-proof #292.
% 141.43/20.76 | | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | End of split
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | (99) all_57_15 = e1 & op(e0, e0) = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | ALPHA: (99) implies:
% 141.43/20.76 | | | | | | | | | | | | (100) op(e0, e0) = e1
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | | REF_CLOSE: (9), (21), (27), (100) are inconsistent by
% 141.43/20.76 | | | | | | | | | | | | sub-proof #237.
% 141.43/20.76 | | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | | End of split
% 141.43/20.76 | | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | End of split
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | Case 2:
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | (101) all_54_6 = e0
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | | REF_CLOSE: (36), (38), (101) are inconsistent by sub-proof
% 141.43/20.76 | | | | | | | | | | #759.
% 141.43/20.76 | | | | | | | | | |
% 141.43/20.76 | | | | | | | | | End of split
% 141.43/20.76 | | | | | | | | |
% 141.43/20.76 | | | | | | | | End of split
% 141.43/20.76 | | | | | | | |
% 141.43/20.76 | | | | | | | End of split
% 141.43/20.76 | | | | | | |
% 141.43/20.76 | | | | | | End of split
% 141.43/20.76 | | | | | |
% 141.43/20.76 | | | | | Case 2:
% 141.43/20.76 | | | | | |
% 141.43/20.77 | | | | | | (102) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.43/20.77 | | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.43/20.77 | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 141.43/20.77 | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 141.43/20.77 | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 &
% 141.43/20.77 | | | | | | op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 141.43/20.77 | | | | | | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.43/20.77 | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.43/20.77 | | | | | | all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 141.43/20.77 | | | | | | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.43/20.77 | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 &
% 141.43/20.77 | | | | | | op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1)
% 141.43/20.77 | | | | | | = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.43/20.77 | | | | | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0)
% 141.43/20.77 | | | | | | = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.43/20.77 | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.77 | | | | | | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 141.43/20.77 | | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1)
% 141.43/20.77 | | | | | | | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.77 | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.77 | | | | | | | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.43/20.77 | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0)
% 141.43/20.77 | | | | | | | ( ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.43/20.77 | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.77 | | | | | | | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.43/20.77 | | | | | | $i(all_56_8))))
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | BETA: splitting (102) gives:
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | Case 1:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | (103) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3
% 141.43/20.77 | | | | | | | & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3)
% 141.43/20.77 | | | | | | | = all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 &
% 141.43/20.77 | | | | | | | op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2)
% 141.43/20.77 | | | | | | | = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 &
% 141.43/20.77 | | | | | | | op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 141.43/20.77 | | | | | | | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.43/20.77 | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 141.43/20.77 | | | | | | | all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 141.43/20.77 | | | | | | | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.43/20.77 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 &
% 141.43/20.77 | | | | | | | op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1)
% 141.43/20.77 | | | | | | | = all_56_14 & $i(all_56_14)))
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | ALPHA: (103) implies:
% 141.43/20.77 | | | | | | | (104) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) &
% 141.43/20.77 | | | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | REF_CLOSE: (3), (17), (24), (27), (104) are inconsistent by
% 141.43/20.77 | | | | | | | sub-proof #295.
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | Case 2:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | (105) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3
% 141.43/20.77 | | | | | | | & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.77 | | | | | | | = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 &
% 141.43/20.77 | | | | | | | op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2)
% 141.43/20.77 | | | | | | | = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 &
% 141.43/20.77 | | | | | | | op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.77 | | | | | | | = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 &
% 141.43/20.77 | | | | | | | op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.43/20.77 | | | | | | | all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2,
% 141.43/20.77 | | | | | | | e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 141.43/20.77 | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.43/20.77 | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.43/20.77 | | | | | | | all_56_8 & $i(all_56_8)))
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | ALPHA: (105) implies:
% 141.43/20.77 | | | | | | | (106) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0)
% 141.43/20.77 | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | REF_CLOSE: (27), (33), (37), (48), (106) are inconsistent by
% 141.43/20.77 | | | | | | | sub-proof #856.
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | End of split
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | End of split
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | End of split
% 141.43/20.77 | | | |
% 141.43/20.77 | | | End of split
% 141.43/20.77 | | |
% 141.43/20.77 | | Case 2:
% 141.43/20.77 | | |
% 141.43/20.77 | | | (107) all_54_4 = e1 | all_54_4 = e0
% 141.43/20.77 | | |
% 141.43/20.77 | | | REF_CLOSE: (12), (14), (31), (107) are inconsistent by sub-proof #793.
% 141.43/20.77 | | |
% 141.43/20.77 | | End of split
% 141.43/20.77 | |
% 141.43/20.77 | End of split
% 141.43/20.77 |
% 141.43/20.77 End of proof
% 141.43/20.77
% 141.43/20.77 Sub-proof #219 shows that the following formulas are inconsistent:
% 141.43/20.77 ----------------------------------------------------------------
% 141.43/20.77 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.77 (2) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.43/20.77 (3) op(e1, e3) = all_52_2
% 141.43/20.77 (4) op(e1, e1) = e3
% 141.43/20.77 (5) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.77 (6) ~ (all_52_7 = e0)
% 141.43/20.77 (7) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.77 (8) ~ (all_52_9 = all_52_13)
% 141.43/20.77 (9) op(e0, e3) = all_52_3
% 141.43/20.77 (10) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.77 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.77 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.77 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.77 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.43/20.77 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.77 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.43/20.77 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.77 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.77 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.77 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.77 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.43/20.77 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.43/20.77 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.77 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.43/20.77 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.43/20.77 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.77 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.77 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.77 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.43/20.77 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.77 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.77 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.77 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.77 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.77 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.77 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.77 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.77 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.77 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.43/20.77 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.77 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.43/20.77 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.77 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.77 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.77 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.77 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.77 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.77 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.77 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.77 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.77 (11) all_54_12 = all_52_3
% 141.43/20.77 (12) ~ (all_52_1 = e0)
% 141.43/20.77 (13) ~ (e3 = e0)
% 141.43/20.77 (14) op(e2, e3) = all_52_1
% 141.43/20.77 (15) ~ (e1 = e0)
% 141.43/20.77 (16) ~ (all_52_1 = all_52_2)
% 141.43/20.77 (17) op(e0, e0) = e2
% 141.43/20.77 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.77 (19) ~ (all_52_9 = e3)
% 141.43/20.77 (20) ~ (all_52_13 = e2)
% 141.43/20.77 (21) op(e0, e2) = all_52_7
% 141.43/20.77 (22) all_54_4 = all_52_1
% 141.43/20.77 (23) ~ (all_52_2 = all_52_3)
% 141.43/20.77 (24) op(e2, e2) = e0
% 141.43/20.77 (25) op(e2, e1) = all_52_9
% 141.43/20.77 (26) ~ (all_52_3 = e2)
% 141.43/20.77 (27) op(e2, e0) = all_52_13
% 141.43/20.77
% 141.43/20.77 Begin of proof
% 141.43/20.77 |
% 141.43/20.77 | BETA: splitting (2) gives:
% 141.43/20.77 |
% 141.43/20.77 | Case 1:
% 141.43/20.77 | |
% 141.43/20.77 | | (28) all_57_5 = e2 & op(e2, e1) = e2
% 141.43/20.77 | |
% 141.43/20.77 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.43/20.77 | | (14), (15), (16), (17), (18), (19), (21), (22), (23), (24), (25),
% 141.43/20.77 | | (26), (27), (28) are inconsistent by sub-proof #228.
% 141.43/20.77 | |
% 141.43/20.77 | Case 2:
% 141.43/20.77 | |
% 141.43/20.77 | | (29) all_57_10 = e2 & op(e2, e0) = e2
% 141.43/20.77 | |
% 141.43/20.77 | | ALPHA: (29) implies:
% 141.43/20.77 | | (30) op(e2, e0) = e2
% 141.43/20.77 | |
% 141.43/20.77 | | REF_CLOSE: (18), (20), (27), (30) are inconsistent by sub-proof #1030.
% 141.43/20.77 | |
% 141.43/20.77 | End of split
% 141.43/20.77 |
% 141.43/20.77 End of proof
% 141.43/20.77
% 141.43/20.77 Sub-proof #220 shows that the following formulas are inconsistent:
% 141.43/20.77 ----------------------------------------------------------------
% 141.43/20.77 (1) ~ (all_52_4 = all_52_7)
% 141.43/20.77 (2) ~ (all_52_1 = all_52_3)
% 141.43/20.77 (3) ~ (all_52_13 = e0)
% 141.43/20.77 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.43/20.77 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.77 (5) op(e1, e3) = all_52_2
% 141.43/20.77 (6) op(e1, e1) = e3
% 141.43/20.77 (7) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) = all_24_1
% 141.43/20.77 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2) =
% 141.43/20.77 all_24_1 & $i(all_24_1))
% 141.43/20.77 (8) ~ (all_52_8 = e3)
% 141.43/20.77 (9) ~ (all_52_4 = e0)
% 141.43/20.77 (10) ~ (e2 = e1)
% 141.43/20.77 (11) op(e3, e3) = e3
% 141.43/20.77 (12) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.43/20.77 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.43/20.77 (13) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.77 (14) ~ (all_52_7 = e0)
% 141.43/20.77 (15) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 141.43/20.77 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 141.43/20.77 e0) = all_16_1 & $i(all_16_1))
% 141.43/20.77 (16) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 141.43/20.77 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2,
% 141.43/20.77 e0) = all_18_1 & $i(all_18_1))
% 141.43/20.77 (17) all_54_3 = all_52_12
% 141.43/20.77 (18) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.77 (19) ~ (all_52_9 = all_52_13)
% 141.43/20.77 (20) op(e0, e3) = all_52_3
% 141.43/20.77 (21) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.77 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.77 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.77 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.77 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.43/20.77 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.77 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.43/20.77 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.77 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.77 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.77 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.77 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.43/20.77 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.43/20.77 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.77 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.43/20.77 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.43/20.77 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.77 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.77 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.77 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.43/20.77 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.77 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.77 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.77 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.77 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.77 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.77 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.77 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.77 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.77 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.43/20.77 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.77 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.43/20.77 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.77 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.77 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.77 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.77 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.77 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.77 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.77 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.77 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.77 (22) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.77 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.43/20.77 e1)
% 141.43/20.77 (23) all_54_12 = all_52_3
% 141.43/20.77 (24) ~ (all_52_1 = e0)
% 141.43/20.77 (25) ~ (e3 = e0)
% 141.43/20.77 (26) op(e1, e1) = all_4_2
% 141.43/20.77 (27) ~ (all_52_4 = e3)
% 141.43/20.77 (28) op(e3, e1) = all_52_8
% 141.43/20.77 (29) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.43/20.77 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.43/20.77 (30) op(e2, e3) = all_52_1
% 141.43/20.77 (31) all_40_2 = e2
% 141.43/20.77 (32) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.43/20.77 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.43/20.77 (33) ~ (all_52_8 = all_52_12)
% 141.43/20.77 (34) ~ (e1 = e0)
% 141.43/20.77 (35) op(e3, e2) = all_52_4
% 141.43/20.77 (36) ~ (e2 = e0)
% 141.43/20.77 (37) ~ (all_40_2 = e2) | ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 &
% 141.43/20.77 op(e0, e2) = all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 =
% 141.43/20.77 e1) & op(e0, e2) = all_40_1 & $i(all_40_1))
% 141.43/20.77 (38) ~ (e3 = e2)
% 141.43/20.77 (39) op(e3, e0) = all_52_12
% 141.43/20.77 (40) all_57_10 = e3 & op(e2, e0) = e3
% 141.43/20.77 (41) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.43/20.77 (42) ~ (all_52_1 = all_52_2)
% 141.43/20.77 (43) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.43/20.77 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.43/20.77 (44) ~ (all_4_2 = e2)
% 141.43/20.77 (45) op(e0, e0) = e2
% 141.43/20.77 (46) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.77 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.77 (47) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.77 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.77 (48) ~ (all_52_12 = all_52_13)
% 141.43/20.77 (49) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.77 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.77 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.77 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.77 (50) ~ (all_52_13 = e2)
% 141.43/20.77 (51) ~ (e3 = e1)
% 141.43/20.77 (52) op(e0, e2) = all_52_7
% 141.43/20.77 (53) all_54_4 = all_52_1
% 141.43/20.77 (54) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.77 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.77 (55) ~ (all_52_12 = e2)
% 141.43/20.77 (56) ~ (all_52_2 = all_52_3)
% 141.43/20.77 (57) op(e2, e2) = e0
% 141.43/20.77 (58) op(e2, e1) = all_52_9
% 141.43/20.77 (59) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.77 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.77 (60) ~ (all_52_3 = e2)
% 141.43/20.77 (61) op(e2, e0) = all_52_13
% 141.43/20.77 (62) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.43/20.77 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.43/20.77
% 141.43/20.77 Begin of proof
% 141.43/20.77 |
% 141.43/20.77 | ALPHA: (40) implies:
% 141.43/20.77 | (63) op(e2, e0) = e3
% 141.43/20.77 |
% 141.43/20.77 | BETA: splitting (62) gives:
% 141.43/20.77 |
% 141.43/20.77 | Case 1:
% 141.43/20.77 | |
% 141.43/20.77 | | (64) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.43/20.77 | | e3)
% 141.43/20.77 | |
% 141.43/20.77 | | REF_CLOSE: (25), (27), (35), (47), (57), (64) are inconsistent by sub-proof
% 141.43/20.77 | | #1023.
% 141.43/20.77 | |
% 141.43/20.77 | Case 2:
% 141.43/20.77 | |
% 141.43/20.77 | | (65) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.43/20.77 | | e3)
% 141.43/20.77 | |
% 141.43/20.77 | | BETA: splitting (65) gives:
% 141.43/20.77 | |
% 141.43/20.77 | | Case 1:
% 141.43/20.77 | | |
% 141.43/20.77 | | | (66) all_57_7 = e3 & op(e1, e2) = e3
% 141.43/20.77 | | |
% 141.43/20.77 | | | REF_CLOSE: (6), (10), (12), (25), (26), (29), (34), (36), (38), (43),
% 141.43/20.77 | | | (44), (47), (51), (66) are inconsistent by sub-proof #233.
% 141.43/20.77 | | |
% 141.43/20.77 | | Case 2:
% 141.43/20.77 | | |
% 141.43/20.77 | | | (67) all_57_13 = e3 & op(e0, e2) = e3
% 141.43/20.77 | | |
% 141.43/20.77 | | | ALPHA: (67) implies:
% 141.43/20.77 | | | (68) op(e0, e2) = e3
% 141.43/20.77 | | |
% 141.43/20.77 | | | GROUND_INST: instantiating (47) with all_52_7, e3, e2, e0, simplifying
% 141.43/20.77 | | | with (52), (68) gives:
% 141.43/20.77 | | | (69) all_52_7 = e3
% 141.43/20.77 | | |
% 141.43/20.77 | | | GROUND_INST: instantiating (47) with all_52_13, e3, e0, e2, simplifying
% 141.43/20.77 | | | with (61), (63) gives:
% 141.43/20.77 | | | (70) all_52_13 = e3
% 141.43/20.77 | | |
% 141.43/20.77 | | | REDUCE: (19), (70) imply:
% 141.43/20.77 | | | (71) ~ (all_52_9 = e3)
% 141.43/20.77 | | |
% 141.43/20.77 | | | REDUCE: (48), (70) imply:
% 141.43/20.77 | | | (72) ~ (all_52_12 = e3)
% 141.43/20.77 | | |
% 141.43/20.77 | | | BETA: splitting (37) gives:
% 141.43/20.77 | | |
% 141.43/20.77 | | | Case 1:
% 141.43/20.77 | | | |
% 141.43/20.77 | | | | (73) ~ (all_40_2 = e2)
% 141.43/20.77 | | | |
% 141.43/20.77 | | | | REDUCE: (31), (73) imply:
% 141.43/20.77 | | | | (74) $false
% 141.43/20.77 | | | |
% 141.43/20.77 | | | | CLOSE: (74) is inconsistent.
% 141.43/20.77 | | | |
% 141.43/20.77 | | | Case 2:
% 141.43/20.77 | | | |
% 141.43/20.77 | | | | (75) ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 141.43/20.77 | | | | all_40_1 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e1)
% 141.43/20.77 | | | | & op(e0, e2) = all_40_1 & $i(all_40_1))
% 141.43/20.77 | | | |
% 141.43/20.77 | | | | BETA: splitting (75) gives:
% 141.43/20.77 | | | |
% 141.43/20.77 | | | | Case 1:
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | (76) ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2)
% 141.43/20.77 | | | | | = all_40_1 & $i(all_40_0) & $i(all_40_1)
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | ALPHA: (76) implies:
% 141.43/20.77 | | | | | (77) ~ (all_40_0 = e3)
% 141.43/20.77 | | | | | (78) op(e0, e2) = all_40_1
% 141.43/20.77 | | | | | (79) op(all_40_1, e0) = all_40_0
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | BETA: splitting (7) gives:
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | Case 1:
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | (80) ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0,
% 141.43/20.77 | | | | | | e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | ALPHA: (80) implies:
% 141.43/20.77 | | | | | | (81) ~ (all_24_0 = e1)
% 141.43/20.77 | | | | | | (82) op(e0, e2) = all_24_1
% 141.43/20.77 | | | | | | (83) op(all_24_1, e0) = all_24_0
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | BETA: splitting (15) gives:
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | Case 1:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | (84) ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2,
% 141.43/20.77 | | | | | | | e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | ALPHA: (84) implies:
% 141.43/20.77 | | | | | | | (85) op(e2, e0) = all_16_1
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | BETA: splitting (16) gives:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | Case 1:
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | (86) ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 &
% 141.43/20.77 | | | | | | | | op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | ALPHA: (86) implies:
% 141.43/20.77 | | | | | | | | (87) op(e2, e0) = all_18_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (68), (78) gives:
% 141.43/20.77 | | | | | | | | (88) all_40_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_24_1, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (78), (82) gives:
% 141.43/20.77 | | | | | | | | (89) all_40_1 = all_24_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (63), (87) gives:
% 141.43/20.77 | | | | | | | | (90) all_18_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_16_1, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (85), (87) gives:
% 141.43/20.77 | | | | | | | | (91) all_18_1 = all_16_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (88), (89) imply:
% 141.43/20.77 | | | | | | | | (92) all_24_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | SIMP: (92) implies:
% 141.43/20.77 | | | | | | | | (93) all_24_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (90), (91) imply:
% 141.43/20.77 | | | | | | | | (94) all_16_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 141.43/20.77 | | | | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.43/20.77 | | | | | | | | (25), (26), (27), (28), (30), (32), (33), (34), (35),
% 141.43/20.77 | | | | | | | | (36), (38), (39), (41), (42), (44), (45), (46), (47),
% 141.43/20.77 | | | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 141.43/20.77 | | | | | | | | (59), (60), (61), (71), (72), (77), (79), (81), (83),
% 141.43/20.77 | | | | | | | | (85), (87), (88), (93), (94) are inconsistent by
% 141.43/20.77 | | | | | | | | sub-proof #224.
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | Case 2:
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | (95) ~ (all_18_1 = e1) & op(e2, e0) = all_18_1 &
% 141.43/20.77 | | | | | | | | $i(all_18_1)
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | ALPHA: (95) implies:
% 141.43/20.77 | | | | | | | | (96) ~ (all_18_1 = e1)
% 141.43/20.77 | | | | | | | | (97) op(e2, e0) = all_18_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (68), (78) gives:
% 141.43/20.77 | | | | | | | | (98) all_40_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_24_1, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (78), (82) gives:
% 141.43/20.77 | | | | | | | | (99) all_40_1 = all_24_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (63), (97) gives:
% 141.43/20.77 | | | | | | | | (100) all_18_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_16_1, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (85), (97) gives:
% 141.43/20.77 | | | | | | | | (101) all_18_1 = all_16_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (98), (99) imply:
% 141.43/20.77 | | | | | | | | (102) all_24_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | SIMP: (102) implies:
% 141.43/20.77 | | | | | | | | (103) all_24_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (100), (101) imply:
% 141.43/20.77 | | | | | | | | (104) all_16_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 141.43/20.77 | | | | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.43/20.77 | | | | | | | | (25), (26), (27), (28), (30), (32), (33), (34), (35),
% 141.43/20.77 | | | | | | | | (36), (38), (39), (41), (42), (44), (45), (46), (47),
% 141.43/20.77 | | | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 141.43/20.77 | | | | | | | | (59), (60), (61), (71), (72), (77), (79), (81), (83),
% 141.43/20.77 | | | | | | | | (85), (97), (98), (103), (104) are inconsistent by
% 141.43/20.77 | | | | | | | | sub-proof #224.
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | End of split
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | Case 2:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | (105) ~ (all_16_1 = e3) & op(e2, e0) = all_16_1 & $i(all_16_1)
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | REF_CLOSE: (16), (47), (63), (105) are inconsistent by sub-proof
% 141.43/20.77 | | | | | | | #223.
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | End of split
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | Case 2:
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | (106) ~ (all_24_1 = e3) & op(e0, e2) = all_24_1 & $i(all_24_1)
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | REF_CLOSE: (47), (68), (78), (106) are inconsistent by sub-proof
% 141.43/20.77 | | | | | | #222.
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | End of split
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | Case 2:
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | (107) ~ (all_40_1 = e1) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | ALPHA: (107) implies:
% 141.43/20.77 | | | | | (108) ~ (all_40_1 = e1)
% 141.43/20.77 | | | | | (109) op(e0, e2) = all_40_1
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | BETA: splitting (7) gives:
% 141.43/20.77 | | | | |
% 141.43/20.77 | | | | | Case 1:
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | (110) ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0,
% 141.43/20.77 | | | | | | e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | ALPHA: (110) implies:
% 141.43/20.77 | | | | | | (111) ~ (all_24_0 = e1)
% 141.43/20.77 | | | | | | (112) op(e0, e2) = all_24_1
% 141.43/20.77 | | | | | | (113) op(all_24_1, e0) = all_24_0
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | BETA: splitting (15) gives:
% 141.43/20.77 | | | | | |
% 141.43/20.77 | | | | | | Case 1:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | (114) ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2,
% 141.43/20.77 | | | | | | | e0) = all_16_1 & $i(all_16_0) & $i(all_16_1)
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | ALPHA: (114) implies:
% 141.43/20.77 | | | | | | | (115) op(e2, e0) = all_16_1
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | BETA: splitting (16) gives:
% 141.43/20.77 | | | | | | |
% 141.43/20.77 | | | | | | | Case 1:
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | (116) ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 &
% 141.43/20.77 | | | | | | | | op(e2, e0) = all_18_1 & $i(all_18_0) & $i(all_18_1)
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | ALPHA: (116) implies:
% 141.43/20.77 | | | | | | | | (117) op(e2, e0) = all_18_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (68), (109) gives:
% 141.43/20.77 | | | | | | | | (118) all_40_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_24_1, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (109), (112) gives:
% 141.43/20.77 | | | | | | | | (119) all_40_1 = all_24_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (63), (117) gives:
% 141.43/20.77 | | | | | | | | (120) all_18_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_16_1, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (115), (117) gives:
% 141.43/20.77 | | | | | | | | (121) all_18_1 = all_16_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (118), (119) imply:
% 141.43/20.77 | | | | | | | | (122) all_24_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | SIMP: (122) implies:
% 141.43/20.77 | | | | | | | | (123) all_24_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (120), (121) imply:
% 141.43/20.77 | | | | | | | | (124) all_16_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 141.43/20.77 | | | | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.43/20.77 | | | | | | | | (25), (26), (27), (28), (30), (32), (33), (34), (35),
% 141.43/20.77 | | | | | | | | (36), (38), (39), (41), (42), (44), (45), (46), (47),
% 141.43/20.77 | | | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 141.43/20.77 | | | | | | | | (59), (60), (61), (71), (72), (111), (113), (115),
% 141.43/20.77 | | | | | | | | (117), (123), (124) are inconsistent by sub-proof
% 141.43/20.77 | | | | | | | | #221.
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | Case 2:
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | (125) ~ (all_18_1 = e1) & op(e2, e0) = all_18_1 &
% 141.43/20.77 | | | | | | | | $i(all_18_1)
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | ALPHA: (125) implies:
% 141.43/20.77 | | | | | | | | (126) ~ (all_18_1 = e1)
% 141.43/20.77 | | | | | | | | (127) op(e2, e0) = all_18_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (68), (109) gives:
% 141.43/20.77 | | | | | | | | (128) all_40_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_24_1, all_40_1, e2, e0,
% 141.43/20.77 | | | | | | | | simplifying with (109), (112) gives:
% 141.43/20.77 | | | | | | | | (129) all_40_1 = all_24_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with e3, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (63), (127) gives:
% 141.43/20.77 | | | | | | | | (130) all_18_1 = e3
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | GROUND_INST: instantiating (47) with all_16_1, all_18_1, e0, e2,
% 141.43/20.77 | | | | | | | | simplifying with (115), (127) gives:
% 141.43/20.77 | | | | | | | | (131) all_18_1 = all_16_1
% 141.43/20.77 | | | | | | | |
% 141.43/20.77 | | | | | | | | COMBINE_EQS: (128), (129) imply:
% 141.43/20.78 | | | | | | | | (132) all_24_1 = e3
% 141.43/20.78 | | | | | | | |
% 141.43/20.78 | | | | | | | | SIMP: (132) implies:
% 141.43/20.78 | | | | | | | | (133) all_24_1 = e3
% 141.43/20.78 | | | | | | | |
% 141.43/20.78 | | | | | | | | COMBINE_EQS: (130), (131) imply:
% 141.43/20.78 | | | | | | | | (134) all_16_1 = e3
% 141.43/20.78 | | | | | | | |
% 141.43/20.78 | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (13), (14),
% 141.43/20.78 | | | | | | | | (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.43/20.78 | | | | | | | | (25), (26), (27), (28), (30), (32), (33), (34), (35),
% 141.43/20.78 | | | | | | | | (36), (38), (39), (41), (42), (44), (45), (46), (47),
% 141.43/20.78 | | | | | | | | (49), (51), (52), (53), (54), (55), (56), (57), (58),
% 141.43/20.78 | | | | | | | | (59), (60), (61), (71), (72), (111), (113), (115),
% 141.43/20.78 | | | | | | | | (127), (133), (134) are inconsistent by sub-proof
% 141.43/20.78 | | | | | | | | #221.
% 141.43/20.78 | | | | | | | |
% 141.43/20.78 | | | | | | | End of split
% 141.43/20.78 | | | | | | |
% 141.43/20.78 | | | | | | Case 2:
% 141.43/20.78 | | | | | | |
% 141.43/20.78 | | | | | | | (135) ~ (all_16_1 = e3) & op(e2, e0) = all_16_1 & $i(all_16_1)
% 141.43/20.78 | | | | | | |
% 141.43/20.78 | | | | | | | REF_CLOSE: (16), (47), (63), (135) are inconsistent by sub-proof
% 141.43/20.78 | | | | | | | #223.
% 141.43/20.78 | | | | | | |
% 141.43/20.78 | | | | | | End of split
% 141.43/20.78 | | | | | |
% 141.43/20.78 | | | | | Case 2:
% 141.43/20.78 | | | | | |
% 141.43/20.78 | | | | | | (136) ~ (all_24_1 = e3) & op(e0, e2) = all_24_1 & $i(all_24_1)
% 141.43/20.78 | | | | | |
% 141.43/20.78 | | | | | | REF_CLOSE: (47), (68), (109), (136) are inconsistent by sub-proof
% 141.43/20.78 | | | | | | #222.
% 141.43/20.78 | | | | | |
% 141.43/20.78 | | | | | End of split
% 141.43/20.78 | | | | |
% 141.43/20.78 | | | | End of split
% 141.43/20.78 | | | |
% 141.43/20.78 | | | End of split
% 141.43/20.78 | | |
% 141.43/20.78 | | End of split
% 141.43/20.78 | |
% 141.43/20.78 | End of split
% 141.43/20.78 |
% 141.43/20.78 End of proof
% 141.43/20.78
% 141.43/20.78 Sub-proof #221 shows that the following formulas are inconsistent:
% 141.43/20.78 ----------------------------------------------------------------
% 141.43/20.78 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.78 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.43/20.78 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.78 (3) op(e1, e3) = all_52_2
% 141.43/20.78 (4) op(e1, e1) = e3
% 141.43/20.78 (5) ~ (all_52_12 = e3)
% 141.43/20.78 (6) ~ (all_52_8 = e3)
% 141.43/20.78 (7) ~ (all_52_4 = e0)
% 141.43/20.78 (8) ~ (e2 = e1)
% 141.43/20.78 (9) all_16_1 = e3
% 141.43/20.78 (10) op(e3, e3) = e3
% 141.43/20.78 (11) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.78 (12) ~ (all_52_7 = e0)
% 141.43/20.78 (13) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 141.43/20.78 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 141.43/20.78 e0) = all_16_1 & $i(all_16_1))
% 141.43/20.78 (14) all_54_3 = all_52_12
% 141.43/20.78 (15) op(all_24_1, e0) = all_24_0
% 141.43/20.78 (16) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.78 (17) ~ (all_52_9 = all_52_13)
% 141.43/20.78 (18) op(e0, e3) = all_52_3
% 141.43/20.78 (19) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.78 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.78 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.78 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.78 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.78 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.43/20.78 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.78 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.78 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.78 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.78 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.43/20.78 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.43/20.78 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.78 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.43/20.78 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.43/20.78 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.78 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.78 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.43/20.78 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.78 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.78 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.78 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.78 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.78 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.78 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.78 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.78 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.43/20.78 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.78 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.43/20.78 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.78 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.78 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.78 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.78 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.78 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.78 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.78 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.78 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.78 (20) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.78 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.43/20.78 e1)
% 141.43/20.78 (21) all_54_12 = all_52_3
% 141.43/20.78 (22) ~ (all_52_1 = e0)
% 141.43/20.78 (23) ~ (e3 = e0)
% 141.43/20.78 (24) op(e1, e1) = all_4_2
% 141.43/20.78 (25) ~ (all_52_4 = e3)
% 141.43/20.78 (26) op(e3, e1) = all_52_8
% 141.43/20.78 (27) op(e2, e3) = all_52_1
% 141.43/20.78 (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.43/20.78 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.43/20.78 (29) all_24_1 = e3
% 141.43/20.78 (30) ~ (all_52_8 = all_52_12)
% 141.43/20.78 (31) ~ (e1 = e0)
% 141.43/20.78 (32) op(e3, e2) = all_52_4
% 141.43/20.78 (33) ~ (e2 = e0)
% 141.43/20.78 (34) op(e2, e0) = all_18_1
% 141.43/20.78 (35) ~ (e3 = e2)
% 141.43/20.78 (36) op(e3, e0) = all_52_12
% 141.43/20.78 (37) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.43/20.78 (38) ~ (all_52_1 = all_52_2)
% 141.43/20.78 (39) ~ (all_4_2 = e2)
% 141.43/20.78 (40) op(e0, e0) = e2
% 141.43/20.78 (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.78 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.78 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.78 (43) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.78 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.78 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.78 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.78 (44) ~ (all_52_9 = e3)
% 141.43/20.78 (45) ~ (e3 = e1)
% 141.43/20.78 (46) op(e0, e2) = all_52_7
% 141.43/20.78 (47) all_54_4 = all_52_1
% 141.43/20.78 (48) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.78 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.78 (49) ~ (all_52_12 = e2)
% 141.43/20.78 (50) ~ (all_52_2 = all_52_3)
% 141.43/20.78 (51) op(e2, e2) = e0
% 141.43/20.78 (52) ~ (all_24_0 = e1)
% 141.43/20.78 (53) op(e2, e0) = all_16_1
% 141.43/20.78 (54) op(e2, e1) = all_52_9
% 141.43/20.78 (55) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.78 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.78 (56) ~ (all_52_3 = e2)
% 141.43/20.78 (57) op(e2, e0) = all_52_13
% 141.43/20.78
% 141.43/20.78 Begin of proof
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (15), (29) imply:
% 141.43/20.78 | (58) op(e3, e0) = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (9), (53) imply:
% 141.43/20.78 | (59) op(e2, e0) = e3
% 141.43/20.78 |
% 141.43/20.78 | GROUND_INST: instantiating (42) with all_52_12, all_24_0, e0, e3, simplifying
% 141.43/20.78 | with (36), (58) gives:
% 141.43/20.78 | (60) all_52_12 = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | COMBINE_EQS: (14), (60) imply:
% 141.43/20.78 | (61) all_54_3 = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (30), (60) imply:
% 141.43/20.78 | (62) ~ (all_52_8 = all_24_0)
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (5), (60) imply:
% 141.43/20.78 | (63) ~ (all_24_0 = e3)
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (49), (60) imply:
% 141.43/20.78 | (64) ~ (all_24_0 = e2)
% 141.43/20.78 |
% 141.43/20.78 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 141.43/20.78 | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 141.43/20.78 | (27), (28), (31), (32), (33), (34), (35), (36), (37), (38), (39),
% 141.43/20.78 | (40), (41), (42), (43), (44), (45), (46), (47), (48), (50), (51),
% 141.43/20.78 | (52), (54), (55), (56), (57), (59), (61), (62), (63), (64) are
% 141.43/20.78 | inconsistent by sub-proof #225.
% 141.43/20.78 |
% 141.43/20.78 End of proof
% 141.43/20.78
% 141.43/20.78 Sub-proof #222 shows that the following formulas are inconsistent:
% 141.43/20.78 ----------------------------------------------------------------
% 141.43/20.78 (1) ~ (all_24_1 = e3) & op(e0, e2) = all_24_1 & $i(all_24_1)
% 141.43/20.78 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.78 (3) op(e0, e2) = all_40_1
% 141.43/20.78 (4) op(e0, e2) = e3
% 141.43/20.78
% 141.43/20.78 Begin of proof
% 141.43/20.78 |
% 141.43/20.78 | ALPHA: (1) implies:
% 141.43/20.78 | (5) ~ (all_24_1 = e3)
% 141.43/20.78 | (6) op(e0, e2) = all_24_1
% 141.43/20.78 |
% 141.43/20.78 | GROUND_INST: instantiating (2) with e3, all_40_1, e2, e0, simplifying with
% 141.43/20.78 | (3), (4) gives:
% 141.43/20.78 | (7) all_40_1 = e3
% 141.43/20.78 |
% 141.43/20.78 | GROUND_INST: instantiating (2) with all_24_1, all_40_1, e2, e0, simplifying
% 141.43/20.78 | with (3), (6) gives:
% 141.43/20.78 | (8) all_40_1 = all_24_1
% 141.43/20.78 |
% 141.43/20.78 | COMBINE_EQS: (7), (8) imply:
% 141.43/20.78 | (9) all_24_1 = e3
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (5), (9) imply:
% 141.43/20.78 | (10) $false
% 141.43/20.78 |
% 141.43/20.78 | CLOSE: (10) is inconsistent.
% 141.43/20.78 |
% 141.43/20.78 End of proof
% 141.43/20.78
% 141.43/20.78 Sub-proof #223 shows that the following formulas are inconsistent:
% 141.43/20.78 ----------------------------------------------------------------
% 141.43/20.78 (1) ~ (all_16_1 = e3) & op(e2, e0) = all_16_1 & $i(all_16_1)
% 141.43/20.78 (2) op(e2, e0) = e3
% 141.43/20.78 (3) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) = all_18_1
% 141.43/20.78 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0) =
% 141.43/20.78 all_18_1 & $i(all_18_1))
% 141.43/20.78 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.78
% 141.43/20.78 Begin of proof
% 141.43/20.78 |
% 141.43/20.78 | ALPHA: (1) implies:
% 141.43/20.78 | (5) ~ (all_16_1 = e3)
% 141.43/20.78 | (6) op(e2, e0) = all_16_1
% 141.43/20.78 |
% 141.43/20.78 | BETA: splitting (3) gives:
% 141.43/20.78 |
% 141.43/20.78 | Case 1:
% 141.43/20.78 | |
% 141.43/20.78 | | (7) ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 141.43/20.78 | | all_18_1 & $i(all_18_0) & $i(all_18_1)
% 141.43/20.78 | |
% 141.43/20.78 | | ALPHA: (7) implies:
% 141.43/20.78 | | (8) op(e2, e0) = all_18_1
% 141.43/20.78 | |
% 141.43/20.78 | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #343.
% 141.43/20.78 | |
% 141.43/20.78 | Case 2:
% 141.43/20.78 | |
% 141.43/20.78 | | (9) ~ (all_18_1 = e1) & op(e2, e0) = all_18_1 & $i(all_18_1)
% 141.43/20.78 | |
% 141.43/20.78 | | ALPHA: (9) implies:
% 141.43/20.78 | | (10) op(e2, e0) = all_18_1
% 141.43/20.78 | |
% 141.43/20.78 | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #343.
% 141.43/20.78 | |
% 141.43/20.78 | End of split
% 141.43/20.78 |
% 141.43/20.78 End of proof
% 141.43/20.78
% 141.43/20.78 Sub-proof #224 shows that the following formulas are inconsistent:
% 141.43/20.78 ----------------------------------------------------------------
% 141.43/20.78 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.78 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.43/20.78 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.78 (3) op(e1, e3) = all_52_2
% 141.43/20.78 (4) op(e1, e1) = e3
% 141.43/20.78 (5) ~ (all_52_12 = e3)
% 141.43/20.78 (6) ~ (all_52_8 = e3)
% 141.43/20.78 (7) op(all_40_1, e0) = all_40_0
% 141.43/20.78 (8) ~ (all_52_4 = e0)
% 141.43/20.78 (9) ~ (e2 = e1)
% 141.43/20.78 (10) all_16_1 = e3
% 141.43/20.78 (11) op(e3, e3) = e3
% 141.43/20.78 (12) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.78 (13) ~ (all_52_7 = e0)
% 141.43/20.78 (14) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 141.43/20.78 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 141.43/20.78 e0) = all_16_1 & $i(all_16_1))
% 141.43/20.78 (15) all_40_1 = e3
% 141.43/20.78 (16) all_54_3 = all_52_12
% 141.43/20.78 (17) op(all_24_1, e0) = all_24_0
% 141.43/20.78 (18) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.78 (19) ~ (all_52_9 = all_52_13)
% 141.43/20.78 (20) op(e0, e3) = all_52_3
% 141.43/20.78 (21) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.78 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.78 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.78 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.78 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.78 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.43/20.78 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.78 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.78 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.78 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.78 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.43/20.78 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.43/20.78 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.78 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.43/20.78 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.43/20.78 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.78 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.78 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.43/20.78 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.78 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.78 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.78 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.78 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.78 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.78 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.78 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.78 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.43/20.78 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.78 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.43/20.78 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.78 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.78 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.78 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.78 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.78 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.78 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.78 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.78 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.78 (22) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.78 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.43/20.78 e1)
% 141.43/20.78 (23) all_54_12 = all_52_3
% 141.43/20.78 (24) ~ (all_52_1 = e0)
% 141.43/20.78 (25) ~ (e3 = e0)
% 141.43/20.78 (26) op(e1, e1) = all_4_2
% 141.43/20.78 (27) ~ (all_52_4 = e3)
% 141.43/20.78 (28) op(e3, e1) = all_52_8
% 141.43/20.78 (29) op(e2, e3) = all_52_1
% 141.43/20.78 (30) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.43/20.78 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.43/20.78 (31) all_24_1 = e3
% 141.43/20.78 (32) ~ (all_52_8 = all_52_12)
% 141.43/20.78 (33) ~ (e1 = e0)
% 141.43/20.78 (34) ~ (all_40_0 = e3)
% 141.43/20.78 (35) op(e3, e2) = all_52_4
% 141.43/20.78 (36) ~ (e2 = e0)
% 141.43/20.78 (37) op(e2, e0) = all_18_1
% 141.43/20.78 (38) ~ (e3 = e2)
% 141.43/20.78 (39) op(e3, e0) = all_52_12
% 141.43/20.78 (40) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.43/20.78 (41) ~ (all_52_1 = all_52_2)
% 141.43/20.78 (42) ~ (all_4_2 = e2)
% 141.43/20.78 (43) op(e0, e0) = e2
% 141.43/20.78 (44) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.78 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.78 (45) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.78 (46) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.78 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.78 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.78 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.78 (47) ~ (all_52_9 = e3)
% 141.43/20.78 (48) ~ (e3 = e1)
% 141.43/20.78 (49) op(e0, e2) = all_52_7
% 141.43/20.78 (50) all_54_4 = all_52_1
% 141.43/20.78 (51) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.78 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.78 (52) ~ (all_52_12 = e2)
% 141.43/20.78 (53) ~ (all_52_2 = all_52_3)
% 141.43/20.78 (54) op(e2, e2) = e0
% 141.43/20.78 (55) ~ (all_24_0 = e1)
% 141.43/20.78 (56) op(e2, e0) = all_16_1
% 141.43/20.78 (57) op(e2, e1) = all_52_9
% 141.43/20.78 (58) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.78 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.78 (59) ~ (all_52_3 = e2)
% 141.43/20.78 (60) op(e2, e0) = all_52_13
% 141.43/20.78
% 141.43/20.78 Begin of proof
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (7), (15) imply:
% 141.43/20.78 | (61) op(e3, e0) = all_40_0
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (17), (31) imply:
% 141.43/20.78 | (62) op(e3, e0) = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (10), (56) imply:
% 141.43/20.78 | (63) op(e2, e0) = e3
% 141.43/20.78 |
% 141.43/20.78 | GROUND_INST: instantiating (45) with all_52_12, all_24_0, e0, e3, simplifying
% 141.43/20.78 | with (39), (62) gives:
% 141.43/20.78 | (64) all_52_12 = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | GROUND_INST: instantiating (45) with all_52_12, all_40_0, e0, e3, simplifying
% 141.43/20.78 | with (39), (61) gives:
% 141.43/20.78 | (65) all_52_12 = all_40_0
% 141.43/20.78 |
% 141.43/20.78 | COMBINE_EQS: (64), (65) imply:
% 141.43/20.78 | (66) all_40_0 = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | SIMP: (66) implies:
% 141.43/20.78 | (67) all_40_0 = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | COMBINE_EQS: (16), (64) imply:
% 141.43/20.78 | (68) all_54_3 = all_24_0
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (32), (64) imply:
% 141.43/20.78 | (69) ~ (all_52_8 = all_24_0)
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (52), (64) imply:
% 141.43/20.78 | (70) ~ (all_24_0 = e2)
% 141.43/20.78 |
% 141.43/20.78 | REDUCE: (34), (67) imply:
% 141.43/20.78 | (71) ~ (all_24_0 = e3)
% 141.43/20.78 |
% 141.43/20.78 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (11), (12), (13), (14),
% 141.43/20.78 | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27), (28),
% 141.43/20.78 | (29), (30), (33), (35), (36), (37), (38), (39), (40), (41), (42),
% 141.43/20.78 | (43), (44), (45), (46), (47), (48), (49), (50), (51), (53), (54),
% 141.43/20.78 | (55), (57), (58), (59), (60), (63), (68), (69), (70), (71) are
% 141.43/20.78 | inconsistent by sub-proof #225.
% 141.43/20.78 |
% 141.43/20.78 End of proof
% 141.43/20.78
% 141.43/20.78 Sub-proof #225 shows that the following formulas are inconsistent:
% 141.43/20.78 ----------------------------------------------------------------
% 141.43/20.78 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.78 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.43/20.78 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.78 (3) op(e1, e3) = all_52_2
% 141.43/20.78 (4) op(e1, e1) = e3
% 141.43/20.78 (5) ~ (all_52_12 = e3)
% 141.43/20.78 (6) ~ (all_24_0 = e2)
% 141.43/20.78 (7) op(e2, e0) = e3
% 141.43/20.78 (8) ~ (all_52_8 = e3)
% 141.43/20.78 (9) ~ (all_52_4 = e0)
% 141.43/20.78 (10) ~ (e2 = e1)
% 141.43/20.78 (11) op(e3, e3) = e3
% 141.43/20.78 (12) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.78 (13) ~ (all_52_7 = e0)
% 141.43/20.78 (14) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 141.43/20.78 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 141.43/20.78 e0) = all_16_1 & $i(all_16_1))
% 141.43/20.78 (15) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.78 (16) ~ (all_52_9 = all_52_13)
% 141.43/20.78 (17) op(e0, e3) = all_52_3
% 141.43/20.78 (18) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.78 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.78 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.78 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.78 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.78 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.43/20.78 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.78 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.78 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.78 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.78 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.43/20.78 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.43/20.78 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.78 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.43/20.78 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.43/20.78 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.78 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.78 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.43/20.78 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.78 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.78 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.78 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.78 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.78 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.78 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.78 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.78 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.78 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.43/20.78 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.78 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.43/20.78 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.78 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.78 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.78 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.78 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.78 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.78 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.78 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.78 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.78 (19) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.78 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.43/20.78 e1)
% 141.43/20.78 (20) all_54_12 = all_52_3
% 141.43/20.78 (21) ~ (all_52_1 = e0)
% 141.43/20.78 (22) ~ (e3 = e0)
% 141.43/20.78 (23) ~ (all_52_8 = all_24_0)
% 141.43/20.78 (24) op(e1, e1) = all_4_2
% 141.43/20.78 (25) ~ (all_52_4 = e3)
% 141.43/20.78 (26) op(e3, e1) = all_52_8
% 141.43/20.78 (27) op(e2, e3) = all_52_1
% 141.43/20.78 (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.43/20.78 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.43/20.78 (29) ~ (all_24_0 = e3)
% 141.43/20.78 (30) ~ (e1 = e0)
% 141.43/20.78 (31) op(e3, e2) = all_52_4
% 141.43/20.78 (32) ~ (e2 = e0)
% 141.43/20.78 (33) op(e2, e0) = all_18_1
% 141.43/20.78 (34) ~ (e3 = e2)
% 141.43/20.78 (35) op(e3, e0) = all_52_12
% 141.43/20.78 (36) all_54_3 = all_24_0
% 141.43/20.78 (37) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.43/20.78 (38) ~ (all_52_1 = all_52_2)
% 141.43/20.78 (39) ~ (all_4_2 = e2)
% 141.43/20.78 (40) op(e0, e0) = e2
% 141.43/20.78 (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.78 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.78 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.78 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.78 (43) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.78 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.78 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.78 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.78 (44) ~ (all_52_9 = e3)
% 141.43/20.78 (45) ~ (e3 = e1)
% 141.43/20.78 (46) op(e0, e2) = all_52_7
% 141.43/20.78 (47) all_54_4 = all_52_1
% 141.43/20.79 (48) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.79 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.79 (49) ~ (all_52_2 = all_52_3)
% 141.43/20.79 (50) op(e2, e2) = e0
% 141.43/20.79 (51) ~ (all_24_0 = e1)
% 141.43/20.79 (52) op(e2, e1) = all_52_9
% 141.43/20.79 (53) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.79 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.79 (54) ~ (all_52_3 = e2)
% 141.43/20.79 (55) op(e2, e0) = all_52_13
% 141.43/20.79
% 141.43/20.79 Begin of proof
% 141.43/20.79 |
% 141.43/20.79 | BETA: splitting (28) gives:
% 141.43/20.79 |
% 141.43/20.79 | Case 1:
% 141.43/20.79 | |
% 141.43/20.79 | | (56) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 141.43/20.79 | | e1)
% 141.43/20.79 | |
% 141.43/20.79 | | BETA: splitting (56) gives:
% 141.43/20.79 | |
% 141.43/20.79 | | Case 1:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (57) all_57_0 = e1 & op(e3, e3) = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (57) implies:
% 141.43/20.79 | | | (58) op(e3, e3) = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (11), (42), (45), (58) are inconsistent by sub-proof #838.
% 141.43/20.79 | | |
% 141.43/20.79 | | Case 2:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (59) all_57_1 = e1 & op(e3, e2) = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (59) implies:
% 141.43/20.79 | | | (60) op(e3, e2) = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (7), (14), (33), (42), (60) are inconsistent by sub-proof #342.
% 141.43/20.79 | | |
% 141.43/20.79 | | End of split
% 141.43/20.79 | |
% 141.43/20.79 | Case 2:
% 141.43/20.79 | |
% 141.43/20.79 | | (61) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 141.43/20.79 | | e1)
% 141.43/20.79 | |
% 141.43/20.79 | | BETA: splitting (61) gives:
% 141.43/20.79 | |
% 141.43/20.79 | | Case 1:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (62) all_57_4 = e1 & op(e3, e1) = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (62) implies:
% 141.43/20.79 | | | (63) all_57_4 = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (1), (2), (3), (4), (10), (12), (13), (15), (16), (17), (18),
% 141.43/20.79 | | | (19), (20), (21), (22), (24), (27), (30), (32), (34), (38),
% 141.43/20.79 | | | (39), (40), (41), (42), (43), (44), (45), (46), (47), (49),
% 141.43/20.79 | | | (50), (52), (54), (55), (63) are inconsistent by sub-proof
% 141.43/20.79 | | | #227.
% 141.43/20.79 | | |
% 141.43/20.79 | | Case 2:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (64) all_57_9 = e1 & op(e3, e0) = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (64) implies:
% 141.43/20.79 | | | (65) all_57_9 = e1
% 141.43/20.79 | | |
% 141.43/20.79 | | | BETA: splitting (37) gives:
% 141.43/20.79 | | |
% 141.43/20.79 | | | Case 1:
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | (66) all_54_3 = e3
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | COMBINE_EQS: (36), (66) imply:
% 141.43/20.79 | | | | (67) all_24_0 = e3
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | SIMP: (67) implies:
% 141.43/20.79 | | | | (68) all_24_0 = e3
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | REDUCE: (29), (68) imply:
% 141.43/20.79 | | | | (69) $false
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | CLOSE: (69) is inconsistent.
% 141.43/20.79 | | | |
% 141.43/20.79 | | | Case 2:
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | (70) ~ (all_54_3 = e3)
% 141.43/20.79 | | | | (71) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | BETA: splitting (71) gives:
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | Case 1:
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | (72) all_54_3 = e2
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | COMBINE_EQS: (36), (72) imply:
% 141.43/20.79 | | | | | (73) all_24_0 = e2
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | SIMP: (73) implies:
% 141.43/20.79 | | | | | (74) all_24_0 = e2
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | REDUCE: (6), (74) imply:
% 141.43/20.79 | | | | | (75) $false
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | CLOSE: (75) is inconsistent.
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | Case 2:
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | (76) all_54_3 = e1 | all_54_3 = e0
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | BETA: splitting (76) gives:
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | Case 1:
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | (77) all_54_3 = e1
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | COMBINE_EQS: (36), (77) imply:
% 141.43/20.79 | | | | | | (78) all_24_0 = e1
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | SIMP: (78) implies:
% 141.43/20.79 | | | | | | (79) all_24_0 = e1
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | REDUCE: (51), (79) imply:
% 141.43/20.79 | | | | | | (80) $false
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | CLOSE: (80) is inconsistent.
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | Case 2:
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | (81) all_54_3 = e0
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | COMBINE_EQS: (36), (81) imply:
% 141.43/20.79 | | | | | | (82) all_24_0 = e0
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | SIMP: (82) implies:
% 141.43/20.79 | | | | | | (83) all_24_0 = e0
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | REDUCE: (23), (83) imply:
% 141.43/20.79 | | | | | | (84) ~ (all_52_8 = e0)
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | REDUCE: (29), (83) imply:
% 141.43/20.79 | | | | | | (85) ~ (e3 = e0)
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | REDUCE: (51), (83) imply:
% 141.43/20.79 | | | | | | (86) ~ (e1 = e0)
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | | REF_CLOSE: (5), (8), (9), (22), (25), (26), (30), (31), (35), (42),
% 141.43/20.79 | | | | | | (48), (53), (65), (84) are inconsistent by sub-proof
% 141.43/20.79 | | | | | | #226.
% 141.43/20.79 | | | | | |
% 141.43/20.79 | | | | | End of split
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | End of split
% 141.43/20.79 | | | |
% 141.43/20.79 | | | End of split
% 141.43/20.79 | | |
% 141.43/20.79 | | End of split
% 141.43/20.79 | |
% 141.43/20.79 | End of split
% 141.43/20.79 |
% 141.43/20.79 End of proof
% 141.43/20.79
% 141.43/20.79 Sub-proof #226 shows that the following formulas are inconsistent:
% 141.43/20.79 ----------------------------------------------------------------
% 141.43/20.79 (1) ~ (all_52_12 = e3)
% 141.43/20.79 (2) ~ (all_52_8 = e3)
% 141.43/20.79 (3) ~ (all_52_4 = e0)
% 141.43/20.79 (4) all_57_9 = e1
% 141.43/20.79 (5) ~ (e3 = e0)
% 141.43/20.79 (6) ~ (all_52_4 = e3)
% 141.43/20.79 (7) op(e3, e1) = all_52_8
% 141.43/20.79 (8) ~ (e1 = e0)
% 141.43/20.79 (9) op(e3, e2) = all_52_4
% 141.43/20.79 (10) op(e3, e0) = all_52_12
% 141.43/20.79 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.79 (12) ~ (all_52_8 = e0)
% 141.43/20.79 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.79 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.79 (14) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.79 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.79
% 141.43/20.79 Begin of proof
% 141.43/20.79 |
% 141.43/20.79 | BETA: splitting (14) gives:
% 141.43/20.79 |
% 141.43/20.79 | Case 1:
% 141.43/20.79 | |
% 141.43/20.79 | | (15) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 141.43/20.79 | | e0)
% 141.43/20.79 | |
% 141.43/20.79 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (10), (11), (13), (15) are
% 141.43/20.79 | | inconsistent by sub-proof #1101.
% 141.43/20.79 | |
% 141.43/20.79 | Case 2:
% 141.43/20.79 | |
% 141.43/20.79 | | (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 141.43/20.79 | | e0)
% 141.43/20.79 | |
% 141.43/20.79 | | BETA: splitting (16) gives:
% 141.43/20.79 | |
% 141.43/20.79 | | Case 1:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (17) all_57_4 = e0 & op(e3, e1) = e0
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (7), (11), (12), (17) are inconsistent by sub-proof #981.
% 141.43/20.79 | | |
% 141.43/20.79 | | Case 2:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (18) all_57_9 = e0 & op(e3, e0) = e0
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (18) implies:
% 141.43/20.79 | | | (19) all_57_9 = e0
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (4), (8), (19) are inconsistent by sub-proof #1079.
% 141.43/20.79 | | |
% 141.43/20.79 | | End of split
% 141.43/20.79 | |
% 141.43/20.79 | End of split
% 141.43/20.79 |
% 141.43/20.79 End of proof
% 141.43/20.79
% 141.43/20.79 Sub-proof #227 shows that the following formulas are inconsistent:
% 141.43/20.79 ----------------------------------------------------------------
% 141.43/20.79 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.79 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.43/20.79 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.79 (3) op(e1, e3) = all_52_2
% 141.43/20.79 (4) op(e1, e1) = e3
% 141.43/20.79 (5) ~ (e2 = e1)
% 141.43/20.79 (6) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.79 (7) ~ (all_52_7 = e0)
% 141.43/20.79 (8) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.79 (9) ~ (all_52_9 = all_52_13)
% 141.43/20.79 (10) op(e0, e3) = all_52_3
% 141.43/20.79 (11) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.79 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.79 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.79 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.79 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.43/20.79 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.79 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.43/20.79 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.79 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.79 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.79 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.79 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.43/20.79 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.43/20.79 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.43/20.79 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.43/20.79 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.43/20.79 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.79 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.79 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.79 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.43/20.79 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.79 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.79 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.79 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.79 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.79 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.79 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.79 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.79 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.79 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.43/20.79 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.79 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.43/20.79 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.79 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.43/20.79 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.79 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.79 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.43/20.79 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.79 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.79 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.43/20.79 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.79 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.79 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.43/20.79 e1)
% 141.43/20.79 (13) all_54_12 = all_52_3
% 141.43/20.79 (14) ~ (all_52_1 = e0)
% 141.43/20.79 (15) ~ (e3 = e0)
% 141.43/20.79 (16) op(e1, e1) = all_4_2
% 141.43/20.79 (17) op(e2, e3) = all_52_1
% 141.43/20.79 (18) ~ (e1 = e0)
% 141.43/20.79 (19) ~ (e2 = e0)
% 141.43/20.79 (20) ~ (e3 = e2)
% 141.43/20.79 (21) ~ (all_52_1 = all_52_2)
% 141.43/20.79 (22) ~ (all_4_2 = e2)
% 141.43/20.79 (23) op(e0, e0) = e2
% 141.43/20.79 (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.79 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.79 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.79 (26) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.79 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.79 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.79 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.79 (27) ~ (all_52_9 = e3)
% 141.43/20.79 (28) all_57_4 = e1
% 141.43/20.79 (29) ~ (e3 = e1)
% 141.43/20.79 (30) op(e0, e2) = all_52_7
% 141.43/20.79 (31) all_54_4 = all_52_1
% 141.43/20.79 (32) ~ (all_52_2 = all_52_3)
% 141.43/20.79 (33) op(e2, e2) = e0
% 141.43/20.79 (34) op(e2, e1) = all_52_9
% 141.43/20.79 (35) ~ (all_52_3 = e2)
% 141.43/20.79 (36) op(e2, e0) = all_52_13
% 141.43/20.79
% 141.43/20.79 Begin of proof
% 141.43/20.79 |
% 141.43/20.79 | BETA: splitting (24) gives:
% 141.43/20.79 |
% 141.43/20.79 | Case 1:
% 141.43/20.79 | |
% 141.43/20.79 | | (37) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 141.43/20.79 | | e2)
% 141.43/20.79 | |
% 141.43/20.79 | | BETA: splitting (37) gives:
% 141.43/20.79 | |
% 141.43/20.79 | | Case 1:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (38) all_57_4 = e2 & op(e3, e1) = e2
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (5), (28), (38) are inconsistent by sub-proof #1109.
% 141.43/20.79 | | |
% 141.43/20.79 | | Case 2:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (39) all_57_5 = e2 & op(e2, e1) = e2
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (9), (10), (11), (13), (14),
% 141.43/20.79 | | | (15), (17), (18), (21), (23), (25), (27), (30), (31), (32),
% 141.43/20.79 | | | (33), (34), (35), (36), (39) are inconsistent by sub-proof
% 141.43/20.79 | | | #228.
% 141.43/20.79 | | |
% 141.43/20.79 | | End of split
% 141.43/20.79 | |
% 141.43/20.79 | Case 2:
% 141.43/20.79 | |
% 141.43/20.79 | | (40) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 141.43/20.79 | | e2)
% 141.43/20.79 | |
% 141.43/20.79 | | REF_CLOSE: (2), (5), (12), (15), (16), (18), (19), (20), (22), (23), (25),
% 141.43/20.79 | | (26), (29), (40) are inconsistent by sub-proof #766.
% 141.43/20.79 | |
% 141.43/20.79 | End of split
% 141.43/20.79 |
% 141.43/20.79 End of proof
% 141.43/20.79
% 141.43/20.79 Sub-proof #228 shows that the following formulas are inconsistent:
% 141.43/20.79 ----------------------------------------------------------------
% 141.43/20.79 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.79 (2) op(e1, e3) = all_52_2
% 141.43/20.79 (3) op(e1, e1) = e3
% 141.43/20.79 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.79 (5) ~ (all_52_7 = e0)
% 141.43/20.79 (6) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.79 (7) ~ (all_52_9 = all_52_13)
% 141.43/20.79 (8) op(e0, e3) = all_52_3
% 141.43/20.79 (9) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.79 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.79 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.79 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.79 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.43/20.79 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.43/20.79 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.43/20.79 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.43/20.79 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.43/20.79 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.43/20.79 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.43/20.79 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.79 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.43/20.79 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.43/20.79 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.79 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.43/20.79 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.43/20.79 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.43/20.79 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.43/20.79 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.79 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.79 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.79 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.79 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.79 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.79 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.79 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.79 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.43/20.79 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.43/20.79 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.43/20.79 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.43/20.79 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.79 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.43/20.79 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.43/20.79 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.79 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.43/20.79 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.79 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.79 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.43/20.79 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.79 (10) all_54_12 = all_52_3
% 141.43/20.79 (11) ~ (all_52_1 = e0)
% 141.43/20.79 (12) ~ (e3 = e0)
% 141.43/20.79 (13) all_57_5 = e2 & op(e2, e1) = e2
% 141.43/20.79 (14) op(e2, e3) = all_52_1
% 141.43/20.79 (15) ~ (e1 = e0)
% 141.43/20.79 (16) ~ (all_52_1 = all_52_2)
% 141.43/20.79 (17) op(e0, e0) = e2
% 141.43/20.79 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.79 (19) ~ (all_52_9 = e3)
% 141.43/20.79 (20) op(e0, e2) = all_52_7
% 141.43/20.79 (21) all_54_4 = all_52_1
% 141.43/20.79 (22) ~ (all_52_2 = all_52_3)
% 141.43/20.79 (23) op(e2, e2) = e0
% 141.43/20.79 (24) op(e2, e1) = all_52_9
% 141.43/20.79 (25) ~ (all_52_3 = e2)
% 141.43/20.79 (26) op(e2, e0) = all_52_13
% 141.43/20.79
% 141.43/20.79 Begin of proof
% 141.43/20.79 |
% 141.43/20.79 | ALPHA: (13) implies:
% 141.43/20.79 | (27) op(e2, e1) = e2
% 141.43/20.79 |
% 141.43/20.79 | GROUND_INST: instantiating (18) with all_52_9, e2, e1, e2, simplifying with
% 141.43/20.79 | (24), (27) gives:
% 141.43/20.79 | (28) all_52_9 = e2
% 141.43/20.79 |
% 141.43/20.79 | REDUCE: (7), (28) imply:
% 141.43/20.79 | (29) ~ (all_52_13 = e2)
% 141.43/20.79 |
% 141.43/20.79 | SIMP: (29) implies:
% 141.43/20.79 | (30) ~ (all_52_13 = e2)
% 141.43/20.79 |
% 141.43/20.79 | REDUCE: (19), (28) imply:
% 141.43/20.79 | (31) ~ (e3 = e2)
% 141.43/20.79 |
% 141.43/20.79 | SIMP: (31) implies:
% 141.43/20.79 | (32) ~ (e3 = e2)
% 141.43/20.79 |
% 141.43/20.79 | BETA: splitting (9) gives:
% 141.43/20.79 |
% 141.43/20.79 | Case 1:
% 141.43/20.79 | |
% 141.43/20.79 | | (33) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 141.43/20.79 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.79 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.79 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.79 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.43/20.79 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.43/20.79 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.43/20.79 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.79 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.79 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.43/20.79 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.43/20.79 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 141.43/20.79 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.43/20.79 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.43/20.79 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.43/20.79 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.79 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.43/20.79 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.43/20.79 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.43/20.79 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.43/20.79 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.43/20.79 | | $i(all_56_12))))
% 141.43/20.79 | |
% 141.43/20.79 | | BETA: splitting (33) gives:
% 141.43/20.79 | |
% 141.43/20.79 | | Case 1:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (34) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 141.43/20.79 | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.79 | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.79 | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.79 | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.43/20.79 | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.43/20.79 | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.43/20.79 | | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.43/20.79 | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.43/20.79 | | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.43/20.79 | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (34) implies:
% 141.43/20.79 | | | (35) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.43/20.79 | | | e3) = all_56_10 & $i(all_56_10))
% 141.43/20.79 | | | (36) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 141.43/20.79 | | | e3) = all_56_3 & $i(all_56_3))
% 141.43/20.79 | | | (37) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 141.43/20.79 | | | e1) = all_56_13 & $i(all_56_13))
% 141.43/20.79 | | | (38) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2,
% 141.43/20.79 | | | e2) = all_56_11 & $i(all_56_11))
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (10), (11), (12), (14), (16),
% 141.43/20.79 | | | (17), (18), (21), (22), (23), (25), (32), (35), (36), (37),
% 141.43/20.79 | | | (38) are inconsistent by sub-proof #229.
% 141.43/20.79 | | |
% 141.43/20.79 | | Case 2:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (39) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 141.43/20.79 | | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.43/20.79 | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 141.43/20.79 | | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.79 | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.43/20.79 | | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.43/20.79 | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.43/20.79 | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.43/20.79 | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.43/20.79 | | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 141.43/20.79 | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (39) implies:
% 141.43/20.79 | | | (40) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 141.43/20.79 | | | e2) = all_56_12 & $i(all_56_12))
% 141.43/20.79 | | | (41) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.79 | | | e0) = all_56_15 & $i(all_56_15))
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (5), (17), (18), (20), (40), (41) are inconsistent by sub-proof
% 141.43/20.79 | | | #975.
% 141.43/20.79 | | |
% 141.43/20.79 | | End of split
% 141.43/20.79 | |
% 141.43/20.79 | Case 2:
% 141.43/20.79 | |
% 141.43/20.79 | | (42) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.43/20.79 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.43/20.79 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.43/20.79 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.43/20.79 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.43/20.79 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.43/20.79 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.43/20.79 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.43/20.79 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.43/20.79 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.43/20.79 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.43/20.79 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | (
% 141.43/20.79 | | ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.43/20.79 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.43/20.79 | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 141.43/20.79 | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.79 | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.43/20.79 | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.79 | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 141.43/20.79 | | e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.43/20.79 | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.43/20.79 | | $i(all_56_8))))
% 141.43/20.79 | |
% 141.43/20.79 | | REF_CLOSE: (15), (18), (23), (26), (27), (30), (42) are inconsistent by
% 141.43/20.79 | | sub-proof #855.
% 141.43/20.79 | |
% 141.43/20.79 | End of split
% 141.43/20.79 |
% 141.43/20.79 End of proof
% 141.43/20.79
% 141.43/20.79 Sub-proof #229 shows that the following formulas are inconsistent:
% 141.43/20.79 ----------------------------------------------------------------
% 141.43/20.79 (1) ~ (all_52_1 = all_52_3)
% 141.43/20.79 (2) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.43/20.79 all_56_3 & $i(all_56_3))
% 141.43/20.79 (3) op(e1, e3) = all_52_2
% 141.43/20.79 (4) op(e1, e1) = e3
% 141.43/20.79 (5) (all_56_3 = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 141.43/20.79 all_56_11 & $i(all_56_11))
% 141.43/20.79 (6) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.79 (7) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.79 (8) op(e0, e3) = all_52_3
% 141.43/20.79 (9) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.43/20.79 all_56_10 & $i(all_56_10))
% 141.43/20.79 (10) all_54_12 = all_52_3
% 141.43/20.79 (11) ~ (all_52_1 = e0)
% 141.43/20.79 (12) ~ (e3 = e0)
% 141.43/20.79 (13) op(e2, e3) = all_52_1
% 141.43/20.79 (14) ~ (e3 = e2)
% 141.43/20.79 (15) ~ (all_52_1 = all_52_2)
% 141.43/20.79 (16) op(e0, e0) = e2
% 141.43/20.79 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.79 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.79 (18) all_54_4 = all_52_1
% 141.43/20.79 (19) ~ (all_52_2 = all_52_3)
% 141.43/20.79 (20) op(e2, e2) = e0
% 141.43/20.79 (21) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.43/20.79 all_56_13 & $i(all_56_13))
% 141.43/20.79 (22) ~ (all_52_3 = e2)
% 141.43/20.79
% 141.43/20.79 Begin of proof
% 141.43/20.79 |
% 141.43/20.79 | BETA: splitting (9) gives:
% 141.43/20.79 |
% 141.43/20.79 | Case 1:
% 141.43/20.79 | |
% 141.43/20.79 | | (23) all_56_15 = e3 & op(e0, e0) = e3
% 141.43/20.79 | |
% 141.43/20.79 | | ALPHA: (23) implies:
% 141.43/20.79 | | (24) op(e0, e0) = e3
% 141.43/20.79 | |
% 141.43/20.79 | | REF_CLOSE: (14), (16), (17), (24) are inconsistent by sub-proof #1066.
% 141.43/20.79 | |
% 141.43/20.79 | Case 2:
% 141.43/20.79 | |
% 141.43/20.79 | | (25) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.43/20.79 | |
% 141.43/20.79 | | ALPHA: (25) implies:
% 141.43/20.79 | | (26) ~ (all_56_10 = e0)
% 141.43/20.79 | | (27) op(e0, e3) = all_56_10
% 141.43/20.79 | |
% 141.43/20.79 | | BETA: splitting (2) gives:
% 141.43/20.79 | |
% 141.43/20.79 | | Case 1:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (28) all_56_11 = e3 & op(e2, e2) = e3
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (28) implies:
% 141.43/20.79 | | | (29) op(e2, e2) = e3
% 141.43/20.79 | | |
% 141.43/20.79 | | | REF_CLOSE: (12), (17), (20), (29) are inconsistent by sub-proof #1119.
% 141.43/20.79 | | |
% 141.43/20.79 | | Case 2:
% 141.43/20.79 | | |
% 141.43/20.79 | | | (30) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)
% 141.43/20.79 | | |
% 141.43/20.79 | | | ALPHA: (30) implies:
% 141.43/20.79 | | | (31) ~ (all_56_3 = e2)
% 141.43/20.79 | | | (32) op(e2, e3) = all_56_3
% 141.43/20.79 | | |
% 141.43/20.79 | | | BETA: splitting (21) gives:
% 141.43/20.79 | | |
% 141.43/20.79 | | | Case 1:
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | (33) all_56_6 = e1 & op(e1, e3) = e1
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | ALPHA: (33) implies:
% 141.43/20.79 | | | | (34) op(e1, e3) = e1
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | BETA: splitting (5) gives:
% 141.43/20.79 | | | |
% 141.43/20.79 | | | | Case 1:
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | (35) all_56_3 = e2 & op(e2, e3) = e2
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | ALPHA: (35) implies:
% 141.43/20.79 | | | | | (36) op(e2, e3) = e2
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | | REF_CLOSE: (17), (31), (32), (36) are inconsistent by sub-proof #979.
% 141.43/20.79 | | | | |
% 141.43/20.79 | | | | Case 2:
% 141.43/20.79 | | | | |
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | GROUND_INST: instantiating (17) with all_52_3, all_56_10, e3, e0,
% 141.43/20.80 | | | | | simplifying with (8), (27) gives:
% 141.43/20.80 | | | | | (37) all_56_10 = all_52_3
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | GROUND_INST: instantiating (17) with all_52_2, e1, e3, e1, simplifying
% 141.43/20.80 | | | | | with (3), (34) gives:
% 141.43/20.80 | | | | | (38) all_52_2 = e1
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | GROUND_INST: instantiating (17) with all_52_1, all_56_3, e3, e2,
% 141.43/20.80 | | | | | simplifying with (13), (32) gives:
% 141.43/20.80 | | | | | (39) all_56_3 = all_52_1
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REDUCE: (31), (39) imply:
% 141.43/20.80 | | | | | (40) ~ (all_52_1 = e2)
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REDUCE: (26), (37) imply:
% 141.43/20.80 | | | | | (41) ~ (all_52_3 = e0)
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REDUCE: (15), (38) imply:
% 141.43/20.80 | | | | | (42) ~ (all_52_1 = e1)
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REDUCE: (19), (38) imply:
% 141.43/20.80 | | | | | (43) ~ (all_52_3 = e1)
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | SIMP: (43) implies:
% 141.43/20.80 | | | | | (44) ~ (all_52_3 = e1)
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | BETA: splitting (7) gives:
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | Case 1:
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | (45) all_54_4 = e3
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | COMBINE_EQS: (18), (45) imply:
% 141.43/20.80 | | | | | | (46) all_52_1 = e3
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | SIMP: (46) implies:
% 141.43/20.80 | | | | | | (47) all_52_1 = e3
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | REDUCE: (1), (47) imply:
% 141.43/20.80 | | | | | | (48) ~ (all_52_3 = e3)
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | SIMP: (48) implies:
% 141.43/20.80 | | | | | | (49) ~ (all_52_3 = e3)
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | BETA: splitting (6) gives:
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | Case 1:
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | (50) all_54_12 = e3
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | REF_CLOSE: (10), (49), (50) are inconsistent by sub-proof #232.
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | Case 2:
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | (51) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | BETA: splitting (51) gives:
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | Case 1:
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | (52) all_54_12 = e2
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | REF_CLOSE: (10), (22), (52) are inconsistent by sub-proof #231.
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | Case 2:
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | (53) all_54_12 = e1 | all_54_12 = e0
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | REF_CLOSE: (10), (41), (44), (53) are inconsistent by sub-proof
% 141.43/20.80 | | | | | | | | #661.
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | End of split
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | End of split
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | Case 2:
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | (54) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | BETA: splitting (54) gives:
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | | Case 1:
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | (55) all_54_4 = e2
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | REF_CLOSE: (18), (40), (55) are inconsistent by sub-proof #677.
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | Case 2:
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | (56) all_54_4 = e1 | all_54_4 = e0
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | BETA: splitting (56) gives:
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | | Case 1:
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | (57) all_54_4 = e1
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | REF_CLOSE: (18), (42), (57) are inconsistent by sub-proof #795.
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | Case 2:
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | (58) all_54_4 = e0
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | | REF_CLOSE: (11), (18), (58) are inconsistent by sub-proof #794.
% 141.43/20.80 | | | | | | | |
% 141.43/20.80 | | | | | | | End of split
% 141.43/20.80 | | | | | | |
% 141.43/20.80 | | | | | | End of split
% 141.43/20.80 | | | | | |
% 141.43/20.80 | | | | | End of split
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | End of split
% 141.43/20.80 | | | |
% 141.43/20.80 | | | Case 2:
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | (59) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | ALPHA: (59) implies:
% 141.43/20.80 | | | | (60) ~ (all_56_13 = e3)
% 141.43/20.80 | | | | (61) op(e1, e1) = all_56_13
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | REF_CLOSE: (4), (17), (60), (61) are inconsistent by sub-proof #230.
% 141.43/20.80 | | | |
% 141.43/20.80 | | | End of split
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #230 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (2) op(e1, e1) = all_56_13
% 141.43/20.80 (3) op(e1, e1) = e3
% 141.43/20.80 (4) ~ (all_56_13 = e3)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | GROUND_INST: instantiating (1) with e3, all_56_13, e1, e1, simplifying with
% 141.43/20.80 | (2), (3) gives:
% 141.43/20.80 | (5) all_56_13 = e3
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (4), (5) imply:
% 141.43/20.80 | (6) $false
% 141.43/20.80 |
% 141.43/20.80 | CLOSE: (6) is inconsistent.
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #231 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) all_54_12 = all_52_3
% 141.43/20.80 (2) all_54_12 = e2
% 141.43/20.80 (3) ~ (all_52_3 = e2)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | COMBINE_EQS: (1), (2) imply:
% 141.43/20.80 | (4) all_52_3 = e2
% 141.43/20.80 |
% 141.43/20.80 | SIMP: (4) implies:
% 141.43/20.80 | (5) all_52_3 = e2
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (3), (5) imply:
% 141.43/20.80 | (6) $false
% 141.43/20.80 |
% 141.43/20.80 | CLOSE: (6) is inconsistent.
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #232 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) all_54_12 = all_52_3
% 141.43/20.80 (2) all_54_12 = e3
% 141.43/20.80 (3) ~ (all_52_3 = e3)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | COMBINE_EQS: (1), (2) imply:
% 141.43/20.80 | (4) all_52_3 = e3
% 141.43/20.80 |
% 141.43/20.80 | SIMP: (4) implies:
% 141.43/20.80 | (5) all_52_3 = e3
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (3), (5) imply:
% 141.43/20.80 | (6) $false
% 141.43/20.80 |
% 141.43/20.80 | CLOSE: (6) is inconsistent.
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #233 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) op(e1, e1) = e3
% 141.43/20.80 (2) all_57_7 = e3 & op(e1, e2) = e3
% 141.43/20.80 (3) ~ (e2 = e1)
% 141.43/20.80 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.43/20.80 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.43/20.80 (5) ~ (e3 = e0)
% 141.43/20.80 (6) op(e1, e1) = all_4_2
% 141.43/20.80 (7) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.43/20.80 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.43/20.80 (8) ~ (e1 = e0)
% 141.43/20.80 (9) ~ (e2 = e0)
% 141.43/20.80 (10) ~ (e3 = e2)
% 141.43/20.80 (11) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.43/20.80 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.43/20.80 (12) ~ (all_4_2 = e2)
% 141.43/20.80 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (14) ~ (e3 = e1)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | ALPHA: (2) implies:
% 141.43/20.80 | (15) all_57_7 = e3
% 141.43/20.80 |
% 141.43/20.80 | BETA: splitting (4) gives:
% 141.43/20.80 |
% 141.43/20.80 | Case 1:
% 141.43/20.80 | |
% 141.43/20.80 | | (16) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.43/20.80 | | e1)
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (16) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (17) all_57_6 = e1 & op(e1, e3) = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (17) implies:
% 141.43/20.80 | | | (18) all_57_6 = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.43/20.80 | | | (15), (18) are inconsistent by sub-proof #234.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (19) all_57_7 = e1 & op(e1, e2) = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (14), (15), (19) are inconsistent by sub-proof #1058.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | Case 2:
% 141.43/20.80 | |
% 141.43/20.80 | | (20) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.43/20.80 | | e1)
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (20) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (21) all_57_8 = e1 & op(e1, e1) = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (21) implies:
% 141.43/20.80 | | | (22) op(e1, e1) = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (1), (13), (14), (22) are inconsistent by sub-proof #1096.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (23) all_57_11 = e1 & op(e1, e0) = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (23) implies:
% 141.43/20.80 | | | (24) all_57_11 = e1
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.43/20.80 | | | (15), (24) are inconsistent by sub-proof #245.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #234 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) op(e1, e1) = e3
% 141.43/20.80 (2) ~ (e2 = e1)
% 141.43/20.80 (3) ~ (e3 = e0)
% 141.43/20.80 (4) op(e1, e1) = all_4_2
% 141.43/20.80 (5) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.43/20.80 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.43/20.80 (6) ~ (e1 = e0)
% 141.43/20.80 (7) ~ (e2 = e0)
% 141.43/20.80 (8) ~ (e3 = e2)
% 141.43/20.80 (9) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.43/20.80 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.43/20.80 (10) ~ (all_4_2 = e2)
% 141.43/20.80 (11) all_57_6 = e1
% 141.43/20.80 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (13) all_57_7 = e3
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | BETA: splitting (5) gives:
% 141.43/20.80 |
% 141.43/20.80 | Case 1:
% 141.43/20.80 | |
% 141.43/20.80 | | (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 141.43/20.80 | | e0)
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (14) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (15) all_57_6 = e0 & op(e1, e3) = e0
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (6), (11), (15) are inconsistent by sub-proof #427.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (16) all_57_7 = e0 & op(e1, e2) = e0
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (3), (13), (16) are inconsistent by sub-proof #1061.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | Case 2:
% 141.43/20.80 | |
% 141.43/20.80 | | (17) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 141.43/20.80 | | e0)
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (17) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (18) all_57_8 = e0 & op(e1, e1) = e0
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (18) implies:
% 141.43/20.80 | | | (19) op(e1, e1) = e0
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (1), (3), (12), (19) are inconsistent by sub-proof #308.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (20) all_57_11 = e0 & op(e1, e0) = e0
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (20) implies:
% 141.43/20.80 | | | (21) all_57_11 = e0
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (2), (4), (7), (8), (9), (10), (11), (12), (13), (21) are
% 141.43/20.80 | | | inconsistent by sub-proof #411.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #235 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) ~ (all_10_2 = e2)
% 141.43/20.80 (2) ~ (all_10_2 = e1)
% 141.43/20.80 (3) ~ (all_14_2 = e1)
% 141.43/20.80 (4) ~ (e3 = e0)
% 141.43/20.80 (5) op(e0, e0) = all_10_2
% 141.43/20.80 (6) ~ (e1 = e0)
% 141.43/20.80 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (8) op(e2, e2) = e0
% 141.43/20.80 (9) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.43/20.80 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.43/20.80 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.43/20.80 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.43/20.80 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.43/20.80 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 141.43/20.80 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 141.43/20.80 op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 & all_56_15 = e3 & ~
% 141.43/20.80 (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 141.43/20.80 = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4
% 141.43/20.80 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 141.43/20.80 $i(all_56_4)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.43/20.80 op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 141.43/20.80 $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 141.43/20.80 op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 141.43/20.80 $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 141.43/20.80 e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.43/20.80 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.43/20.80 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 141.43/20.80 = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 141.43/20.80 ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.43/20.80 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 141.43/20.80 e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.43/20.80 (10) op(e3, e3) = all_14_2
% 141.43/20.80 (11) ~ (all_14_2 = e0)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | BETA: splitting (9) gives:
% 141.43/20.80 |
% 141.43/20.80 | Case 1:
% 141.43/20.80 | |
% 141.43/20.80 | | (12) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 141.43/20.80 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.43/20.80 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 141.43/20.80 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 141.43/20.80 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 141.43/20.80 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.43/20.80 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 141.43/20.80 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (12) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (13) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 141.43/20.80 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.43/20.80 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 141.43/20.80 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (4), (7), (8), (13) are inconsistent by sub-proof #1118.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (14) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 141.43/20.80 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.43/20.80 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 141.43/20.80 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (3), (7), (10), (14) are inconsistent by sub-proof #316.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | Case 2:
% 141.43/20.80 | |
% 141.43/20.80 | | (15) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.43/20.80 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.43/20.80 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.43/20.80 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 141.43/20.80 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.43/20.80 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.43/20.80 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.43/20.80 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.43/20.80 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.43/20.80 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.43/20.80 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.43/20.80 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.43/20.80 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.80 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.43/20.80 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.43/20.80 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.43/20.80 | | all_56_14 & $i(all_56_14))))
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (15) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (16) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 141.43/20.80 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.43/20.80 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 141.43/20.80 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (6), (7), (8), (10), (11), (16) are inconsistent by sub-proof
% 141.43/20.80 | | | #1116.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (17) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 141.43/20.80 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.43/20.80 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 141.43/20.80 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.43/20.80 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.43/20.80 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.43/20.80 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.43/20.80 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.43/20.80 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.80 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.43/20.80 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.43/20.80 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.43/20.80 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (1), (2), (5), (6), (7), (8), (10), (11), (17) are inconsistent
% 141.43/20.80 | | | by sub-proof #236.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #236 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) ~ (all_10_2 = e2)
% 141.43/20.80 (2) ~ (all_10_2 = e1)
% 141.43/20.80 (3) op(e0, e0) = all_10_2
% 141.43/20.80 (4) ~ (e1 = e0)
% 141.43/20.80 (5) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 141.43/20.80 op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 141.43/20.80 e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 141.43/20.80 = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 141.43/20.80 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.43/20.80 e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.43/20.80 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.43/20.80 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.80 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.43/20.80 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.43/20.80 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.80 $i(all_56_14))))
% 141.43/20.80 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (7) op(e2, e2) = e0
% 141.43/20.80 (8) op(e3, e3) = all_14_2
% 141.43/20.80 (9) ~ (all_14_2 = e0)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | BETA: splitting (5) gives:
% 141.43/20.80 |
% 141.43/20.80 | Case 1:
% 141.43/20.80 | |
% 141.43/20.80 | | (10) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.43/20.80 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.43/20.80 | |
% 141.43/20.80 | | ALPHA: (10) implies:
% 141.43/20.80 | | (11) op(e2, e2) = e1
% 141.43/20.80 | |
% 141.43/20.80 | | REF_CLOSE: (4), (6), (7), (11) are inconsistent by sub-proof #1117.
% 141.43/20.80 | |
% 141.43/20.80 | Case 2:
% 141.43/20.80 | |
% 141.43/20.80 | | (12) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.43/20.80 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.43/20.80 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.43/20.80 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.43/20.80 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.43/20.80 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.43/20.80 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.80 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.43/20.80 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.43/20.80 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.43/20.80 | | all_56_14 & $i(all_56_14))))
% 141.43/20.80 | |
% 141.43/20.80 | | REF_CLOSE: (1), (2), (3), (6), (8), (9), (12) are inconsistent by sub-proof
% 141.43/20.80 | | #272.
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #237 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (2) op(e0, e0) = all_10_2
% 141.43/20.80 (3) op(e0, e0) = e1
% 141.43/20.80 (4) ~ (all_10_2 = e1)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | GROUND_INST: instantiating (1) with all_10_2, e1, e0, e0, simplifying with
% 141.43/20.80 | (2), (3) gives:
% 141.43/20.80 | (5) all_10_2 = e1
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (4), (5) imply:
% 141.43/20.80 | (6) $false
% 141.43/20.80 |
% 141.43/20.80 | CLOSE: (6) is inconsistent.
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #238 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) all_57_2 = e2
% 141.43/20.80 (2) all_57_2 = e0
% 141.43/20.80 (3) ~ (e2 = e0)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | COMBINE_EQS: (1), (2) imply:
% 141.43/20.80 | (4) e2 = e0
% 141.43/20.80 |
% 141.43/20.80 | SIMP: (4) implies:
% 141.43/20.80 | (5) e2 = e0
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (3), (5) imply:
% 141.43/20.80 | (6) $false
% 141.43/20.80 |
% 141.43/20.80 | CLOSE: (6) is inconsistent.
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #239 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) op(e1, e1) = e3
% 141.43/20.80 (2) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.43/20.80 (3) ~ (e3 = e0)
% 141.43/20.80 (4) ~ (e1 = e0)
% 141.43/20.80 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (6) all_57_11 = e1
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | BETA: splitting (2) gives:
% 141.43/20.80 |
% 141.43/20.80 | Case 1:
% 141.43/20.80 | |
% 141.43/20.80 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 141.43/20.80 | |
% 141.43/20.80 | | ALPHA: (7) implies:
% 141.43/20.80 | | (8) op(e1, e1) = e0
% 141.43/20.80 | |
% 141.43/20.80 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #308.
% 141.43/20.80 | |
% 141.43/20.80 | Case 2:
% 141.43/20.80 | |
% 141.43/20.80 | | (9) all_57_11 = e0 & op(e1, e0) = e0
% 141.43/20.80 | |
% 141.43/20.80 | | REF_CLOSE: (4), (6), (9) are inconsistent by sub-proof #808.
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #240 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.80 (1) ~ (e2 = e1)
% 141.43/20.80 (2) ~ (all_38_2 = e1) | ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 &
% 141.43/20.80 op(e2, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 141.43/20.80 e3) & op(e2, e1) = all_38_1 & $i(all_38_1))
% 141.43/20.80 (3) op(e2, e2) = e1
% 141.43/20.80 (4) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.43/20.80 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.43/20.80 (5) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) = all_20_1
% 141.43/20.80 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1) =
% 141.43/20.80 all_20_1 & $i(all_20_1))
% 141.43/20.80 (6) all_38_2 = e1
% 141.43/20.80 (7) op(e0, e0) = all_10_2
% 141.43/20.80 (8) ~ (all_56_15 = e2)
% 141.43/20.80 (9) ~ (e1 = e0)
% 141.43/20.80 (10) ~ (e2 = e0)
% 141.43/20.80 (11) ~ (e3 = e2)
% 141.43/20.80 (12) all_57_9 = e3
% 141.43/20.80 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.80 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.80 (14) op(e0, e0) = all_56_15
% 141.43/20.80 (15) op(e0, e2) = all_56_12
% 141.43/20.80 (16) op(e0, e2) = e3
% 141.43/20.80 (17) all_57_11 = e1
% 141.43/20.80 (18) all_57_2 = e3
% 141.43/20.80 (19) ~ (all_56_12 = e0)
% 141.43/20.80 (20) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.43/20.80 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.43/20.80
% 141.43/20.80 Begin of proof
% 141.43/20.80 |
% 141.43/20.80 | GROUND_INST: instantiating (13) with all_10_2, all_56_15, e0, e0, simplifying
% 141.43/20.80 | with (7), (14) gives:
% 141.43/20.80 | (21) all_56_15 = all_10_2
% 141.43/20.80 |
% 141.43/20.80 | GROUND_INST: instantiating (13) with e3, all_56_12, e2, e0, simplifying with
% 141.43/20.80 | (15), (16) gives:
% 141.43/20.80 | (22) all_56_12 = e3
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (19), (22) imply:
% 141.43/20.80 | (23) ~ (e3 = e0)
% 141.43/20.80 |
% 141.43/20.80 | REDUCE: (8), (21) imply:
% 141.43/20.80 | (24) ~ (all_10_2 = e2)
% 141.43/20.80 |
% 141.43/20.80 | BETA: splitting (4) gives:
% 141.43/20.80 |
% 141.43/20.80 | Case 1:
% 141.43/20.80 | |
% 141.43/20.80 | | (25) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 141.43/20.80 | | e2)
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (25) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (26) all_57_9 = e2 & op(e3, e0) = e2
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (11), (12), (26) are inconsistent by sub-proof #598.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (27) all_57_10 = e2 & op(e2, e0) = e2
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (27) implies:
% 141.43/20.80 | | | (28) all_57_10 = e2
% 141.43/20.80 | | |
% 141.43/20.80 | | | BETA: splitting (20) gives:
% 141.43/20.80 | | |
% 141.43/20.80 | | | Case 1:
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | (29) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2)
% 141.43/20.80 | | | | = e0)
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | BETA: splitting (29) gives:
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | Case 1:
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | (30) all_57_2 = e0 & op(e2, e3) = e0
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REF_CLOSE: (18), (23), (30) are inconsistent by sub-proof #697.
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | Case 2:
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | (31) all_57_3 = e0 & op(e2, e2) = e0
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | ALPHA: (31) implies:
% 141.43/20.80 | | | | | (32) op(e2, e2) = e0
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REF_CLOSE: (3), (9), (13), (32) are inconsistent by sub-proof #1117.
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | End of split
% 141.43/20.80 | | | |
% 141.43/20.80 | | | Case 2:
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | (33) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0)
% 141.43/20.80 | | | | = e0)
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | BETA: splitting (33) gives:
% 141.43/20.80 | | | |
% 141.43/20.80 | | | | Case 1:
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | (34) all_57_5 = e0 & op(e2, e1) = e0
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REF_CLOSE: (2), (5), (6), (13), (16), (34) are inconsistent by
% 141.43/20.80 | | | | | sub-proof #241.
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | Case 2:
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | (35) all_57_10 = e0 & op(e2, e0) = e0
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | ALPHA: (35) implies:
% 141.43/20.80 | | | | | (36) all_57_10 = e0
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | | REF_CLOSE: (10), (28), (36) are inconsistent by sub-proof #609.
% 141.43/20.80 | | | | |
% 141.43/20.80 | | | | End of split
% 141.43/20.80 | | | |
% 141.43/20.80 | | | End of split
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | Case 2:
% 141.43/20.80 | |
% 141.43/20.80 | | (37) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.43/20.80 | | e2)
% 141.43/20.80 | |
% 141.43/20.80 | | BETA: splitting (37) gives:
% 141.43/20.80 | |
% 141.43/20.80 | | Case 1:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (38) all_57_11 = e2 & op(e1, e0) = e2
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (1), (17), (38) are inconsistent by sub-proof #913.
% 141.43/20.80 | | |
% 141.43/20.80 | | Case 2:
% 141.43/20.80 | | |
% 141.43/20.80 | | | (39) all_57_15 = e2 & op(e0, e0) = e2
% 141.43/20.80 | | |
% 141.43/20.80 | | | ALPHA: (39) implies:
% 141.43/20.80 | | | (40) op(e0, e0) = e2
% 141.43/20.80 | | |
% 141.43/20.80 | | | REF_CLOSE: (7), (13), (24), (40) are inconsistent by sub-proof #1115.
% 141.43/20.80 | | |
% 141.43/20.80 | | End of split
% 141.43/20.80 | |
% 141.43/20.80 | End of split
% 141.43/20.80 |
% 141.43/20.80 End of proof
% 141.43/20.80
% 141.43/20.80 Sub-proof #241 shows that the following formulas are inconsistent:
% 141.43/20.80 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (all_38_2 = e1) | ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 &
% 141.43/20.81 op(e2, e1) = all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 =
% 141.43/20.81 e3) & op(e2, e1) = all_38_1 & $i(all_38_1))
% 141.43/20.81 (2) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) = all_20_1
% 141.43/20.81 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1) =
% 141.43/20.81 all_20_1 & $i(all_20_1))
% 141.43/20.81 (3) all_38_2 = e1
% 141.43/20.81 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (5) all_57_5 = e0 & op(e2, e1) = e0
% 141.43/20.81 (6) op(e0, e2) = e3
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | ALPHA: (5) implies:
% 141.43/20.81 | (7) op(e2, e1) = e0
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (1) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (8) ~ (all_38_2 = e1)
% 141.43/20.81 | |
% 141.43/20.81 | | REDUCE: (3), (8) imply:
% 141.43/20.81 | | (9) $false
% 141.43/20.81 | |
% 141.43/20.81 | | CLOSE: (9) is inconsistent.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (10) ( ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 141.43/20.81 | | all_38_1 & $i(all_38_0) & $i(all_38_1)) | ( ~ (all_38_1 = e3) &
% 141.43/20.81 | | op(e2, e1) = all_38_1 & $i(all_38_1))
% 141.43/20.81 | |
% 141.43/20.81 | | BETA: splitting (10) gives:
% 141.43/20.81 | |
% 141.43/20.81 | | Case 1:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (11) ~ (all_38_0 = e0) & op(all_38_1, e2) = all_38_0 & op(e2, e1) =
% 141.43/20.81 | | | all_38_1 & $i(all_38_0) & $i(all_38_1)
% 141.43/20.81 | | |
% 141.43/20.81 | | | ALPHA: (11) implies:
% 141.43/20.81 | | | (12) op(e2, e1) = all_38_1
% 141.43/20.81 | | | (13) op(all_38_1, e2) = all_38_0
% 141.43/20.81 | | |
% 141.43/20.81 | | | BETA: splitting (2) gives:
% 141.43/20.81 | | |
% 141.43/20.81 | | | Case 1:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (14) ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 141.43/20.81 | | | | all_20_1 & $i(all_20_0) & $i(all_20_1)
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | ALPHA: (14) implies:
% 141.43/20.81 | | | | (15) ~ (all_20_0 = e3)
% 141.43/20.81 | | | | (16) op(e2, e1) = all_20_1
% 141.43/20.81 | | | | (17) op(all_20_1, e2) = all_20_0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with all_20_1, all_38_1, e1, e2,
% 141.43/20.81 | | | | simplifying with (12), (16) gives:
% 141.43/20.81 | | | | (18) all_38_1 = all_20_1
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with e0, all_38_1, e1, e2, simplifying
% 141.43/20.81 | | | | with (7), (12) gives:
% 141.43/20.81 | | | | (19) all_38_1 = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | COMBINE_EQS: (18), (19) imply:
% 141.43/20.81 | | | | (20) all_20_1 = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REDUCE: (13), (19) imply:
% 141.43/20.81 | | | | (21) op(e0, e2) = all_38_0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REDUCE: (17), (20) imply:
% 141.43/20.81 | | | | (22) op(e0, e2) = all_20_0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with e3, all_38_0, e2, e0, simplifying
% 141.43/20.81 | | | | with (6), (21) gives:
% 141.43/20.81 | | | | (23) all_38_0 = e3
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with all_20_0, all_38_0, e2, e0,
% 141.43/20.81 | | | | simplifying with (21), (22) gives:
% 141.43/20.81 | | | | (24) all_38_0 = all_20_0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | COMBINE_EQS: (23), (24) imply:
% 141.43/20.81 | | | | (25) all_20_0 = e3
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REDUCE: (15), (25) imply:
% 141.43/20.81 | | | | (26) $false
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | CLOSE: (26) is inconsistent.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | Case 2:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (27) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REF_CLOSE: (4), (7), (12), (27) are inconsistent by sub-proof #242.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | End of split
% 141.43/20.81 | | |
% 141.43/20.81 | | Case 2:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (28) ~ (all_38_1 = e3) & op(e2, e1) = all_38_1 & $i(all_38_1)
% 141.43/20.81 | | |
% 141.43/20.81 | | | ALPHA: (28) implies:
% 141.43/20.81 | | | (29) op(e2, e1) = all_38_1
% 141.43/20.81 | | |
% 141.43/20.81 | | | BETA: splitting (2) gives:
% 141.43/20.81 | | |
% 141.43/20.81 | | | Case 1:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (30) ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 141.43/20.81 | | | | all_20_1 & $i(all_20_0) & $i(all_20_1)
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | ALPHA: (30) implies:
% 141.43/20.81 | | | | (31) ~ (all_20_0 = e3)
% 141.43/20.81 | | | | (32) op(e2, e1) = all_20_1
% 141.43/20.81 | | | | (33) op(all_20_1, e2) = all_20_0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with all_20_1, all_38_1, e1, e2,
% 141.43/20.81 | | | | simplifying with (29), (32) gives:
% 141.43/20.81 | | | | (34) all_38_1 = all_20_1
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with e0, all_38_1, e1, e2, simplifying
% 141.43/20.81 | | | | with (7), (29) gives:
% 141.43/20.81 | | | | (35) all_38_1 = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | COMBINE_EQS: (34), (35) imply:
% 141.43/20.81 | | | | (36) all_20_1 = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REDUCE: (33), (36) imply:
% 141.43/20.81 | | | | (37) op(e0, e2) = all_20_0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | GROUND_INST: instantiating (4) with e3, all_20_0, e2, e0, simplifying
% 141.43/20.81 | | | | with (6), (37) gives:
% 141.43/20.81 | | | | (38) all_20_0 = e3
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REDUCE: (31), (38) imply:
% 141.43/20.81 | | | | (39) $false
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | CLOSE: (39) is inconsistent.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | Case 2:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (40) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REF_CLOSE: (4), (7), (29), (40) are inconsistent by sub-proof #242.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | End of split
% 141.43/20.81 | | |
% 141.43/20.81 | | End of split
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #242 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 141.43/20.81 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (3) op(e2, e1) = all_38_1
% 141.43/20.81 (4) op(e2, e1) = e0
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | ALPHA: (1) implies:
% 141.43/20.81 | (5) ~ (all_20_1 = e0)
% 141.43/20.81 | (6) op(e2, e1) = all_20_1
% 141.43/20.81 |
% 141.43/20.81 | GROUND_INST: instantiating (2) with all_20_1, all_38_1, e1, e2, simplifying
% 141.43/20.81 | with (3), (6) gives:
% 141.43/20.81 | (7) all_38_1 = all_20_1
% 141.43/20.81 |
% 141.43/20.81 | GROUND_INST: instantiating (2) with e0, all_38_1, e1, e2, simplifying with
% 141.43/20.81 | (3), (4) gives:
% 141.43/20.81 | (8) all_38_1 = e0
% 141.43/20.81 |
% 141.43/20.81 | COMBINE_EQS: (7), (8) imply:
% 141.43/20.81 | (9) all_20_1 = e0
% 141.43/20.81 |
% 141.43/20.81 | REDUCE: (5), (9) imply:
% 141.43/20.81 | (10) $false
% 141.43/20.81 |
% 141.43/20.81 | CLOSE: (10) is inconsistent.
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #243 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (2) op(e0, e2) = e3
% 141.43/20.81 (3) op(e0, e2) = e0
% 141.43/20.81 (4) ~ (e3 = e0)
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | GROUND_INST: instantiating (1) with e3, e0, e2, e0, simplifying with (2), (3)
% 141.43/20.81 | gives:
% 141.43/20.81 | (5) e3 = e0
% 141.43/20.81 |
% 141.43/20.81 | REDUCE: (4), (5) imply:
% 141.43/20.81 | (6) $false
% 141.43/20.81 |
% 141.43/20.81 | CLOSE: (6) is inconsistent.
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #244 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (all_52_4 = e3)
% 141.43/20.81 (2) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 141.43/20.81 (3) op(e3, e2) = all_52_4
% 141.43/20.81 (4) op(e3, e3) = e1
% 141.43/20.81 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (6) ~ (e3 = e1)
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (2) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (7) implies:
% 141.43/20.81 | | (8) op(e3, e3) = e3
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #838.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (9) all_57_1 = e3 & op(e3, e2) = e3
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (9) implies:
% 141.43/20.81 | | (10) op(e3, e2) = e3
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #1107.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #245 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) op(e1, e1) = e3
% 141.43/20.81 (2) ~ (e2 = e1)
% 141.43/20.81 (3) ~ (e3 = e0)
% 141.43/20.81 (4) op(e1, e1) = all_4_2
% 141.43/20.81 (5) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.43/20.81 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.43/20.81 (6) ~ (e1 = e0)
% 141.43/20.81 (7) ~ (e2 = e0)
% 141.43/20.81 (8) ~ (e3 = e2)
% 141.43/20.81 (9) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.43/20.81 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.43/20.81 (10) ~ (all_4_2 = e2)
% 141.43/20.81 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (12) all_57_11 = e1
% 141.43/20.81 (13) all_57_7 = e3
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (9) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 141.43/20.81 | | e2)
% 141.43/20.81 | |
% 141.43/20.81 | | BETA: splitting (14) gives:
% 141.43/20.81 | |
% 141.43/20.81 | | Case 1:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (15) all_57_6 = e2 & op(e1, e3) = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | ALPHA: (15) implies:
% 141.43/20.81 | | | (16) all_57_6 = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | BETA: splitting (5) gives:
% 141.43/20.81 | | |
% 141.43/20.81 | | | Case 1:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (17) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 141.43/20.81 | | | | = e0)
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REF_CLOSE: (3), (7), (13), (16), (17) are inconsistent by sub-proof
% 141.43/20.81 | | | | #247.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | Case 2:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (18) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.81 | | | | = e0)
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REF_CLOSE: (1), (3), (6), (11), (12), (18) are inconsistent by sub-proof
% 141.43/20.81 | | | | #246.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | End of split
% 141.43/20.81 | | |
% 141.43/20.81 | | Case 2:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (19) all_57_7 = e2 & op(e1, e2) = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | ALPHA: (19) implies:
% 141.43/20.81 | | | (20) all_57_7 = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | REF_CLOSE: (8), (13), (20) are inconsistent by sub-proof #1098.
% 141.43/20.81 | | |
% 141.43/20.81 | | End of split
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (21) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 141.43/20.81 | | e2)
% 141.43/20.81 | |
% 141.43/20.81 | | BETA: splitting (21) gives:
% 141.43/20.81 | |
% 141.43/20.81 | | Case 1:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (22) all_57_8 = e2 & op(e1, e1) = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | ALPHA: (22) implies:
% 141.43/20.81 | | | (23) op(e1, e1) = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | REF_CLOSE: (4), (10), (11), (23) are inconsistent by sub-proof #1124.
% 141.43/20.81 | | |
% 141.43/20.81 | | Case 2:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (24) all_57_11 = e2 & op(e1, e0) = e2
% 141.43/20.81 | | |
% 141.43/20.81 | | | REF_CLOSE: (2), (12), (24) are inconsistent by sub-proof #913.
% 141.43/20.81 | | |
% 141.43/20.81 | | End of split
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #246 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) op(e1, e1) = e3
% 141.43/20.81 (2) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.43/20.81 (3) ~ (e3 = e0)
% 141.43/20.81 (4) ~ (e1 = e0)
% 141.43/20.81 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (6) all_57_11 = e1
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (2) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (7) implies:
% 141.43/20.81 | | (8) op(e1, e1) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (1), (3), (5), (8) are inconsistent by sub-proof #308.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (9) all_57_11 = e0 & op(e1, e0) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (9) implies:
% 141.43/20.81 | | (10) all_57_11 = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #690.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #247 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0)
% 141.43/20.81 (2) ~ (e3 = e0)
% 141.43/20.81 (3) ~ (e2 = e0)
% 141.43/20.81 (4) all_57_6 = e2
% 141.43/20.81 (5) all_57_7 = e3
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (1) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (6) all_57_6 = e0 & op(e1, e3) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (6) implies:
% 141.43/20.81 | | (7) all_57_6 = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #811.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (8) all_57_7 = e0 & op(e1, e2) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (2), (5), (8) are inconsistent by sub-proof #1061.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #248 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) op(e1, e1) = all_4_2
% 141.43/20.81 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.43/20.81 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.43/20.81 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.43/20.81 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.43/20.81 (3) ~ (e1 = e0)
% 141.43/20.81 (4) op(e3, e3) = e1
% 141.43/20.81 (5) ~ (all_4_2 = e2)
% 141.43/20.81 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (2) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (7) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 141.43/20.81 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (7) implies:
% 141.43/20.81 | | (8) op(e3, e3) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #840.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (9) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.43/20.81 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (9) implies:
% 141.43/20.81 | | (10) op(e1, e1) = e2
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (1), (5), (6), (10) are inconsistent by sub-proof #1124.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #249 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (all_10_2 = e1)
% 141.43/20.81 (2) op(e2, e2) = e1
% 141.43/20.81 (3) op(e1, e1) = all_4_2
% 141.43/20.81 (4) op(e0, e0) = all_10_2
% 141.43/20.81 (5) ~ (e1 = e0)
% 141.43/20.81 (6) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 141.43/20.81 op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 141.43/20.81 e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 141.43/20.81 = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 141.43/20.81 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.43/20.81 e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.43/20.81 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.43/20.81 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.81 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.43/20.81 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.43/20.81 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.81 $i(all_56_14))))
% 141.43/20.81 (7) ~ (all_4_2 = e2)
% 141.43/20.81 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (9) op(e2, e2) = all_6_2
% 141.43/20.81 (10) op(e3, e3) = all_14_2
% 141.43/20.81 (11) ~ (all_14_2 = e0)
% 141.43/20.81 (12) ~ (all_6_2 = e0)
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (6) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (13) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.43/20.81 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (13) implies:
% 141.43/20.81 | | (14) op(e1, e1) = e2
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (3), (7), (8), (14) are inconsistent by sub-proof #1124.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (15) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.43/20.81 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.43/20.81 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.43/20.81 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.43/20.81 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.43/20.81 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.43/20.81 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.81 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.43/20.81 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.43/20.81 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.43/20.81 | | all_56_14 & $i(all_56_14))))
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (1), (2), (4), (5), (8), (9), (10), (11), (12), (15) are
% 141.43/20.81 | | inconsistent by sub-proof #250.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #250 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 141.43/20.81 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.43/20.81 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 141.43/20.81 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.43/20.81 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 141.43/20.81 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.43/20.81 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.43/20.81 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.43/20.81 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 141.43/20.81 = all_56_14 & $i(all_56_14))))
% 141.43/20.81 (2) ~ (all_10_2 = e1)
% 141.43/20.81 (3) op(e2, e2) = e1
% 141.43/20.81 (4) op(e0, e0) = all_10_2
% 141.43/20.81 (5) ~ (e1 = e0)
% 141.43/20.81 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (7) op(e2, e2) = all_6_2
% 141.43/20.81 (8) op(e3, e3) = all_14_2
% 141.43/20.81 (9) ~ (all_14_2 = e0)
% 141.43/20.81 (10) ~ (all_6_2 = e0)
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (1) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (11) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.43/20.81 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (11) implies:
% 141.43/20.81 | | (12) op(e2, e2) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (3), (5), (6), (12) are inconsistent by sub-proof #1117.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (13) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 141.43/20.81 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 141.43/20.81 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 141.43/20.81 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.43/20.81 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 141.43/20.81 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.43/20.81 | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.43/20.81 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.81 | | $i(all_56_14)))
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (13) implies:
% 141.43/20.81 | | (14) op(e0, e0) = all_56_15
% 141.43/20.81 | | (15) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.43/20.81 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.43/20.81 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.43/20.81 | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 141.43/20.81 | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 141.43/20.81 | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.43/20.81 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.81 | | $i(all_56_14))
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (2), (4), (6), (7), (8), (9), (10), (14), (15) are inconsistent
% 141.43/20.81 | | by sub-proof #1120.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #251 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (e2 = e1)
% 141.43/20.81 (2) all_57_14 = e3
% 141.43/20.81 (3) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.43/20.81 (4) op(e0, e0) = e2
% 141.43/20.81 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (6) ~ (e3 = e1)
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (3) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (7) all_57_14 = e1 & op(e0, e1) = e1
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #705.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (8) implies:
% 141.43/20.81 | | (9) op(e0, e0) = e1
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1070.
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #252 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (e2 = e1)
% 141.43/20.81 (2) op(e0, e0) = e3
% 141.43/20.81 (3) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.43/20.81 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.43/20.81 (4) ~ (e3 = e0)
% 141.43/20.81 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.43/20.81 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.43/20.81 (6) ~ (e1 = e0)
% 141.43/20.81 (7) ~ (e2 = e0)
% 141.43/20.81 (8) ~ (e3 = e2)
% 141.43/20.81 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.81 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.43/20.81 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.43/20.81 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.43/20.81 (11) ~ (e3 = e1)
% 141.43/20.81 (12) all_57_13 = e3
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | BETA: splitting (10) gives:
% 141.43/20.81 |
% 141.43/20.81 | Case 1:
% 141.43/20.81 | |
% 141.43/20.81 | | (13) all_57_15 = e0 & op(e0, e0) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (13) implies:
% 141.43/20.81 | | (14) op(e0, e0) = e0
% 141.43/20.81 | |
% 141.43/20.81 | | REF_CLOSE: (2), (4), (9), (14) are inconsistent by sub-proof #751.
% 141.43/20.81 | |
% 141.43/20.81 | Case 2:
% 141.43/20.81 | |
% 141.43/20.81 | | (15) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.43/20.81 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 141.43/20.81 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.43/20.81 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.43/20.81 | |
% 141.43/20.81 | | ALPHA: (15) implies:
% 141.43/20.81 | | (16) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.43/20.81 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.43/20.81 | |
% 141.43/20.81 | | BETA: splitting (16) gives:
% 141.43/20.81 | |
% 141.43/20.81 | | Case 1:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (17) all_57_12 = e0 & op(e0, e3) = e0
% 141.43/20.81 | | |
% 141.43/20.81 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (17) are
% 141.43/20.81 | | | inconsistent by sub-proof #669.
% 141.43/20.81 | | |
% 141.43/20.81 | | Case 2:
% 141.43/20.81 | | |
% 141.43/20.81 | | | (18) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 141.43/20.81 | | | = e0)
% 141.43/20.81 | | |
% 141.43/20.81 | | | BETA: splitting (18) gives:
% 141.43/20.81 | | |
% 141.43/20.81 | | | Case 1:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (19) all_57_13 = e0 & op(e0, e2) = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REF_CLOSE: (4), (12), (19) are inconsistent by sub-proof #1016.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | Case 2:
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | (20) all_57_14 = e0 & op(e0, e1) = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | ALPHA: (20) implies:
% 141.43/20.81 | | | | (21) all_57_14 = e0
% 141.43/20.81 | | | |
% 141.43/20.81 | | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (11), (12), (21) are
% 141.43/20.81 | | | | inconsistent by sub-proof #666.
% 141.43/20.81 | | | |
% 141.43/20.81 | | | End of split
% 141.43/20.81 | | |
% 141.43/20.81 | | End of split
% 141.43/20.81 | |
% 141.43/20.81 | End of split
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #253 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.81 (1) ~ (e2 = e1)
% 141.43/20.81 (2) ~ (e3 = e0)
% 141.43/20.81 (3) all_57_11 = e2
% 141.43/20.81 (4) ~ (e1 = e0)
% 141.43/20.81 (5) ~ (e3 = e2)
% 141.43/20.81 (6) all_57_9 = e3
% 141.43/20.81 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.43/20.81 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.81 (8) op(e0, e0) = e2
% 141.43/20.81 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.81 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.81 (10) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.43/20.81 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.43/20.81 (11) ~ (e3 = e1)
% 141.43/20.81 (12) e3 = e0
% 141.43/20.81
% 141.43/20.81 Begin of proof
% 141.43/20.81 |
% 141.43/20.81 | SIMP: (12) implies:
% 141.43/20.81 | (13) e3 = e0
% 141.43/20.81 |
% 141.43/20.81 | COMBINE_EQS: (6), (13) imply:
% 141.43/20.81 | (14) all_57_9 = e0
% 141.43/20.81 |
% 141.43/20.81 | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (14) are
% 141.43/20.81 | inconsistent by sub-proof #851.
% 141.43/20.81 |
% 141.43/20.81 End of proof
% 141.43/20.81
% 141.43/20.81 Sub-proof #254 shows that the following formulas are inconsistent:
% 141.43/20.81 ----------------------------------------------------------------
% 141.43/20.82 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.43/20.82 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.82 (2) op(e1, e1) = e3
% 141.43/20.82 (3) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.43/20.82 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.43/20.82 (4) ~ (e2 = e1)
% 141.43/20.82 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.43/20.82 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.43/20.82 (6) ~ (all_52_4 = e1)
% 141.43/20.82 (7) ~ (all_52_9 = e2)
% 141.43/20.82 (8) ~ (e3 = e0)
% 141.43/20.82 (9) op(e1, e1) = all_4_2
% 141.43/20.82 (10) all_57_10 = e1
% 141.43/20.82 (11) ~ (all_52_8 = e1)
% 141.43/20.82 (12) op(e3, e1) = all_52_8
% 141.43/20.82 (13) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 141.43/20.82 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 141.43/20.82 (14) all_57_11 = e2
% 141.43/20.82 (15) ~ (e1 = e0)
% 141.43/20.82 (16) op(e2, e2) = e2
% 141.43/20.82 (17) op(e3, e2) = all_52_4
% 141.43/20.82 (18) ~ (e2 = e0)
% 141.43/20.82 (19) ~ (e3 = e2)
% 141.43/20.82 (20) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.43/20.82 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.43/20.82 (21) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.43/20.82 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.82 (22) ~ (all_4_2 = e2)
% 141.43/20.82 (23) op(e0, e0) = e2
% 141.43/20.82 (24) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.82 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.82 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.82 (26) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.43/20.82 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.43/20.82 (27) ~ (e3 = e1)
% 141.43/20.82 (28) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.43/20.82 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.43/20.82 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.43/20.82 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.43/20.82 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.43/20.82 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.43/20.82 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.43/20.82 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.43/20.82 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.43/20.82 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.43/20.82 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.43/20.82 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.43/20.82 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.43/20.82 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.43/20.82 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.43/20.82 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.43/20.82 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.43/20.82 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.43/20.82 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.43/20.82 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.82 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.43/20.82 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.43/20.82 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.82 $i(all_56_14))))
% 141.43/20.82 (29) all_57_8 = e3
% 141.43/20.82 (30) op(e2, e1) = all_52_9
% 141.43/20.82 (31) all_57_2 = e3
% 141.43/20.82 (32) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.82 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.82 (33) all_57_7 = e0
% 141.43/20.82 (34) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.43/20.82 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.43/20.82 (35) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.43/20.82 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | BETA: splitting (35) gives:
% 141.43/20.82 |
% 141.43/20.82 | Case 1:
% 141.43/20.82 | |
% 141.43/20.82 | | (36) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 141.43/20.82 | | e0)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (36) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (37) all_57_2 = e0 & op(e2, e3) = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (37) implies:
% 141.43/20.82 | | | (38) all_57_2 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | COMBINE_EQS: (31), (38) imply:
% 141.43/20.82 | | | (39) e3 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | COMBINE_EQS: (29), (39) imply:
% 141.43/20.82 | | | (40) all_57_8 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (4), (5), (8), (14), (15), (19), (20), (27), (33), (40) are
% 141.43/20.82 | | | inconsistent by sub-proof #436.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (41) all_57_3 = e0 & op(e2, e2) = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (41) implies:
% 141.43/20.82 | | | (42) op(e2, e2) = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (16), (18), (25), (42) are inconsistent by sub-proof #1076.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | Case 2:
% 141.43/20.82 | |
% 141.43/20.82 | | (43) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.43/20.82 | | e0)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (43) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (44) all_57_5 = e0 & op(e2, e1) = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (44) implies:
% 141.43/20.82 | | | (45) all_57_5 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 141.43/20.82 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 141.43/20.82 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 141.43/20.82 | | | (33), (34), (45) are inconsistent by sub-proof #255.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (46) all_57_10 = e0 & op(e2, e0) = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (10), (15), (46) are inconsistent by sub-proof #717.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | End of split
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #255 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.43/20.82 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.43/20.82 (2) op(e1, e1) = e3
% 141.43/20.82 (3) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.43/20.82 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.43/20.82 (4) ~ (e2 = e1)
% 141.43/20.82 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.43/20.82 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.43/20.82 (6) ~ (all_52_4 = e1)
% 141.43/20.82 (7) all_57_5 = e0
% 141.43/20.82 (8) ~ (all_52_9 = e2)
% 141.43/20.82 (9) ~ (e3 = e0)
% 141.43/20.82 (10) op(e1, e1) = all_4_2
% 141.43/20.82 (11) all_57_10 = e1
% 141.43/20.82 (12) ~ (all_52_8 = e1)
% 141.43/20.82 (13) op(e3, e1) = all_52_8
% 141.43/20.82 (14) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 141.43/20.82 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 141.43/20.82 (15) all_57_11 = e2
% 141.43/20.82 (16) ~ (e1 = e0)
% 141.43/20.82 (17) op(e2, e2) = e2
% 141.43/20.82 (18) op(e3, e2) = all_52_4
% 141.43/20.82 (19) ~ (e2 = e0)
% 141.43/20.82 (20) ~ (e3 = e2)
% 141.43/20.82 (21) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.43/20.82 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.43/20.82 (22) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.43/20.82 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.43/20.82 (23) ~ (all_4_2 = e2)
% 141.43/20.82 (24) op(e0, e0) = e2
% 141.43/20.82 (25) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.82 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.82 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.82 (27) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.43/20.82 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.43/20.82 (28) ~ (e3 = e1)
% 141.43/20.82 (29) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.43/20.82 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.43/20.82 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.43/20.82 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.43/20.82 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.43/20.82 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.43/20.82 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.43/20.82 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.43/20.82 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.43/20.82 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.43/20.82 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.43/20.82 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.43/20.82 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.43/20.82 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.43/20.82 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.43/20.82 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.43/20.82 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.43/20.82 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.43/20.82 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.43/20.82 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.82 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.43/20.82 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.43/20.82 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.82 $i(all_56_14))))
% 141.43/20.82 (30) all_57_8 = e3
% 141.43/20.82 (31) op(e2, e1) = all_52_9
% 141.43/20.82 (32) all_57_2 = e3
% 141.43/20.82 (33) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.43/20.82 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.43/20.82 (34) all_57_7 = e0
% 141.43/20.82 (35) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.43/20.82 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | BETA: splitting (14) gives:
% 141.43/20.82 |
% 141.43/20.82 | Case 1:
% 141.43/20.82 | |
% 141.43/20.82 | | (36) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 141.43/20.82 | | e1)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (36) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (37) all_57_4 = e1 & op(e3, e1) = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (12), (13), (26), (37) are inconsistent by sub-proof #349.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (38) all_57_5 = e1 & op(e2, e1) = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (7), (16), (38) are inconsistent by sub-proof #258.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | Case 2:
% 141.43/20.82 | |
% 141.43/20.82 | | (39) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 141.43/20.82 | | e1)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (39) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (40) all_57_8 = e1 & op(e1, e1) = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (40) implies:
% 141.43/20.82 | | | (41) op(e1, e1) = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (2), (26), (28), (41) are inconsistent by sub-proof #1096.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (42) all_57_14 = e1 & op(e0, e1) = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (42) implies:
% 141.43/20.82 | | | (43) all_57_14 = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | BETA: splitting (33) gives:
% 141.43/20.82 | | |
% 141.43/20.82 | | | Case 1:
% 141.43/20.82 | | | |
% 141.43/20.82 | | | | (44) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 141.43/20.82 | | | | = e0)
% 141.43/20.82 | | | |
% 141.43/20.82 | | | | BETA: splitting (44) gives:
% 141.43/20.82 | | | |
% 141.43/20.82 | | | | Case 1:
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | (45) all_57_0 = e0 & op(e3, e3) = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | ALPHA: (45) implies:
% 141.43/20.82 | | | | | (46) op(e3, e3) = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | REF_CLOSE: (4), (16), (17), (19), (20), (24), (26), (29), (46) are
% 141.43/20.82 | | | | | inconsistent by sub-proof #642.
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | Case 2:
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | (47) all_57_1 = e0 & op(e3, e2) = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | ALPHA: (47) implies:
% 141.43/20.82 | | | | | (48) all_57_1 = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | BETA: splitting (35) gives:
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | Case 1:
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | | (49) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 141.43/20.82 | | | | | | e2) = e3)
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | | BETA: splitting (49) gives:
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | | Case 1:
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | (50) all_57_1 = e3 & op(e3, e2) = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | ALPHA: (50) implies:
% 141.43/20.82 | | | | | | | (51) all_57_1 = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | COMBINE_EQS: (48), (51) imply:
% 141.43/20.82 | | | | | | | (52) e3 = e0
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | SIMP: (52) implies:
% 141.43/20.82 | | | | | | | (53) e3 = e0
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | COMBINE_EQS: (30), (53) imply:
% 141.43/20.82 | | | | | | | (54) all_57_8 = e0
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | REF_CLOSE: (4), (5), (9), (15), (16), (20), (21), (28), (34), (54)
% 141.43/20.82 | | | | | | | are inconsistent by sub-proof #436.
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | Case 2:
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | (55) all_57_3 = e3 & op(e2, e2) = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | ALPHA: (55) implies:
% 141.43/20.82 | | | | | | | (56) op(e2, e2) = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | REF_CLOSE: (17), (20), (26), (56) are inconsistent by sub-proof
% 141.43/20.82 | | | | | | | #728.
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | End of split
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | Case 2:
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | | (57) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 141.43/20.82 | | | | | | e2) = e3)
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | | BETA: splitting (57) gives:
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | | Case 1:
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | (58) all_57_7 = e3 & op(e1, e2) = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | ALPHA: (58) implies:
% 141.43/20.82 | | | | | | | (59) all_57_7 = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | COMBINE_EQS: (34), (59) imply:
% 141.43/20.82 | | | | | | | (60) e3 = e0
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | SIMP: (60) implies:
% 141.43/20.82 | | | | | | | (61) e3 = e0
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | COMBINE_EQS: (30), (61) imply:
% 141.43/20.82 | | | | | | | (62) all_57_8 = e0
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | REF_CLOSE: (4), (5), (9), (15), (16), (20), (21), (28), (34), (62)
% 141.43/20.82 | | | | | | | are inconsistent by sub-proof #436.
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | Case 2:
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | (63) all_57_13 = e3 & op(e0, e2) = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | ALPHA: (63) implies:
% 141.43/20.82 | | | | | | | (64) all_57_13 = e3
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | BETA: splitting (1) gives:
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | | Case 1:
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | | (65) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 &
% 141.43/20.82 | | | | | | | | op(e2, e2) = e1)
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | | BETA: splitting (65) gives:
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | | Case 1:
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | (66) all_57_1 = e1 & op(e3, e2) = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | REF_CLOSE: (6), (18), (26), (66) are inconsistent by sub-proof
% 141.43/20.82 | | | | | | | | | #844.
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | Case 2:
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | (67) all_57_3 = e1 & op(e2, e2) = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | ALPHA: (67) implies:
% 141.43/20.82 | | | | | | | | | (68) op(e2, e2) = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | REF_CLOSE: (3), (4), (7), (11), (19), (20), (26), (32), (68)
% 141.43/20.82 | | | | | | | | | are inconsistent by sub-proof #592.
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | End of split
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | Case 2:
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | | (69) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 &
% 141.43/20.82 | | | | | | | | op(e0, e2) = e1)
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | | BETA: splitting (69) gives:
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | | Case 1:
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | (70) all_57_7 = e1 & op(e1, e2) = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | ALPHA: (70) implies:
% 141.43/20.82 | | | | | | | | | (71) all_57_7 = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | REF_CLOSE: (16), (34), (71) are inconsistent by sub-proof
% 141.43/20.82 | | | | | | | | | #712.
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | Case 2:
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | (72) all_57_13 = e1 & op(e0, e2) = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | ALPHA: (72) implies:
% 141.43/20.82 | | | | | | | | | (73) all_57_13 = e1
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | | REF_CLOSE: (28), (64), (73) are inconsistent by sub-proof
% 141.43/20.82 | | | | | | | | | #1001.
% 141.43/20.82 | | | | | | | | |
% 141.43/20.82 | | | | | | | | End of split
% 141.43/20.82 | | | | | | | |
% 141.43/20.82 | | | | | | | End of split
% 141.43/20.82 | | | | | | |
% 141.43/20.82 | | | | | | End of split
% 141.43/20.82 | | | | | |
% 141.43/20.82 | | | | | End of split
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | End of split
% 141.43/20.82 | | | |
% 141.43/20.82 | | | Case 2:
% 141.43/20.82 | | | |
% 141.43/20.82 | | | | (74) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 141.43/20.82 | | | | = e0)
% 141.43/20.82 | | | |
% 141.43/20.82 | | | | BETA: splitting (74) gives:
% 141.43/20.82 | | | |
% 141.43/20.82 | | | | Case 1:
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | (75) all_57_4 = e0 & op(e3, e1) = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | ALPHA: (75) implies:
% 141.43/20.82 | | | | | (76) all_57_4 = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | REF_CLOSE: (4), (8), (10), (19), (23), (25), (26), (31), (43), (76)
% 141.43/20.82 | | | | | are inconsistent by sub-proof #256.
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | Case 2:
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | (77) all_57_9 = e0 & op(e3, e0) = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | ALPHA: (77) implies:
% 141.43/20.82 | | | | | (78) all_57_9 = e0
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | | REF_CLOSE: (4), (9), (15), (16), (20), (22), (24), (26), (27), (28),
% 141.43/20.82 | | | | | (78) are inconsistent by sub-proof #851.
% 141.43/20.82 | | | | |
% 141.43/20.82 | | | | End of split
% 141.43/20.82 | | | |
% 141.43/20.82 | | | End of split
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | End of split
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #256 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) ~ (e2 = e1)
% 141.43/20.82 (2) all_57_4 = e0
% 141.43/20.82 (3) ~ (all_52_9 = e2)
% 141.43/20.82 (4) op(e1, e1) = all_4_2
% 141.43/20.82 (5) all_57_14 = e1
% 141.43/20.82 (6) ~ (e2 = e0)
% 141.43/20.82 (7) ~ (all_4_2 = e2)
% 141.43/20.82 (8) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.43/20.82 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.82 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.82 (10) op(e2, e1) = all_52_9
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | BETA: splitting (8) gives:
% 141.43/20.82 |
% 141.43/20.82 | Case 1:
% 141.43/20.82 | |
% 141.43/20.82 | | (11) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 141.43/20.82 | | e2)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (11) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (12) all_57_4 = e2 & op(e3, e1) = e2
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (12) implies:
% 141.43/20.82 | | | (13) all_57_4 = e2
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #1050.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (14) all_57_5 = e2 & op(e2, e1) = e2
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (14) implies:
% 141.43/20.82 | | | (15) op(e2, e1) = e2
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (3), (9), (10), (15) are inconsistent by sub-proof #890.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | Case 2:
% 141.43/20.82 | |
% 141.43/20.82 | | (16) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 141.43/20.82 | | e2)
% 141.43/20.82 | |
% 141.43/20.82 | | REF_CLOSE: (1), (4), (5), (7), (9), (16) are inconsistent by sub-proof #257.
% 141.43/20.82 | |
% 141.43/20.82 | End of split
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #257 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.43/20.82 (2) ~ (e2 = e1)
% 141.43/20.82 (3) op(e1, e1) = all_4_2
% 141.43/20.82 (4) all_57_14 = e1
% 141.43/20.82 (5) ~ (all_4_2 = e2)
% 141.43/20.82 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | BETA: splitting (1) gives:
% 141.43/20.82 |
% 141.43/20.82 | Case 1:
% 141.43/20.82 | |
% 141.43/20.82 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 141.43/20.82 | |
% 141.43/20.82 | | ALPHA: (7) implies:
% 141.43/20.82 | | (8) op(e1, e1) = e2
% 141.43/20.82 | |
% 141.43/20.82 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1124.
% 141.43/20.82 | |
% 141.43/20.82 | Case 2:
% 141.43/20.82 | |
% 141.43/20.82 | | (9) all_57_14 = e2 & op(e0, e1) = e2
% 141.43/20.82 | |
% 141.43/20.82 | | ALPHA: (9) implies:
% 141.43/20.82 | | (10) all_57_14 = e2
% 141.43/20.82 | |
% 141.43/20.82 | | REF_CLOSE: (2), (4), (10) are inconsistent by sub-proof #1048.
% 141.43/20.82 | |
% 141.43/20.82 | End of split
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #258 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) all_57_5 = e1 & op(e2, e1) = e1
% 141.43/20.82 (2) all_57_5 = e0
% 141.43/20.82 (3) ~ (e1 = e0)
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | ALPHA: (1) implies:
% 141.43/20.82 | (4) all_57_5 = e1
% 141.43/20.82 |
% 141.43/20.82 | COMBINE_EQS: (2), (4) imply:
% 141.43/20.82 | (5) e1 = e0
% 141.43/20.82 |
% 141.43/20.82 | REDUCE: (3), (5) imply:
% 141.43/20.82 | (6) $false
% 141.43/20.82 |
% 141.43/20.82 | CLOSE: (6) is inconsistent.
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #259 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) ~ (all_52_8 = e3)
% 141.43/20.82 (2) ~ (e3 = e0)
% 141.43/20.82 (3) op(e3, e1) = all_52_8
% 141.43/20.82 (4) all_57_9 = e2
% 141.43/20.82 (5) ~ (e3 = e2)
% 141.43/20.82 (6) op(e3, e3) = e1
% 141.43/20.82 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.82 (8) ~ (e3 = e1)
% 141.43/20.82 (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.82 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.82 (10) all_57_1 = e0
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | BETA: splitting (9) gives:
% 141.43/20.82 |
% 141.43/20.82 | Case 1:
% 141.43/20.82 | |
% 141.43/20.82 | | (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 141.43/20.82 | | e3)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (11) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (12) all_57_0 = e3 & op(e3, e3) = e3
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (12) implies:
% 141.43/20.82 | | | (13) op(e3, e3) = e3
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (6), (7), (8), (13) are inconsistent by sub-proof #838.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (14) all_57_1 = e3 & op(e3, e2) = e3
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #408.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | Case 2:
% 141.43/20.82 | |
% 141.43/20.82 | | (15) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 141.43/20.82 | | e3)
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (15) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (16) all_57_4 = e3 & op(e3, e1) = e3
% 141.43/20.82 | | |
% 141.43/20.82 | | | ALPHA: (16) implies:
% 141.43/20.82 | | | (17) op(e3, e1) = e3
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (1), (3), (7), (17) are inconsistent by sub-proof #1106.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (18) all_57_9 = e3 & op(e3, e0) = e3
% 141.43/20.82 | | |
% 141.43/20.82 | | | REF_CLOSE: (4), (5), (18) are inconsistent by sub-proof #479.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | End of split
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #260 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.82 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.82 (2) op(e3, e1) = all_34_1
% 141.43/20.82 (3) op(e3, e1) = e0
% 141.43/20.82 (4) ~ (all_34_1 = e0)
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | GROUND_INST: instantiating (1) with e0, all_34_1, e1, e3, simplifying with
% 141.43/20.82 | (2), (3) gives:
% 141.43/20.82 | (5) all_34_1 = e0
% 141.43/20.82 |
% 141.43/20.82 | REDUCE: (4), (5) imply:
% 141.43/20.82 | (6) $false
% 141.43/20.82 |
% 141.43/20.82 | CLOSE: (6) is inconsistent.
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #261 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) ~ (all_22_0 = e1)
% 141.43/20.82 (2) ~ (all_22_0 = e2)
% 141.43/20.82 (3) ~ (all_22_0 = e0)
% 141.43/20.82 (4) all_54_4 = all_22_0
% 141.43/20.82 (5) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 141.43/20.82
% 141.43/20.82 Begin of proof
% 141.43/20.82 |
% 141.43/20.82 | BETA: splitting (5) gives:
% 141.43/20.82 |
% 141.43/20.82 | Case 1:
% 141.43/20.82 | |
% 141.43/20.82 | | (6) all_54_4 = e2
% 141.43/20.82 | |
% 141.43/20.82 | | COMBINE_EQS: (4), (6) imply:
% 141.43/20.82 | | (7) all_22_0 = e2
% 141.43/20.82 | |
% 141.43/20.82 | | SIMP: (7) implies:
% 141.43/20.82 | | (8) all_22_0 = e2
% 141.43/20.82 | |
% 141.43/20.82 | | REDUCE: (2), (8) imply:
% 141.43/20.82 | | (9) $false
% 141.43/20.82 | |
% 141.43/20.82 | | CLOSE: (9) is inconsistent.
% 141.43/20.82 | |
% 141.43/20.82 | Case 2:
% 141.43/20.82 | |
% 141.43/20.82 | | (10) all_54_4 = e1 | all_54_4 = e0
% 141.43/20.82 | |
% 141.43/20.82 | | BETA: splitting (10) gives:
% 141.43/20.82 | |
% 141.43/20.82 | | Case 1:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (11) all_54_4 = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | COMBINE_EQS: (4), (11) imply:
% 141.43/20.82 | | | (12) all_22_0 = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | SIMP: (12) implies:
% 141.43/20.82 | | | (13) all_22_0 = e1
% 141.43/20.82 | | |
% 141.43/20.82 | | | REDUCE: (1), (13) imply:
% 141.43/20.82 | | | (14) $false
% 141.43/20.82 | | |
% 141.43/20.82 | | | CLOSE: (14) is inconsistent.
% 141.43/20.82 | | |
% 141.43/20.82 | | Case 2:
% 141.43/20.82 | | |
% 141.43/20.82 | | | (15) all_54_4 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | COMBINE_EQS: (4), (15) imply:
% 141.43/20.82 | | | (16) all_22_0 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | SIMP: (16) implies:
% 141.43/20.82 | | | (17) all_22_0 = e0
% 141.43/20.82 | | |
% 141.43/20.82 | | | REDUCE: (3), (17) imply:
% 141.43/20.82 | | | (18) $false
% 141.43/20.82 | | |
% 141.43/20.82 | | | CLOSE: (18) is inconsistent.
% 141.43/20.82 | | |
% 141.43/20.82 | | End of split
% 141.43/20.82 | |
% 141.43/20.82 | End of split
% 141.43/20.82 |
% 141.43/20.82 End of proof
% 141.43/20.82
% 141.43/20.82 Sub-proof #262 shows that the following formulas are inconsistent:
% 141.43/20.82 ----------------------------------------------------------------
% 141.43/20.82 (1) ~ (all_52_3 = all_52_7)
% 141.43/20.82 (2) op(e1, e3) = all_52_2
% 141.43/20.82 (3) op(e1, e1) = e3
% 141.43/20.82 (4) ~ (all_52_8 = e3)
% 141.43/20.82 (5) ~ (e2 = e1)
% 141.43/20.82 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.43/20.82 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.43/20.82 (7) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.82 (8) op(e0, e3) = all_52_3
% 141.43/20.83 (9) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.83 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.83 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.83 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.83 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.43/20.83 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.43/20.83 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.43/20.83 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.43/20.83 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.43/20.83 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.43/20.83 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.43/20.83 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.43/20.83 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.43/20.83 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.83 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.43/20.83 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.43/20.83 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.43/20.83 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.43/20.83 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.83 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.83 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.83 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.83 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.83 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.83 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.83 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.43/20.83 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.43/20.83 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.43/20.83 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.43/20.83 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.43/20.83 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.43/20.83 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.83 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.43/20.83 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.83 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.83 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.43/20.83 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.83 (10) all_54_12 = all_52_3
% 141.43/20.83 (11) op(e1, e1) = all_4_2
% 141.43/20.83 (12) op(e3, e1) = all_52_8
% 141.43/20.83 (13) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.43/20.83 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.43/20.83 (14) op(e2, e2) = e2
% 141.43/20.83 (15) ~ (all_52_3 = e1)
% 141.43/20.83 (16) ~ (e3 = e2)
% 141.43/20.83 (17) ~ (all_52_2 = e1)
% 141.43/20.83 (18) op(e3, e3) = e1
% 141.43/20.83 (19) ~ (all_4_2 = e2)
% 141.43/20.83 (20) op(e0, e0) = e2
% 141.43/20.83 (21) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.83 (22) ~ (e3 = e1)
% 141.43/20.83 (23) op(e0, e2) = all_52_7
% 141.43/20.83 (24) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.43/20.83 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.43/20.83 (25) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.43/20.83 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.43/20.83 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.43/20.83 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.43/20.83 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.43/20.83 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.43/20.83 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.43/20.83 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.43/20.83 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.43/20.83 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.43/20.83 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.43/20.83 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.43/20.83 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.43/20.83 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.43/20.83 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.43/20.83 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.43/20.83 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.43/20.83 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.43/20.83 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.43/20.83 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.83 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.43/20.83 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.43/20.83 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.83 $i(all_56_14))))
% 141.43/20.83 (26) all_57_11 = e3
% 141.43/20.83 (27) ~ (all_52_3 = e3)
% 141.43/20.83 (28) ~ (all_52_3 = e2)
% 141.43/20.83
% 141.43/20.83 Begin of proof
% 141.43/20.83 |
% 141.43/20.83 | BETA: splitting (7) gives:
% 141.43/20.83 |
% 141.43/20.83 | Case 1:
% 141.43/20.83 | |
% 141.43/20.83 | | (29) all_54_12 = e3
% 141.43/20.83 | |
% 141.43/20.83 | | COMBINE_EQS: (10), (29) imply:
% 141.43/20.83 | | (30) all_52_3 = e3
% 141.43/20.83 | |
% 141.43/20.83 | | REDUCE: (27), (30) imply:
% 141.43/20.83 | | (31) $false
% 141.43/20.83 | |
% 141.43/20.83 | | CLOSE: (31) is inconsistent.
% 141.43/20.83 | |
% 141.43/20.83 | Case 2:
% 141.43/20.83 | |
% 141.43/20.83 | | (32) ~ (all_54_12 = e3)
% 141.43/20.83 | | (33) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.83 | |
% 141.43/20.83 | | BETA: splitting (33) gives:
% 141.43/20.83 | |
% 141.43/20.83 | | Case 1:
% 141.43/20.83 | | |
% 141.43/20.83 | | | (34) all_54_12 = e2
% 141.43/20.83 | | |
% 141.43/20.83 | | | COMBINE_EQS: (10), (34) imply:
% 141.43/20.83 | | | (35) all_52_3 = e2
% 141.43/20.83 | | |
% 141.43/20.83 | | | REDUCE: (28), (35) imply:
% 141.43/20.83 | | | (36) $false
% 141.43/20.83 | | |
% 141.43/20.83 | | | CLOSE: (36) is inconsistent.
% 141.43/20.83 | | |
% 141.43/20.83 | | Case 2:
% 141.43/20.83 | | |
% 141.43/20.83 | | | (37) ~ (all_54_12 = e2)
% 141.43/20.83 | | | (38) all_54_12 = e1 | all_54_12 = e0
% 141.43/20.83 | | |
% 141.43/20.83 | | | BETA: splitting (38) gives:
% 141.43/20.83 | | |
% 141.43/20.83 | | | Case 1:
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | (39) all_54_12 = e1
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REF_CLOSE: (10), (15), (39) are inconsistent by sub-proof #662.
% 141.43/20.83 | | | |
% 141.43/20.83 | | | Case 2:
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | (40) all_54_12 = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | COMBINE_EQS: (10), (40) imply:
% 141.43/20.83 | | | | (41) all_52_3 = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (41) implies:
% 141.43/20.83 | | | | (42) all_52_3 = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (1), (42) imply:
% 141.43/20.83 | | | | (43) ~ (all_52_7 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (43) implies:
% 141.43/20.83 | | | | (44) ~ (all_52_7 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (27), (42) imply:
% 141.43/20.83 | | | | (45) ~ (e3 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (45) implies:
% 141.43/20.83 | | | | (46) ~ (e3 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (28), (42) imply:
% 141.43/20.83 | | | | (47) ~ (e2 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (47) implies:
% 141.43/20.83 | | | | (48) ~ (e2 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (15), (42) imply:
% 141.43/20.83 | | | | (49) ~ (e1 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (49) implies:
% 141.43/20.83 | | | | (50) ~ (e1 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (8), (42) imply:
% 141.43/20.83 | | | | (51) op(e0, e3) = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | BETA: splitting (6) gives:
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | Case 1:
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | (52) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 141.43/20.83 | | | | | e2) = e1)
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | BETA: splitting (52) gives:
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | Case 1:
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | (53) all_57_6 = e1 & op(e1, e3) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | ALPHA: (53) implies:
% 141.43/20.83 | | | | | | (54) op(e1, e3) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | REF_CLOSE: (2), (17), (21), (54) are inconsistent by sub-proof #332.
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | Case 2:
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | (55) all_57_7 = e1 & op(e1, e2) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | ALPHA: (55) implies:
% 141.43/20.83 | | | | | | (56) all_57_7 = e1
% 141.43/20.83 | | | | | | (57) op(e1, e2) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | BETA: splitting (9) gives:
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | Case 1:
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | | (58) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 141.43/20.83 | | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2)
% 141.43/20.83 | | | | | | | = all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 &
% 141.43/20.83 | | | | | | | op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1)
% 141.43/20.83 | | | | | | | = all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 141.43/20.83 | | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.43/20.83 | | | | | | | = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.43/20.83 | | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3)
% 141.43/20.83 | | | | | | | = all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 &
% 141.43/20.83 | | | | | | | op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.43/20.83 | | | | | | | = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 141.43/20.83 | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3)
% 141.43/20.83 | | | | | | | = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.43/20.83 | | | | | | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2)
% 141.43/20.83 | | | | | | | = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9
% 141.43/20.83 | | | | | | | & $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) =
% 141.43/20.83 | | | | | | | e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13
% 141.43/20.83 | | | | | | | & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) =
% 141.43/20.83 | | | | | | | e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.83 | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0)
% 141.43/20.83 | | | | | | | | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.43/20.83 | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) =
% 141.43/20.83 | | | | | | | e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.43/20.83 | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2)
% 141.43/20.83 | | | | | | | | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.43/20.83 | | | | | | | $i(all_56_12))))
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | | BETA: splitting (58) gives:
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | | Case 1:
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | (59) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 141.43/20.83 | | | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2)
% 141.43/20.83 | | | | | | | | = all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 &
% 141.43/20.83 | | | | | | | | op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1)
% 141.43/20.83 | | | | | | | | = all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 141.43/20.83 | | | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.43/20.83 | | | | | | | | = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.43/20.83 | | | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3)
% 141.43/20.83 | | | | | | | | = all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 &
% 141.43/20.83 | | | | | | | | op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.43/20.83 | | | | | | | | = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 141.43/20.83 | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3)
% 141.43/20.83 | | | | | | | | = all_56_10 & $i(all_56_10)))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | ALPHA: (59) implies:
% 141.43/20.83 | | | | | | | | (60) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 =
% 141.43/20.83 | | | | | | | | e0) & op(e0, e3) = all_56_10 & $i(all_56_10))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | REF_CLOSE: (16), (20), (21), (51), (60) are inconsistent by
% 141.43/20.83 | | | | | | | | sub-proof #953.
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | Case 2:
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | (61) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3
% 141.43/20.83 | | | | | | | | & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3,
% 141.43/20.83 | | | | | | | | e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1
% 141.43/20.83 | | | | | | | | & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.43/20.83 | | | | | | | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 =
% 141.43/20.83 | | | | | | | | e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.43/20.83 | | | | | | | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0
% 141.43/20.83 | | | | | | | | & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.43/20.83 | | | | | | | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 =
% 141.43/20.83 | | | | | | | | e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.43/20.83 | | | | | | | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 141.43/20.83 | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 141.43/20.83 | | | | | | | | e2) = all_56_12 & $i(all_56_12)))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | ALPHA: (61) implies:
% 141.43/20.83 | | | | | | | | (62) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1)
% 141.43/20.83 | | | | | | | | & op(e1, e2) = all_56_7 & $i(all_56_7))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | REF_CLOSE: (11), (19), (21), (57), (62) are inconsistent by
% 141.43/20.83 | | | | | | | | sub-proof #421.
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | End of split
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | Case 2:
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | | (63) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3
% 141.43/20.83 | | | | | | | & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3,
% 141.43/20.83 | | | | | | | e3) = all_56_9 & $i(all_56_9))) & ((all_56_4 = e2
% 141.43/20.83 | | | | | | | & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.83 | | | | | | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 =
% 141.43/20.83 | | | | | | | e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.43/20.83 | | | | | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1
% 141.43/20.83 | | | | | | | & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 141.43/20.83 | | | | | | | e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0
% 141.43/20.83 | | | | | | | & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.83 | | | | | | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 =
% 141.43/20.83 | | | | | | | e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.43/20.83 | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0,
% 141.43/20.83 | | | | | | | e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 141.43/20.83 | | | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.43/20.83 | | | | | | | = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 &
% 141.43/20.83 | | | | | | | op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2)
% 141.43/20.83 | | | | | | | = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 &
% 141.43/20.83 | | | | | | | op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.43/20.83 | | | | | | | = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 &
% 141.43/20.83 | | | | | | | op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0)
% 141.43/20.83 | | | | | | | = all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 &
% 141.43/20.83 | | | | | | | op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.83 | | | | | | | = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 141.43/20.83 | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0)
% 141.43/20.83 | | | | | | | = all_56_8 & $i(all_56_8))))
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | | BETA: splitting (63) gives:
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | | Case 1:
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | (64) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3
% 141.43/20.83 | | | | | | | | & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3,
% 141.43/20.83 | | | | | | | | e3) = all_56_9 & $i(all_56_9))) & ((all_56_4 = e2
% 141.43/20.83 | | | | | | | | & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.83 | | | | | | | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 =
% 141.43/20.83 | | | | | | | | e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.43/20.83 | | | | | | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1
% 141.43/20.83 | | | | | | | | & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 141.43/20.83 | | | | | | | | e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0
% 141.43/20.83 | | | | | | | | & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.43/20.83 | | | | | | | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 =
% 141.43/20.83 | | | | | | | | e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.43/20.83 | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | ALPHA: (64) implies:
% 141.43/20.83 | | | | | | | | (65) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1)
% 141.43/20.83 | | | | | | | | & op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | REF_CLOSE: (4), (12), (18), (21), (65) are inconsistent by
% 141.43/20.83 | | | | | | | | sub-proof #295.
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | Case 2:
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | (66) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3
% 141.43/20.83 | | | | | | | | & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3,
% 141.43/20.83 | | | | | | | | e3) = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2
% 141.43/20.83 | | | | | | | | & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.43/20.83 | | | | | | | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 =
% 141.43/20.83 | | | | | | | | e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 141.43/20.83 | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.83 | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3)
% 141.43/20.83 | | | | | | | | & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.83 | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 =
% 141.43/20.83 | | | | | | | | e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.43/20.83 | | | | | | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 =
% 141.43/20.83 | | | | | | | | e1) & op(e1, e0) = all_56_8 & $i(all_56_8)))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | ALPHA: (66) implies:
% 141.43/20.83 | | | | | | | | (67) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3)
% 141.43/20.83 | | | | | | | | & op(e3, e0) = all_56_2 & $i(all_56_2))
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | BETA: splitting (67) gives:
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | | Case 1:
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | (68) all_56_9 = e0 & op(e3, e3) = e0
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | ALPHA: (68) implies:
% 141.43/20.83 | | | | | | | | | (69) op(e3, e3) = e0
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | REF_CLOSE: (5), (14), (16), (20), (21), (25), (48), (50), (69)
% 141.43/20.83 | | | | | | | | | are inconsistent by sub-proof #642.
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | Case 2:
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | (70) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.43/20.83 | | | | | | | | | $i(all_56_2)
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | ALPHA: (70) implies:
% 141.43/20.83 | | | | | | | | | (71) ~ (all_56_2 = e3)
% 141.43/20.83 | | | | | | | | | (72) op(e3, e0) = all_56_2
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | BETA: splitting (24) gives:
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | | Case 1:
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | (73) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 141.43/20.83 | | | | | | | | | | op(e3, e2) = e3)
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | BETA: splitting (73) gives:
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | Case 1:
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | (74) all_57_0 = e3 & op(e3, e3) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | ALPHA: (74) implies:
% 141.43/20.83 | | | | | | | | | | | (75) op(e3, e3) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | REF_CLOSE: (18), (21), (22), (75) are inconsistent by
% 141.43/20.83 | | | | | | | | | | | sub-proof #838.
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | Case 2:
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | (76) all_57_1 = e3 & op(e3, e2) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | ALPHA: (76) implies:
% 141.43/20.83 | | | | | | | | | | | (77) all_57_1 = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | REF_CLOSE: (13), (14), (21), (23), (44), (46), (48), (50),
% 141.43/20.83 | | | | | | | | | | | (56), (77) are inconsistent by sub-proof #286.
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | End of split
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | Case 2:
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | (78) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 141.43/20.83 | | | | | | | | | | op(e3, e0) = e3)
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | BETA: splitting (78) gives:
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | Case 1:
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | (79) all_57_4 = e3 & op(e3, e1) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | ALPHA: (79) implies:
% 141.43/20.83 | | | | | | | | | | | (80) op(e3, e1) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | REF_CLOSE: (4), (12), (21), (80) are inconsistent by
% 141.43/20.83 | | | | | | | | | | | sub-proof #1106.
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | Case 2:
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | (81) all_57_9 = e3 & op(e3, e0) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | ALPHA: (81) implies:
% 141.43/20.83 | | | | | | | | | | | (82) op(e3, e0) = e3
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | | REF_CLOSE: (21), (71), (72), (82) are inconsistent by
% 141.43/20.83 | | | | | | | | | | | sub-proof #274.
% 141.43/20.83 | | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | | End of split
% 141.43/20.83 | | | | | | | | | |
% 141.43/20.83 | | | | | | | | | End of split
% 141.43/20.83 | | | | | | | | |
% 141.43/20.83 | | | | | | | | End of split
% 141.43/20.83 | | | | | | | |
% 141.43/20.83 | | | | | | | End of split
% 141.43/20.83 | | | | | | |
% 141.43/20.83 | | | | | | End of split
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | End of split
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | Case 2:
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | (83) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 141.43/20.83 | | | | | e0) = e1)
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | BETA: splitting (83) gives:
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | Case 1:
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | (84) all_57_8 = e1 & op(e1, e1) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | ALPHA: (84) implies:
% 141.43/20.83 | | | | | | (85) op(e1, e1) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | REF_CLOSE: (3), (21), (22), (85) are inconsistent by sub-proof
% 141.43/20.83 | | | | | | #1096.
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | Case 2:
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | (86) all_57_11 = e1 & op(e1, e0) = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | ALPHA: (86) implies:
% 141.43/20.83 | | | | | | (87) all_57_11 = e1
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | | REF_CLOSE: (22), (26), (87) are inconsistent by sub-proof #912.
% 141.43/20.83 | | | | | |
% 141.43/20.83 | | | | | End of split
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | End of split
% 141.43/20.83 | | | |
% 141.43/20.83 | | | End of split
% 141.43/20.83 | | |
% 141.43/20.83 | | End of split
% 141.43/20.83 | |
% 141.43/20.83 | End of split
% 141.43/20.83 |
% 141.43/20.83 End of proof
% 141.43/20.83
% 141.43/20.83 Sub-proof #263 shows that the following formulas are inconsistent:
% 141.43/20.83 ----------------------------------------------------------------
% 141.43/20.83 (1) op(e1, e1) = e3
% 141.43/20.83 (2) ~ (e3 = e0)
% 141.43/20.83 (3) ~ (all_52_11 = e0)
% 141.43/20.83 (4) op(e0, e1) = all_52_11
% 141.43/20.83 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.83 (6) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.43/20.83
% 141.43/20.83 Begin of proof
% 141.43/20.83 |
% 141.43/20.83 | BETA: splitting (6) gives:
% 141.43/20.83 |
% 141.43/20.83 | Case 1:
% 141.43/20.83 | |
% 141.43/20.83 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 141.43/20.83 | |
% 141.43/20.83 | | ALPHA: (7) implies:
% 141.43/20.83 | | (8) op(e1, e1) = e0
% 141.43/20.83 | |
% 141.43/20.83 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #308.
% 141.43/20.83 | |
% 141.43/20.83 | Case 2:
% 141.43/20.83 | |
% 141.43/20.83 | | (9) all_57_14 = e0 & op(e0, e1) = e0
% 141.43/20.83 | |
% 141.43/20.83 | | ALPHA: (9) implies:
% 141.43/20.83 | | (10) op(e0, e1) = e0
% 141.43/20.83 | |
% 141.43/20.83 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #886.
% 141.43/20.83 | |
% 141.43/20.83 | End of split
% 141.43/20.83 |
% 141.43/20.83 End of proof
% 141.43/20.83
% 141.43/20.83 Sub-proof #264 shows that the following formulas are inconsistent:
% 141.43/20.83 ----------------------------------------------------------------
% 141.43/20.83 (1) all_57_5 = e0 & op(e2, e1) = e0
% 141.43/20.83 (2) all_57_5 = e1
% 141.43/20.83 (3) ~ (e1 = e0)
% 141.43/20.83
% 141.43/20.83 Begin of proof
% 141.43/20.83 |
% 141.43/20.83 | ALPHA: (1) implies:
% 141.43/20.83 | (4) all_57_5 = e0
% 141.43/20.83 |
% 141.43/20.83 | COMBINE_EQS: (2), (4) imply:
% 141.43/20.83 | (5) e1 = e0
% 141.43/20.83 |
% 141.43/20.83 | REDUCE: (3), (5) imply:
% 141.43/20.83 | (6) $false
% 141.43/20.83 |
% 141.43/20.83 | CLOSE: (6) is inconsistent.
% 141.43/20.83 |
% 141.43/20.83 End of proof
% 141.43/20.83
% 141.43/20.83 Sub-proof #265 shows that the following formulas are inconsistent:
% 141.43/20.83 ----------------------------------------------------------------
% 141.43/20.83 (1) ~ (all_52_3 = all_52_7)
% 141.43/20.83 (2) ~ (all_52_8 = e3)
% 141.43/20.83 (3) ~ (e2 = e1)
% 141.43/20.83 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.83 (5) op(e0, e3) = all_52_3
% 141.43/20.83 (6) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.43/20.83 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.43/20.83 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.43/20.83 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.43/20.83 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.43/20.83 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.43/20.83 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.43/20.83 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.43/20.83 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.43/20.83 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.43/20.83 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.43/20.83 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.43/20.83 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.43/20.83 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.43/20.83 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.43/20.83 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.43/20.83 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.43/20.83 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.43/20.83 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.43/20.83 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.43/20.83 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.43/20.83 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.43/20.83 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.83 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.43/20.83 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.43/20.83 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.43/20.83 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.43/20.83 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.43/20.83 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.43/20.83 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.43/20.83 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.43/20.83 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.83 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.43/20.83 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.43/20.83 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.43/20.83 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.43/20.83 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.43/20.83 (7) all_54_12 = all_52_3
% 141.43/20.83 (8) op(e3, e1) = all_52_8
% 141.43/20.83 (9) op(e2, e2) = e2
% 141.43/20.83 (10) ~ (all_52_3 = e1)
% 141.43/20.83 (11) ~ (e3 = e2)
% 141.43/20.83 (12) op(e3, e3) = e1
% 141.43/20.83 (13) op(e0, e0) = e2
% 141.43/20.83 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.83 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.83 (15) op(e0, e2) = all_52_7
% 141.43/20.83 (16) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.43/20.83 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.43/20.83 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.43/20.83 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.43/20.83 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.43/20.83 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.43/20.83 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.43/20.83 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.43/20.83 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.43/20.83 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.43/20.83 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.43/20.83 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.43/20.83 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.43/20.83 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.43/20.83 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.43/20.83 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.43/20.83 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.43/20.83 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.43/20.83 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.43/20.83 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.43/20.83 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.43/20.83 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.43/20.83 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.43/20.83 $i(all_56_14))))
% 141.43/20.83 (17) ~ (all_52_3 = e3)
% 141.43/20.83 (18) ~ (all_52_3 = e2)
% 141.43/20.83 (19) op(e3, e0) = e3
% 141.43/20.83
% 141.43/20.83 Begin of proof
% 141.43/20.83 |
% 141.43/20.83 | BETA: splitting (4) gives:
% 141.43/20.83 |
% 141.43/20.83 | Case 1:
% 141.43/20.83 | |
% 141.43/20.83 | | (20) all_54_12 = e3
% 141.43/20.83 | |
% 141.43/20.83 | | COMBINE_EQS: (7), (20) imply:
% 141.43/20.83 | | (21) all_52_3 = e3
% 141.43/20.83 | |
% 141.43/20.83 | | REDUCE: (17), (21) imply:
% 141.43/20.83 | | (22) $false
% 141.43/20.83 | |
% 141.43/20.83 | | CLOSE: (22) is inconsistent.
% 141.43/20.83 | |
% 141.43/20.83 | Case 2:
% 141.43/20.83 | |
% 141.43/20.83 | | (23) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 141.43/20.83 | |
% 141.43/20.83 | | BETA: splitting (23) gives:
% 141.43/20.83 | |
% 141.43/20.83 | | Case 1:
% 141.43/20.83 | | |
% 141.43/20.83 | | | (24) all_54_12 = e2
% 141.43/20.83 | | |
% 141.43/20.83 | | | COMBINE_EQS: (7), (24) imply:
% 141.43/20.83 | | | (25) all_52_3 = e2
% 141.43/20.83 | | |
% 141.43/20.83 | | | REDUCE: (18), (25) imply:
% 141.43/20.83 | | | (26) $false
% 141.43/20.83 | | |
% 141.43/20.83 | | | CLOSE: (26) is inconsistent.
% 141.43/20.83 | | |
% 141.43/20.83 | | Case 2:
% 141.43/20.83 | | |
% 141.43/20.83 | | | (27) ~ (all_54_12 = e2)
% 141.43/20.83 | | | (28) all_54_12 = e1 | all_54_12 = e0
% 141.43/20.83 | | |
% 141.43/20.83 | | | BETA: splitting (28) gives:
% 141.43/20.83 | | |
% 141.43/20.83 | | | Case 1:
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | (29) all_54_12 = e1
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REF_CLOSE: (7), (10), (29) are inconsistent by sub-proof #662.
% 141.43/20.83 | | | |
% 141.43/20.83 | | | Case 2:
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | (30) all_54_12 = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | COMBINE_EQS: (7), (30) imply:
% 141.43/20.83 | | | | (31) all_52_3 = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (31) implies:
% 141.43/20.83 | | | | (32) all_52_3 = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (1), (32) imply:
% 141.43/20.83 | | | | (33) ~ (all_52_7 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (33) implies:
% 141.43/20.83 | | | | (34) ~ (all_52_7 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (18), (32) imply:
% 141.43/20.83 | | | | (35) ~ (e2 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (35) implies:
% 141.43/20.83 | | | | (36) ~ (e2 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (10), (32) imply:
% 141.43/20.83 | | | | (37) ~ (e1 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | SIMP: (37) implies:
% 141.43/20.83 | | | | (38) ~ (e1 = e0)
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | REDUCE: (5), (32) imply:
% 141.43/20.83 | | | | (39) op(e0, e3) = e0
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | BETA: splitting (6) gives:
% 141.43/20.83 | | | |
% 141.43/20.83 | | | | Case 1:
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | (40) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 141.43/20.83 | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 141.43/20.83 | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 141.43/20.83 | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.43/20.83 | | | | | all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 141.43/20.83 | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.43/20.83 | | | | | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.43/20.83 | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.43/20.83 | | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1,
% 141.43/20.83 | | | | | e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.43/20.83 | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 141.43/20.83 | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.43/20.83 | | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.43/20.83 | | | | | $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 141.43/20.83 | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.83 | | | | | & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2)
% 141.43/20.83 | | | | | & op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9
% 141.43/20.83 | | | | | = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.43/20.83 | | | | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 &
% 141.43/20.83 | | | | | op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 141.43/20.83 | | | | | all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.43/20.83 | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 141.43/20.83 | | | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.43/20.83 | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 141.43/20.83 | | | | | all_56_12 & $i(all_56_12))))
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | | REF_CLOSE: (11), (13), (14), (15), (34), (39), (40) are inconsistent
% 141.43/20.83 | | | | | by sub-proof #952.
% 141.43/20.83 | | | | |
% 141.43/20.83 | | | | Case 2:
% 141.43/20.83 | | | | |
% 141.43/20.84 | | | | | (41) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.43/20.84 | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.43/20.84 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 141.43/20.84 | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.43/20.84 | | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 141.43/20.84 | | | | | ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.84 | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | (
% 141.43/20.84 | | | | | ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.43/20.84 | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | (
% 141.43/20.84 | | | | | ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 141.43/20.84 | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) |
% 141.43/20.84 | | | | | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.84 | | | | | $i(all_56_14)))) | (op(e0, e0) = all_56_15 &
% 141.43/20.84 | | | | | $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 141.43/20.84 | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.43/20.84 | | | | | & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0)
% 141.43/20.84 | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8
% 141.43/20.84 | | | | | = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.43/20.84 | | | | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 &
% 141.43/20.84 | | | | | op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.43/20.84 | | | | | all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2,
% 141.43/20.84 | | | | | e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 141.43/20.84 | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.43/20.84 | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.43/20.84 | | | | | all_56_8 & $i(all_56_8))))
% 141.43/20.84 | | | | |
% 141.43/20.84 | | | | | BETA: splitting (41) gives:
% 141.43/20.84 | | | | |
% 141.43/20.84 | | | | | Case 1:
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | (42) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.43/20.84 | | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.43/20.84 | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 141.43/20.84 | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.43/20.84 | | | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 141.43/20.84 | | | | | | ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.43/20.84 | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | (
% 141.43/20.84 | | | | | | ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.43/20.84 | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | (
% 141.43/20.84 | | | | | | ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 141.43/20.84 | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1) |
% 141.43/20.84 | | | | | | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.43/20.84 | | | | | | $i(all_56_14)))
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | ALPHA: (42) implies:
% 141.43/20.84 | | | | | | (43) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) &
% 141.43/20.84 | | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | REF_CLOSE: (2), (8), (12), (14), (43) are inconsistent by sub-proof
% 141.43/20.84 | | | | | | #295.
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | Case 2:
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | (44) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 141.43/20.84 | | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 141.43/20.84 | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 141.43/20.84 | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 141.43/20.84 | | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 141.43/20.84 | | | | | | ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.43/20.84 | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | (
% 141.43/20.84 | | | | | | ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.43/20.84 | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | (
% 141.43/20.84 | | | | | | ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.43/20.84 | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) | (
% 141.43/20.84 | | | | | | ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.43/20.84 | | | | | | $i(all_56_8)))
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | ALPHA: (44) implies:
% 141.43/20.84 | | | | | | (45) (all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) &
% 141.43/20.84 | | | | | | op(e3, e0) = all_56_2 & $i(all_56_2))
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | BETA: splitting (45) gives:
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | | Case 1:
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | | (46) all_56_9 = e0 & op(e3, e3) = e0
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | | ALPHA: (46) implies:
% 141.43/20.84 | | | | | | | (47) op(e3, e3) = e0
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | | REF_CLOSE: (3), (9), (11), (13), (14), (16), (36), (38), (47) are
% 141.43/20.84 | | | | | | | inconsistent by sub-proof #642.
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | Case 2:
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | | (48) ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2)
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | | ALPHA: (48) implies:
% 141.43/20.84 | | | | | | | (49) ~ (all_56_2 = e3)
% 141.43/20.84 | | | | | | | (50) op(e3, e0) = all_56_2
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | | REF_CLOSE: (14), (19), (49), (50) are inconsistent by sub-proof
% 141.43/20.84 | | | | | | | #274.
% 141.43/20.84 | | | | | | |
% 141.43/20.84 | | | | | | End of split
% 141.43/20.84 | | | | | |
% 141.43/20.84 | | | | | End of split
% 141.43/20.84 | | | | |
% 141.43/20.84 | | | | End of split
% 141.43/20.84 | | | |
% 141.43/20.84 | | | End of split
% 141.43/20.84 | | |
% 141.43/20.84 | | End of split
% 141.43/20.84 | |
% 141.43/20.84 | End of split
% 141.43/20.84 |
% 141.43/20.84 End of proof
% 141.43/20.84
% 141.43/20.84 Sub-proof #266 shows that the following formulas are inconsistent:
% 141.43/20.84 ----------------------------------------------------------------
% 141.43/20.84 (1) all_57_9 = e0 & op(e3, e0) = e0
% 141.43/20.84 (2) all_57_9 = e3
% 141.43/20.84 (3) ~ (e3 = e0)
% 141.43/20.84
% 141.43/20.84 Begin of proof
% 141.43/20.84 |
% 141.43/20.84 | ALPHA: (1) implies:
% 141.43/20.84 | (4) all_57_9 = e0
% 141.43/20.84 |
% 141.43/20.84 | COMBINE_EQS: (2), (4) imply:
% 141.43/20.84 | (5) e3 = e0
% 141.43/20.84 |
% 141.43/20.84 | REDUCE: (3), (5) imply:
% 141.43/20.84 | (6) $false
% 141.43/20.84 |
% 141.43/20.84 | CLOSE: (6) is inconsistent.
% 141.43/20.84 |
% 141.43/20.84 End of proof
% 141.43/20.84
% 141.43/20.84 Sub-proof #267 shows that the following formulas are inconsistent:
% 141.43/20.84 ----------------------------------------------------------------
% 141.43/20.84 (1) all_57_1 = e0 & op(e3, e2) = e0
% 141.43/20.84 (2) all_57_1 = e2
% 141.43/20.84 (3) ~ (e2 = e0)
% 141.43/20.84
% 141.43/20.84 Begin of proof
% 141.43/20.84 |
% 141.43/20.84 | ALPHA: (1) implies:
% 141.43/20.84 | (4) all_57_1 = e0
% 141.43/20.84 |
% 141.43/20.84 | COMBINE_EQS: (2), (4) imply:
% 141.43/20.84 | (5) e2 = e0
% 141.43/20.84 |
% 141.43/20.84 | REDUCE: (3), (5) imply:
% 141.43/20.84 | (6) $false
% 141.43/20.84 |
% 141.43/20.84 | CLOSE: (6) is inconsistent.
% 141.43/20.84 |
% 141.43/20.84 End of proof
% 141.43/20.84
% 141.43/20.84 Sub-proof #268 shows that the following formulas are inconsistent:
% 141.43/20.84 ----------------------------------------------------------------
% 141.43/20.84 (1) op(e1, e1) = e3
% 141.43/20.84 (2) ~ (all_52_14 = e1)
% 141.43/20.84 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.84 (4) ~ (e3 = e1)
% 141.43/20.84 (5) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.43/20.84 (6) op(e1, e0) = all_52_14
% 141.43/20.84
% 141.43/20.84 Begin of proof
% 141.43/20.84 |
% 141.43/20.84 | BETA: splitting (5) gives:
% 141.43/20.84 |
% 141.43/20.84 | Case 1:
% 141.43/20.84 | |
% 141.43/20.84 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 141.43/20.84 | |
% 141.43/20.84 | | ALPHA: (7) implies:
% 141.43/20.84 | | (8) op(e1, e1) = e1
% 141.43/20.84 | |
% 141.43/20.84 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1096.
% 141.43/20.84 | |
% 141.43/20.84 | Case 2:
% 141.43/20.84 | |
% 141.43/20.84 | | (9) all_57_11 = e1 & op(e1, e0) = e1
% 141.43/20.84 | |
% 141.43/20.84 | | ALPHA: (9) implies:
% 141.43/20.84 | | (10) op(e1, e0) = e1
% 141.43/20.84 | |
% 141.43/20.84 | | REF_CLOSE: (2), (3), (6), (10) are inconsistent by sub-proof #459.
% 141.43/20.84 | |
% 141.43/20.84 | End of split
% 141.43/20.84 |
% 141.43/20.84 End of proof
% 141.43/20.84
% 141.43/20.84 Sub-proof #269 shows that the following formulas are inconsistent:
% 141.43/20.84 ----------------------------------------------------------------
% 141.43/20.84 (1) op(e0, e3) = e2
% 141.43/20.84 (2) all_46_2 = e3
% 141.43/20.84 (3) op(e2, e0) = e1
% 141.43/20.84 (4) op(e0, e3) = all_52_3
% 141.43/20.84 (5) ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 &
% 141.43/20.84 op(e0, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 141.43/20.84 e1) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 141.43/20.84 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.43/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.43/20.84 (7) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) = all_42_1
% 141.43/20.84 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0, e3) =
% 141.43/20.84 all_42_1 & $i(all_42_1))
% 141.43/20.84 (8) op(e2, e0) = all_52_13
% 141.43/20.84
% 141.43/20.84 Begin of proof
% 141.43/20.84 |
% 141.43/20.84 | GROUND_INST: instantiating (6) with all_52_3, e2, e3, e0, simplifying with
% 141.43/20.84 | (1), (4) gives:
% 141.43/20.84 | (9) all_52_3 = e2
% 141.43/20.84 |
% 141.43/20.84 | GROUND_INST: instantiating (6) with all_52_13, e1, e0, e2, simplifying with
% 141.43/20.84 | (3), (8) gives:
% 141.43/20.84 | (10) all_52_13 = e1
% 141.43/20.84 |
% 141.43/20.84 | BETA: splitting (5) gives:
% 141.43/20.84 |
% 141.43/20.84 | Case 1:
% 141.43/20.84 | |
% 141.43/20.84 | | (11) ~ (all_46_2 = e3)
% 141.43/20.84 | |
% 141.43/20.84 | | REDUCE: (2), (11) imply:
% 141.43/20.84 | | (12) $false
% 141.43/20.84 | |
% 141.43/20.84 | | CLOSE: (12) is inconsistent.
% 141.43/20.84 | |
% 141.43/20.84 | Case 2:
% 141.43/20.84 | |
% 141.43/20.84 | | (13) ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 141.43/20.84 | | all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e1) &
% 141.43/20.84 | | op(e0, e3) = all_46_1 & $i(all_46_1))
% 141.43/20.84 | |
% 141.43/20.84 | | BETA: splitting (13) gives:
% 141.43/20.84 | |
% 141.43/20.84 | | Case 1:
% 141.43/20.84 | | |
% 141.43/20.84 | | | (14) ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 141.43/20.84 | | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 141.43/20.84 | | |
% 141.43/20.84 | | | ALPHA: (14) implies:
% 141.43/20.84 | | | (15) op(e0, e3) = all_46_1
% 141.43/20.84 | | | (16) op(all_46_1, e0) = all_46_0
% 141.43/20.84 | | |
% 141.43/20.84 | | | BETA: splitting (7) gives:
% 141.43/20.84 | | |
% 141.43/20.84 | | | Case 1:
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | (17) ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 141.43/20.84 | | | | all_42_1 & $i(all_42_0) & $i(all_42_1)
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | ALPHA: (17) implies:
% 141.43/20.84 | | | | (18) ~ (all_42_0 = e1)
% 141.43/20.84 | | | | (19) op(e0, e3) = all_42_1
% 141.43/20.84 | | | | (20) op(all_42_1, e0) = all_42_0
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | GROUND_INST: instantiating (6) with e2, all_46_1, e3, e0, simplifying
% 141.43/20.84 | | | | with (1), (15) gives:
% 141.43/20.84 | | | | (21) all_46_1 = e2
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | GROUND_INST: instantiating (6) with all_42_1, all_46_1, e3, e0,
% 141.43/20.84 | | | | simplifying with (15), (19) gives:
% 141.43/20.84 | | | | (22) all_46_1 = all_42_1
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | COMBINE_EQS: (21), (22) imply:
% 141.43/20.84 | | | | (23) all_42_1 = e2
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | REDUCE: (16), (21) imply:
% 141.43/20.84 | | | | (24) op(e2, e0) = all_46_0
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | REDUCE: (20), (23) imply:
% 141.43/20.84 | | | | (25) op(e2, e0) = all_42_0
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | GROUND_INST: instantiating (6) with e1, all_46_0, e0, e2, simplifying
% 141.43/20.84 | | | | with (3), (24) gives:
% 141.43/20.84 | | | | (26) all_46_0 = e1
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | GROUND_INST: instantiating (6) with all_42_0, all_46_0, e0, e2,
% 141.43/20.84 | | | | simplifying with (24), (25) gives:
% 141.43/20.84 | | | | (27) all_46_0 = all_42_0
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | COMBINE_EQS: (26), (27) imply:
% 141.43/20.84 | | | | (28) all_42_0 = e1
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | SIMP: (28) implies:
% 141.43/20.84 | | | | (29) all_42_0 = e1
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | REDUCE: (18), (29) imply:
% 141.43/20.84 | | | | (30) $false
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | CLOSE: (30) is inconsistent.
% 141.43/20.84 | | | |
% 141.43/20.84 | | | Case 2:
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | (31) ~ (all_42_1 = e2) & op(e0, e3) = all_42_1 & $i(all_42_1)
% 141.43/20.84 | | | |
% 141.43/20.84 | | | | REF_CLOSE: (1), (6), (13), (31) are inconsistent by sub-proof #270.
% 141.43/20.84 | | | |
% 141.43/20.84 | | | End of split
% 141.43/20.84 | | |
% 141.43/20.84 | | Case 2:
% 141.43/20.84 | | |
% 141.43/20.84 | | | (32) ~ (all_46_1 = e1) & op(e0, e3) = all_46_1 & $i(all_46_1)
% 141.43/20.84 | | |
% 141.43/20.84 | | | ALPHA: (32) implies:
% 141.43/20.84 | | | (33) op(e0, e3) = all_46_1
% 141.43/20.84 | | |
% 141.43/20.84 | | | BETA: splitting (7) gives:
% 141.43/20.84 | | |
% 141.43/20.84 | | | Case 1:
% 141.43/20.84 | | | |
% 141.52/20.84 | | | | (34) ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 141.52/20.84 | | | | all_42_1 & $i(all_42_0) & $i(all_42_1)
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | ALPHA: (34) implies:
% 141.52/20.84 | | | | (35) ~ (all_42_0 = e1)
% 141.52/20.84 | | | | (36) op(e0, e3) = all_42_1
% 141.52/20.84 | | | | (37) op(all_42_1, e0) = all_42_0
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | GROUND_INST: instantiating (6) with e2, all_46_1, e3, e0, simplifying
% 141.52/20.84 | | | | with (1), (33) gives:
% 141.52/20.84 | | | | (38) all_46_1 = e2
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | GROUND_INST: instantiating (6) with all_42_1, all_46_1, e3, e0,
% 141.52/20.84 | | | | simplifying with (33), (36) gives:
% 141.52/20.84 | | | | (39) all_46_1 = all_42_1
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | COMBINE_EQS: (38), (39) imply:
% 141.52/20.84 | | | | (40) all_42_1 = e2
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | REDUCE: (37), (40) imply:
% 141.52/20.84 | | | | (41) op(e2, e0) = all_42_0
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | GROUND_INST: instantiating (6) with e1, all_42_0, e0, e2, simplifying
% 141.52/20.84 | | | | with (3), (41) gives:
% 141.52/20.84 | | | | (42) all_42_0 = e1
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | REDUCE: (35), (42) imply:
% 141.52/20.84 | | | | (43) $false
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | CLOSE: (43) is inconsistent.
% 141.52/20.84 | | | |
% 141.52/20.84 | | | Case 2:
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | (44) ~ (all_42_1 = e2) & op(e0, e3) = all_42_1 & $i(all_42_1)
% 141.52/20.84 | | | |
% 141.52/20.84 | | | | REF_CLOSE: (1), (6), (13), (44) are inconsistent by sub-proof #270.
% 141.52/20.84 | | | |
% 141.52/20.84 | | | End of split
% 141.52/20.84 | | |
% 141.52/20.84 | | End of split
% 141.52/20.84 | |
% 141.52/20.84 | End of split
% 141.52/20.84 |
% 141.52/20.84 End of proof
% 141.52/20.84
% 141.52/20.84 Sub-proof #270 shows that the following formulas are inconsistent:
% 141.52/20.84 ----------------------------------------------------------------
% 141.52/20.84 (1) ~ (all_42_1 = e2) & op(e0, e3) = all_42_1 & $i(all_42_1)
% 141.52/20.84 (2) op(e0, e3) = e2
% 141.52/20.84 (3) ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) = all_46_1
% 141.52/20.84 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e1) & op(e0, e3) =
% 141.52/20.84 all_46_1 & $i(all_46_1))
% 141.52/20.84 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.84
% 141.52/20.84 Begin of proof
% 141.52/20.84 |
% 141.52/20.84 | ALPHA: (1) implies:
% 141.52/20.84 | (5) ~ (all_42_1 = e2)
% 141.52/20.84 | (6) op(e0, e3) = all_42_1
% 141.52/20.84 |
% 141.52/20.84 | BETA: splitting (3) gives:
% 141.52/20.84 |
% 141.52/20.84 | Case 1:
% 141.52/20.84 | |
% 141.52/20.84 | | (7) ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 141.52/20.84 | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (7) implies:
% 141.52/20.84 | | (8) op(e0, e3) = all_46_1
% 141.52/20.84 | |
% 141.52/20.84 | | REF_CLOSE: (2), (4), (5), (6), (8) are inconsistent by sub-proof #557.
% 141.52/20.84 | |
% 141.52/20.84 | Case 2:
% 141.52/20.84 | |
% 141.52/20.84 | | (9) ~ (all_46_1 = e1) & op(e0, e3) = all_46_1 & $i(all_46_1)
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (9) implies:
% 141.52/20.84 | | (10) op(e0, e3) = all_46_1
% 141.52/20.84 | |
% 141.52/20.84 | | REF_CLOSE: (2), (4), (5), (6), (10) are inconsistent by sub-proof #557.
% 141.52/20.84 | |
% 141.52/20.84 | End of split
% 141.52/20.84 |
% 141.52/20.84 End of proof
% 141.52/20.84
% 141.52/20.84 Sub-proof #271 shows that the following formulas are inconsistent:
% 141.52/20.84 ----------------------------------------------------------------
% 141.52/20.84 (1) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.52/20.84 all_56_11 & $i(all_56_11))
% 141.52/20.84 (2) ~ (all_56_5 = e2)
% 141.52/20.84 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.84 (4) op(e2, e2) = e0
% 141.52/20.84
% 141.52/20.84 Begin of proof
% 141.52/20.84 |
% 141.52/20.84 | BETA: splitting (1) gives:
% 141.52/20.84 |
% 141.52/20.84 | Case 1:
% 141.52/20.84 | |
% 141.52/20.84 | | (5) all_56_5 = e2 & op(e2, e0) = e2
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (5) implies:
% 141.52/20.84 | | (6) all_56_5 = e2
% 141.52/20.84 | |
% 141.52/20.84 | | REDUCE: (2), (6) imply:
% 141.52/20.84 | | (7) $false
% 141.52/20.84 | |
% 141.52/20.84 | | CLOSE: (7) is inconsistent.
% 141.52/20.84 | |
% 141.52/20.84 | Case 2:
% 141.52/20.84 | |
% 141.52/20.84 | | (8) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (8) implies:
% 141.52/20.84 | | (9) ~ (all_56_11 = e0)
% 141.52/20.84 | | (10) op(e2, e2) = all_56_11
% 141.52/20.84 | |
% 141.52/20.84 | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #857.
% 141.52/20.84 | |
% 141.52/20.84 | End of split
% 141.52/20.84 |
% 141.52/20.84 End of proof
% 141.52/20.84
% 141.52/20.84 Sub-proof #272 shows that the following formulas are inconsistent:
% 141.52/20.84 ----------------------------------------------------------------
% 141.52/20.84 (1) ~ (all_10_2 = e2)
% 141.52/20.84 (2) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 141.52/20.84 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.52/20.84 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 141.52/20.84 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.52/20.84 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 141.52/20.84 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.84 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/20.84 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.84 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 141.52/20.84 = all_56_14 & $i(all_56_14))))
% 141.52/20.84 (3) ~ (all_10_2 = e1)
% 141.52/20.84 (4) op(e0, e0) = all_10_2
% 141.52/20.84 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.84 (6) op(e3, e3) = all_14_2
% 141.52/20.84 (7) ~ (all_14_2 = e0)
% 141.52/20.84
% 141.52/20.84 Begin of proof
% 141.52/20.84 |
% 141.52/20.84 | BETA: splitting (2) gives:
% 141.52/20.84 |
% 141.52/20.84 | Case 1:
% 141.52/20.84 | |
% 141.52/20.84 | | (8) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.52/20.84 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (8) implies:
% 141.52/20.84 | | (9) op(e0, e0) = e2
% 141.52/20.84 | |
% 141.52/20.84 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1115.
% 141.52/20.84 | |
% 141.52/20.84 | Case 2:
% 141.52/20.84 | |
% 141.52/20.84 | | (10) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 141.52/20.84 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 141.52/20.84 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 141.52/20.84 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.84 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 141.52/20.84 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.52/20.84 | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.52/20.84 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.84 | | $i(all_56_14)))
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (10) implies:
% 141.52/20.84 | | (11) op(e0, e0) = all_56_15
% 141.52/20.84 | | (12) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.84 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.84 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.52/20.84 | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 141.52/20.84 | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 141.52/20.84 | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.52/20.84 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.84 | | $i(all_56_14))
% 141.52/20.84 | |
% 141.52/20.84 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (11), (12) are inconsistent by
% 141.52/20.84 | | sub-proof #1114.
% 141.52/20.84 | |
% 141.52/20.84 | End of split
% 141.52/20.84 |
% 141.52/20.84 End of proof
% 141.52/20.84
% 141.52/20.84 Sub-proof #273 shows that the following formulas are inconsistent:
% 141.52/20.84 ----------------------------------------------------------------
% 141.52/20.84 (1) ~ (e2 = e1)
% 141.52/20.84 (2) ~ (all_52_12 = e1)
% 141.52/20.84 (3) all_57_11 = e2
% 141.52/20.84 (4) ~ (e1 = e0)
% 141.52/20.84 (5) all_57_10 = e3
% 141.52/20.84 (6) op(e3, e0) = all_52_12
% 141.52/20.84 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.84 (8) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/20.84 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.84 (9) ~ (e3 = e1)
% 141.52/20.84 (10) all_57_15 = e0
% 141.52/20.84
% 141.52/20.84 Begin of proof
% 141.52/20.84 |
% 141.52/20.84 | BETA: splitting (8) gives:
% 141.52/20.84 |
% 141.52/20.84 | Case 1:
% 141.52/20.84 | |
% 141.52/20.84 | | (11) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 141.52/20.84 | | e1)
% 141.52/20.84 | |
% 141.52/20.84 | | BETA: splitting (11) gives:
% 141.52/20.84 | |
% 141.52/20.84 | | Case 1:
% 141.52/20.84 | | |
% 141.52/20.84 | | | (12) all_57_9 = e1 & op(e3, e0) = e1
% 141.52/20.84 | | |
% 141.52/20.84 | | | REF_CLOSE: (2), (6), (7), (12) are inconsistent by sub-proof #461.
% 141.52/20.84 | | |
% 141.52/20.84 | | Case 2:
% 141.52/20.84 | | |
% 141.52/20.84 | | | (13) all_57_10 = e1 & op(e2, e0) = e1
% 141.52/20.84 | | |
% 141.52/20.84 | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #929.
% 141.52/20.84 | | |
% 141.52/20.84 | | End of split
% 141.52/20.84 | |
% 141.52/20.84 | Case 2:
% 141.52/20.84 | |
% 141.52/20.84 | | (14) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.84 | | e1)
% 141.52/20.84 | |
% 141.52/20.84 | | BETA: splitting (14) gives:
% 141.52/20.84 | |
% 141.52/20.84 | | Case 1:
% 141.52/20.84 | | |
% 141.52/20.84 | | | (15) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/20.84 | | |
% 141.52/20.84 | | | ALPHA: (15) implies:
% 141.52/20.84 | | | (16) all_57_11 = e1
% 141.52/20.84 | | |
% 141.52/20.84 | | | REF_CLOSE: (1), (3), (16) are inconsistent by sub-proof #810.
% 141.52/20.84 | | |
% 141.52/20.84 | | Case 2:
% 141.52/20.84 | | |
% 141.52/20.84 | | | (17) all_57_15 = e1 & op(e0, e0) = e1
% 141.52/20.84 | | |
% 141.52/20.84 | | | ALPHA: (17) implies:
% 141.52/20.84 | | | (18) all_57_15 = e1
% 141.52/20.84 | | |
% 141.52/20.84 | | | REF_CLOSE: (4), (10), (18) are inconsistent by sub-proof #291.
% 141.52/20.84 | | |
% 141.52/20.84 | | End of split
% 141.52/20.84 | |
% 141.52/20.84 | End of split
% 141.52/20.84 |
% 141.52/20.84 End of proof
% 141.52/20.84
% 141.52/20.84 Sub-proof #274 shows that the following formulas are inconsistent:
% 141.52/20.84 ----------------------------------------------------------------
% 141.52/20.84 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.84 (2) op(e3, e0) = all_56_2
% 141.52/20.84 (3) op(e3, e0) = e3
% 141.52/20.84 (4) ~ (all_56_2 = e3)
% 141.52/20.84
% 141.52/20.84 Begin of proof
% 141.52/20.84 |
% 141.52/20.84 | GROUND_INST: instantiating (1) with e3, all_56_2, e0, e3, simplifying with
% 141.52/20.84 | (2), (3) gives:
% 141.52/20.84 | (5) all_56_2 = e3
% 141.52/20.84 |
% 141.52/20.84 | REDUCE: (4), (5) imply:
% 141.52/20.84 | (6) $false
% 141.52/20.84 |
% 141.52/20.84 | CLOSE: (6) is inconsistent.
% 141.52/20.84 |
% 141.52/20.84 End of proof
% 141.52/20.84
% 141.52/20.84 Sub-proof #275 shows that the following formulas are inconsistent:
% 141.52/20.84 ----------------------------------------------------------------
% 141.52/20.84 (1) op(e1, e3) = all_52_2
% 141.52/20.84 (2) op(e1, e1) = e3
% 141.52/20.84 (3) ~ (e2 = e1)
% 141.52/20.84 (4) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.52/20.84 all_56_10 & $i(all_56_10))
% 141.52/20.84 (5) ~ (e3 = e0)
% 141.52/20.84 (6) op(e0, e0) = e1
% 141.52/20.84 (7) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.52/20.84 all_56_15 & $i(all_56_15))
% 141.52/20.84 (8) op(e2, e2) = e2
% 141.52/20.84 (9) ~ (all_52_2 = e1)
% 141.52/20.84 (10) op(e3, e3) = e1
% 141.52/20.84 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.84 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.84 (12) ~ (e3 = e1)
% 141.52/20.84 (13) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.84 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.84 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.52/20.84 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.84 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.84 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.52/20.84 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.52/20.84 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.52/20.84 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.52/20.84 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.52/20.84 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.52/20.84 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.84 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.84 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.84 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.84 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.84 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.84 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.84 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.84 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.84 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.84 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.84 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.84 $i(all_56_14))))
% 141.52/20.84 (14) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.52/20.84 all_56_13 & $i(all_56_13))
% 141.52/20.84
% 141.52/20.84 Begin of proof
% 141.52/20.84 |
% 141.52/20.84 | BETA: splitting (4) gives:
% 141.52/20.84 |
% 141.52/20.84 | Case 1:
% 141.52/20.84 | |
% 141.52/20.84 | | (15) all_56_15 = e3 & op(e0, e0) = e3
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (15) implies:
% 141.52/20.84 | | (16) op(e0, e0) = e3
% 141.52/20.84 | |
% 141.52/20.84 | | REF_CLOSE: (6), (11), (12), (16) are inconsistent by sub-proof #732.
% 141.52/20.84 | |
% 141.52/20.84 | Case 2:
% 141.52/20.84 | |
% 141.52/20.84 | | (17) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.84 | |
% 141.52/20.84 | | ALPHA: (17) implies:
% 141.52/20.84 | | (18) ~ (all_56_10 = e0)
% 141.52/20.84 | | (19) op(e0, e3) = all_56_10
% 141.52/20.84 | |
% 141.52/20.84 | | BETA: splitting (7) gives:
% 141.52/20.84 | |
% 141.52/20.84 | | Case 1:
% 141.52/20.84 | | |
% 141.52/20.84 | | | (20) all_56_10 = e0 & op(e0, e3) = e0
% 141.52/20.84 | | |
% 141.52/20.84 | | | ALPHA: (20) implies:
% 141.52/20.84 | | | (21) op(e0, e3) = e0
% 141.52/20.84 | | |
% 141.52/20.84 | | | REF_CLOSE: (11), (18), (19), (21) are inconsistent by sub-proof #954.
% 141.52/20.84 | | |
% 141.52/20.84 | | Case 2:
% 141.52/20.84 | | |
% 141.52/20.85 | | | (22) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.52/20.85 | | |
% 141.52/20.85 | | | ALPHA: (22) implies:
% 141.52/20.85 | | | (23) ~ (all_56_15 = e3)
% 141.52/20.85 | | | (24) op(e0, e0) = all_56_15
% 141.52/20.85 | | |
% 141.52/20.85 | | | BETA: splitting (14) gives:
% 141.52/20.85 | | |
% 141.52/20.85 | | | Case 1:
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | (25) all_56_6 = e1 & op(e1, e3) = e1
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | ALPHA: (25) implies:
% 141.52/20.85 | | | | (26) op(e1, e3) = e1
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | REF_CLOSE: (1), (9), (11), (26) are inconsistent by sub-proof #332.
% 141.52/20.85 | | | |
% 141.52/20.85 | | | Case 2:
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | (27) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | ALPHA: (27) implies:
% 141.52/20.85 | | | | (28) ~ (all_56_13 = e3)
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | BETA: splitting (13) gives:
% 141.52/20.85 | | | |
% 141.52/20.85 | | | | Case 1:
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | | (29) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3,
% 141.52/20.85 | | | | | e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 &
% 141.52/20.85 | | | | | $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~
% 141.52/20.85 | | | | | (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 &
% 141.52/20.85 | | | | | op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 & all_56_13
% 141.52/20.85 | | | | | = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.85 | | | | | all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1
% 141.52/20.85 | | | | | & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 &
% 141.52/20.85 | | | | | op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | | BETA: splitting (29) gives:
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | | Case 1:
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | (30) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) &
% 141.52/20.85 | | | | | | op(e3, e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3
% 141.52/20.85 | | | | | | & $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~
% 141.52/20.85 | | | | | | (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3
% 141.52/20.85 | | | | | | & op(e2, e2) = e3 & $i(all_56_3))
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | REF_CLOSE: (3), (10), (11), (30) are inconsistent by sub-proof #298.
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | Case 2:
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | (31) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) &
% 141.52/20.85 | | | | | | op(e3, e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3
% 141.52/20.85 | | | | | | & $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 & ~
% 141.52/20.85 | | | | | | (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6
% 141.52/20.85 | | | | | | & op(e1, e1) = e3 & $i(all_56_6))
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | REF_CLOSE: (28), (31) are inconsistent by sub-proof #297.
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | End of split
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | Case 2:
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | | (32) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 141.52/20.85 | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 141.52/20.85 | | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 141.52/20.85 | | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 141.52/20.85 | | | | | op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.85 | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 141.52/20.85 | | | | | op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.52/20.85 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 141.52/20.85 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 141.52/20.85 | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.85 | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.52/20.85 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.52/20.85 | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 141.52/20.85 | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.52/20.85 | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 141.52/20.85 | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.85 | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.52/20.85 | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.85 | | | | | e1) = all_56_14 & $i(all_56_14))))
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | | BETA: splitting (32) gives:
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | | Case 1:
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | (33) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 141.52/20.85 | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3
% 141.52/20.85 | | | | | | & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 141.52/20.85 | | | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4
% 141.52/20.85 | | | | | | & op(e1, e1) = e2 & $i(all_56_4))
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | BETA: splitting (33) gives:
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | Case 1:
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | | (34) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) &
% 141.52/20.85 | | | | | | | op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3
% 141.52/20.85 | | | | | | | & $i(all_56_2)
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | | ALPHA: (34) implies:
% 141.52/20.85 | | | | | | | (35) op(e0, e0) = e3
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | | REF_CLOSE: (11), (23), (24), (35) are inconsistent by sub-proof
% 141.52/20.85 | | | | | | | #740.
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | Case 2:
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | | (36) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 141.52/20.85 | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2
% 141.52/20.85 | | | | | | | & $i(all_56_4)
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | | ALPHA: (36) implies:
% 141.52/20.85 | | | | | | | (37) op(e2, e2) = e1
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | | REF_CLOSE: (3), (8), (11), (37) are inconsistent by sub-proof
% 141.52/20.85 | | | | | | | #749.
% 141.52/20.85 | | | | | | |
% 141.52/20.85 | | | | | | End of split
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | Case 2:
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | (38) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.52/20.85 | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2
% 141.52/20.85 | | | | | | & $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 141.52/20.85 | | | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 141.52/20.85 | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.52/20.85 | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 =
% 141.52/20.85 | | | | | | e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0,
% 141.52/20.85 | | | | | | e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.85 | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 141.52/20.85 | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13
% 141.52/20.85 | | | | | | = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.52/20.85 | | | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.85 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 141.52/20.85 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.85 | | | | | | $i(all_56_14))))
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | | REF_CLOSE: (2), (3), (5), (6), (8), (11), (12), (38) are
% 141.52/20.85 | | | | | | inconsistent by sub-proof #276.
% 141.52/20.85 | | | | | |
% 141.52/20.85 | | | | | End of split
% 141.52/20.85 | | | | |
% 141.52/20.85 | | | | End of split
% 141.52/20.85 | | | |
% 141.52/20.85 | | | End of split
% 141.52/20.85 | | |
% 141.52/20.85 | | End of split
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #276 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) op(e1, e1) = e3
% 141.52/20.85 (2) ~ (e2 = e1)
% 141.52/20.85 (3) ~ (e3 = e0)
% 141.52/20.85 (4) op(e0, e0) = e1
% 141.52/20.85 (5) op(e2, e2) = e2
% 141.52/20.85 (6) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 &
% 141.52/20.85 op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 141.52/20.85 e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0)
% 141.52/20.85 = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15
% 141.52/20.85 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.52/20.85 e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.85 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.52/20.85 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.85 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.85 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.85 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.85 $i(all_56_14))))
% 141.52/20.85 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.85 (8) ~ (e3 = e1)
% 141.52/20.85
% 141.52/20.85 Begin of proof
% 141.52/20.85 |
% 141.52/20.85 | BETA: splitting (6) gives:
% 141.52/20.85 |
% 141.52/20.85 | Case 1:
% 141.52/20.85 | |
% 141.52/20.85 | | (9) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.52/20.85 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.52/20.85 | |
% 141.52/20.85 | | ALPHA: (9) implies:
% 141.52/20.85 | | (10) op(e2, e2) = e1
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (2), (5), (7), (10) are inconsistent by sub-proof #749.
% 141.52/20.85 | |
% 141.52/20.85 | Case 2:
% 141.52/20.85 | |
% 141.52/20.85 | | (11) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.52/20.85 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.52/20.85 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.85 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.85 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.85 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/20.85 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.85 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.52/20.85 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.52/20.85 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.52/20.85 | | all_56_14 & $i(all_56_14))))
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (11) are inconsistent by sub-proof
% 141.52/20.85 | | #277.
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #277 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) op(e1, e1) = e3
% 141.52/20.85 (2) ~ (e2 = e1)
% 141.52/20.85 (3) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 141.52/20.85 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.52/20.85 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 141.52/20.85 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.52/20.85 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 141.52/20.85 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.85 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/20.85 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.85 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 141.52/20.85 = all_56_14 & $i(all_56_14))))
% 141.52/20.85 (4) ~ (e3 = e0)
% 141.52/20.85 (5) op(e0, e0) = e1
% 141.52/20.85 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.85 (7) ~ (e3 = e1)
% 141.52/20.85
% 141.52/20.85 Begin of proof
% 141.52/20.85 |
% 141.52/20.85 | BETA: splitting (3) gives:
% 141.52/20.85 |
% 141.52/20.85 | Case 1:
% 141.52/20.85 | |
% 141.52/20.85 | | (8) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.52/20.85 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 141.52/20.85 | |
% 141.52/20.85 | | ALPHA: (8) implies:
% 141.52/20.85 | | (9) op(e0, e0) = e2
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #1070.
% 141.52/20.85 | |
% 141.52/20.85 | Case 2:
% 141.52/20.85 | |
% 141.52/20.85 | | (10) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 141.52/20.85 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 141.52/20.85 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 141.52/20.85 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.85 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 141.52/20.85 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.52/20.85 | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.52/20.85 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.85 | | $i(all_56_14)))
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (10) are inconsistent by sub-proof
% 141.52/20.85 | | #278.
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #278 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) op(e1, e1) = e3
% 141.52/20.85 (2) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 141.52/20.85 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.52/20.85 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 141.52/20.85 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.85 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0
% 141.52/20.85 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.52/20.85 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14
% 141.52/20.85 & $i(all_56_14)))
% 141.52/20.85 (3) ~ (e2 = e1)
% 141.52/20.85 (4) ~ (e3 = e0)
% 141.52/20.85 (5) op(e0, e0) = e1
% 141.52/20.85 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.85 (7) ~ (e3 = e1)
% 141.52/20.85
% 141.52/20.85 Begin of proof
% 141.52/20.85 |
% 141.52/20.85 | ALPHA: (2) implies:
% 141.52/20.85 | (8) op(e0, e0) = all_56_15
% 141.52/20.85 | (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 141.52/20.85 | & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.85 | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.52/20.85 | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.85 | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.52/20.85 | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 141.52/20.85 | e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/20.85 |
% 141.52/20.85 | GROUND_INST: instantiating (6) with e1, all_56_15, e0, e0, simplifying with
% 141.52/20.85 | (5), (8) gives:
% 141.52/20.85 | (10) all_56_15 = e1
% 141.52/20.85 |
% 141.52/20.85 | BETA: splitting (9) gives:
% 141.52/20.85 |
% 141.52/20.85 | Case 1:
% 141.52/20.85 | |
% 141.52/20.85 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.85 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.85 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.52/20.85 | | e2) = all_56_12 & $i(all_56_12))
% 141.52/20.85 | |
% 141.52/20.85 | | BETA: splitting (11) gives:
% 141.52/20.85 | |
% 141.52/20.85 | | Case 1:
% 141.52/20.85 | | |
% 141.52/20.85 | | | (12) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 141.52/20.85 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.85 | | |
% 141.52/20.85 | | | ALPHA: (12) implies:
% 141.52/20.85 | | | (13) all_56_15 = e3
% 141.52/20.85 | | |
% 141.52/20.85 | | | COMBINE_EQS: (10), (13) imply:
% 141.52/20.85 | | | (14) e3 = e1
% 141.52/20.85 | | |
% 141.52/20.85 | | | SIMP: (14) implies:
% 141.52/20.85 | | | (15) e3 = e1
% 141.52/20.85 | | |
% 141.52/20.85 | | | REDUCE: (7), (15) imply:
% 141.52/20.85 | | | (16) $false
% 141.52/20.85 | | |
% 141.52/20.85 | | | CLOSE: (16) is inconsistent.
% 141.52/20.85 | | |
% 141.52/20.85 | | Case 2:
% 141.52/20.85 | | |
% 141.52/20.85 | | | (17) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.85 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/20.85 | | |
% 141.52/20.85 | | | REF_CLOSE: (3), (10), (17) are inconsistent by sub-proof #458.
% 141.52/20.85 | | |
% 141.52/20.85 | | End of split
% 141.52/20.85 | |
% 141.52/20.85 | Case 2:
% 141.52/20.85 | |
% 141.52/20.85 | | (18) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/20.85 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.85 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.85 | | e1) = all_56_14 & $i(all_56_14))
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (1), (4), (6), (18) are inconsistent by sub-proof #279.
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #279 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.52/20.85 op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 141.52/20.85 e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.85 $i(all_56_14))
% 141.52/20.85 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.85 (3) op(e1, e1) = e3
% 141.52/20.85 (4) ~ (e3 = e0)
% 141.52/20.85
% 141.52/20.85 Begin of proof
% 141.52/20.85 |
% 141.52/20.85 | BETA: splitting (1) gives:
% 141.52/20.85 |
% 141.52/20.85 | Case 1:
% 141.52/20.85 | |
% 141.52/20.85 | | (5) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/20.85 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 141.52/20.85 | |
% 141.52/20.85 | | ALPHA: (5) implies:
% 141.52/20.85 | | (6) op(e1, e1) = e0
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #308.
% 141.52/20.85 | |
% 141.52/20.85 | Case 2:
% 141.52/20.85 | |
% 141.52/20.85 | | (7) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 141.52/20.85 | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 141.52/20.85 | |
% 141.52/20.85 | | ALPHA: (7) implies:
% 141.52/20.85 | | (8) op(e1, e1) = e0
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #308.
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #280 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.52/20.85 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.52/20.85 (2) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.52/20.85 all_56_15 & $i(all_56_15))
% 141.52/20.85 (3) ~ (all_56_10 = e0)
% 141.52/20.85 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.85
% 141.52/20.85 Begin of proof
% 141.52/20.85 |
% 141.52/20.85 | ALPHA: (1) implies:
% 141.52/20.85 | (5) op(e0, e0) = e3
% 141.52/20.85 |
% 141.52/20.85 | BETA: splitting (2) gives:
% 141.52/20.85 |
% 141.52/20.85 | Case 1:
% 141.52/20.85 | |
% 141.52/20.85 | | (6) all_56_10 = e0 & op(e0, e3) = e0
% 141.52/20.85 | |
% 141.52/20.85 | | ALPHA: (6) implies:
% 141.52/20.85 | | (7) all_56_10 = e0
% 141.52/20.85 | |
% 141.52/20.85 | | REDUCE: (3), (7) imply:
% 141.52/20.85 | | (8) $false
% 141.52/20.85 | |
% 141.52/20.85 | | CLOSE: (8) is inconsistent.
% 141.52/20.85 | |
% 141.52/20.85 | Case 2:
% 141.52/20.85 | |
% 141.52/20.85 | | (9) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.52/20.85 | |
% 141.52/20.85 | | ALPHA: (9) implies:
% 141.52/20.85 | | (10) ~ (all_56_15 = e3)
% 141.52/20.85 | | (11) op(e0, e0) = all_56_15
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (4), (5), (10), (11) are inconsistent by sub-proof #740.
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #281 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) ~ (e2 = e1)
% 141.52/20.85 (2) op(e3, e3) = e2
% 141.52/20.85 (3) all_57_6 = e0
% 141.52/20.85 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.52/20.85 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.52/20.85 (5) ~ (e1 = e0)
% 141.52/20.85 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.85 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.85 (7) ~ (e3 = e1)
% 141.52/20.85 (8) all_57_2 = e3
% 141.52/20.85 (9) all_57_12 = e2
% 141.52/20.85
% 141.52/20.85 Begin of proof
% 141.52/20.85 |
% 141.52/20.85 | BETA: splitting (4) gives:
% 141.52/20.85 |
% 141.52/20.85 | Case 1:
% 141.52/20.85 | |
% 141.52/20.85 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 141.52/20.85 | | e1)
% 141.52/20.85 | |
% 141.52/20.85 | | BETA: splitting (10) gives:
% 141.52/20.85 | |
% 141.52/20.85 | | Case 1:
% 141.52/20.85 | | |
% 141.52/20.85 | | | (11) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/20.85 | | |
% 141.52/20.85 | | | ALPHA: (11) implies:
% 141.52/20.85 | | | (12) op(e3, e3) = e1
% 141.52/20.85 | | |
% 141.52/20.85 | | | REF_CLOSE: (1), (2), (6), (12) are inconsistent by sub-proof #818.
% 141.52/20.85 | | |
% 141.52/20.85 | | Case 2:
% 141.52/20.85 | | |
% 141.52/20.85 | | | (13) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/20.85 | | |
% 141.52/20.85 | | | REF_CLOSE: (7), (8), (13) are inconsistent by sub-proof #939.
% 141.52/20.85 | | |
% 141.52/20.85 | | End of split
% 141.52/20.85 | |
% 141.52/20.85 | Case 2:
% 141.52/20.85 | |
% 141.52/20.85 | | (14) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 141.52/20.85 | | e1)
% 141.52/20.85 | |
% 141.52/20.85 | | REF_CLOSE: (1), (3), (5), (9), (14) are inconsistent by sub-proof #774.
% 141.52/20.85 | |
% 141.52/20.85 | End of split
% 141.52/20.85 |
% 141.52/20.85 End of proof
% 141.52/20.85
% 141.52/20.85 Sub-proof #282 shows that the following formulas are inconsistent:
% 141.52/20.85 ----------------------------------------------------------------
% 141.52/20.85 (1) ~ (all_10_2 = e2)
% 141.52/20.85 (2) ~ (all_52_1 = e2)
% 141.52/20.85 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.52/20.85 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.52/20.85 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.85 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.85 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/20.85 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/20.85 (6) op(e1, e3) = all_52_2
% 141.52/20.85 (7) op(e1, e1) = e3
% 141.52/20.85 (8) ~ (all_52_8 = e3)
% 141.52/20.85 (9) ~ (e2 = e1)
% 141.52/20.85 (10) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.85 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.85 (11) ~ (all_52_7 = e0)
% 141.52/20.85 (12) op(e0, e0) = e0
% 141.52/20.85 (13) op(e0, e3) = all_52_3
% 141.52/20.85 (14) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.85 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.85 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.85 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.85 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.85 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.85 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.85 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.85 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.85 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.85 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.85 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.85 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.85 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.85 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.85 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.85 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.85 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.85 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.85 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.85 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.85 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.85 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.85 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.85 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.85 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.85 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.85 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.85 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.85 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.85 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.85 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.85 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.85 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.85 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.85 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.85 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.85 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.85 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.85 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.85 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.85 (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.52/20.85 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.85 (16) ~ (all_10_2 = e1)
% 141.52/20.85 (17) all_57_7 = e1
% 141.52/20.85 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.85 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.85 e1)
% 141.52/20.85 (19) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.85 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.85 (20) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.52/20.85 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.85 (21) ~ (e3 = e0)
% 141.52/20.85 (22) op(e3, e1) = all_52_8
% 141.52/20.85 (23) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.85 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.85 (24) ~ (all_52_7 = e2)
% 141.52/20.85 (25) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.85 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.85 e2)
% 141.52/20.85 (26) op(e2, e3) = all_52_1
% 141.52/20.85 (27) ~ (all_52_12 = e0)
% 141.52/20.85 (28) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.85 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.85 (29) ~ (all_52_12 = e1)
% 141.52/20.85 (30) op(e0, e0) = all_10_2
% 141.52/20.85 (31) all_57_11 = e2
% 141.52/20.85 (32) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.85 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.85 (33) ~ (e1 = e0)
% 141.52/20.85 (34) op(e2, e2) = e2
% 141.52/20.85 (35) ~ (all_52_3 = e1)
% 141.52/20.85 (36) ~ (e2 = e0)
% 141.52/20.85 (37) ~ (e3 = e2)
% 141.52/20.85 (38) op(e3, e0) = all_52_12
% 141.52/20.85 (39) ~ (all_52_2 = e1)
% 141.52/20.85 (40) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.85 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.85 (41) op(e3, e3) = e1
% 141.52/20.86 (42) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.52/20.86 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.52/20.86 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.86 (44) ~ (all_52_3 = e0)
% 141.52/20.86 (45) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.86 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.86 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.86 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.86 (46) ~ (all_52_13 = e2)
% 141.52/20.86 (47) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/20.86 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.86 (48) ~ (e3 = e1)
% 141.52/20.86 (49) op(e0, e2) = all_52_7
% 141.52/20.86 (50) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.86 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.86 (51) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.86 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.86 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.52/20.86 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.86 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.86 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.52/20.86 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.52/20.86 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.52/20.86 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.52/20.86 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.52/20.86 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.52/20.86 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.86 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.86 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.86 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.86 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.86 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.86 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.86 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.86 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.86 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.86 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.86 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.86 $i(all_56_14))))
% 141.52/20.86 (52) all_57_15 = e0
% 141.52/20.86 (53) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.86 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.86 (54) op(e3, e3) = all_14_2
% 141.52/20.86 (55) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.86 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.86 (56) op(e2, e0) = all_52_13
% 141.52/20.86 (57) ~ (all_14_2 = e0)
% 141.52/20.86 (58) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.86 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.86 (59) all_57_2 = e0
% 141.52/20.86
% 141.52/20.86 Begin of proof
% 141.52/20.86 |
% 141.52/20.86 | BETA: splitting (18) gives:
% 141.52/20.86 |
% 141.52/20.86 | Case 1:
% 141.52/20.86 | |
% 141.52/20.86 | | (60) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 141.52/20.86 | | e1)
% 141.52/20.86 | |
% 141.52/20.86 | | REF_CLOSE: (11), (13), (17), (21), (32), (33), (34), (35), (36), (37), (43),
% 141.52/20.86 | | (48), (49), (58), (60) are inconsistent by sub-proof #284.
% 141.52/20.86 | |
% 141.52/20.86 | Case 2:
% 141.52/20.86 | |
% 141.52/20.86 | | (61) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.86 | | e1)
% 141.52/20.86 | |
% 141.52/20.86 | | BETA: splitting (61) gives:
% 141.52/20.86 | |
% 141.52/20.86 | | Case 1:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (62) all_57_14 = e1 & op(e0, e1) = e1
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (62) implies:
% 141.52/20.86 | | | (63) all_57_14 = e1
% 141.52/20.86 | | |
% 141.52/20.86 | | | BETA: splitting (28) gives:
% 141.52/20.86 | | |
% 141.52/20.86 | | | Case 1:
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | (64) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 141.52/20.86 | | | | = e3)
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | REF_CLOSE: (21), (41), (43), (48), (59), (64) are inconsistent by
% 141.52/20.86 | | | | sub-proof #313.
% 141.52/20.86 | | | |
% 141.52/20.86 | | | Case 2:
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | (65) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 141.52/20.86 | | | | = e3)
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 141.52/20.86 | | | | (12), (13), (14), (15), (16), (18), (19), (20), (21), (22),
% 141.52/20.86 | | | | (23), (24), (25), (26), (27), (29), (30), (31), (32), (33),
% 141.52/20.86 | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 141.52/20.86 | | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 141.52/20.86 | | | | (54), (55), (56), (57), (63), (65) are inconsistent by
% 141.52/20.86 | | | | sub-proof #283.
% 141.52/20.86 | | | |
% 141.52/20.86 | | | End of split
% 141.52/20.86 | | |
% 141.52/20.86 | | Case 2:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (66) all_57_15 = e1 & op(e0, e0) = e1
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (66) implies:
% 141.52/20.86 | | | (67) all_57_15 = e1
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (33), (52), (67) are inconsistent by sub-proof #291.
% 141.52/20.86 | | |
% 141.52/20.86 | | End of split
% 141.52/20.86 | |
% 141.52/20.86 | End of split
% 141.52/20.86 |
% 141.52/20.86 End of proof
% 141.52/20.86
% 141.52/20.86 Sub-proof #283 shows that the following formulas are inconsistent:
% 141.52/20.86 ----------------------------------------------------------------
% 141.52/20.86 (1) ~ (all_10_2 = e2)
% 141.52/20.86 (2) ~ (all_52_1 = e2)
% 141.52/20.86 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.52/20.86 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.52/20.86 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.86 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.86 (5) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.86 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/20.86 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/20.86 (7) op(e1, e3) = all_52_2
% 141.52/20.86 (8) op(e1, e1) = e3
% 141.52/20.86 (9) ~ (all_52_8 = e3)
% 141.52/20.86 (10) ~ (e2 = e1)
% 141.52/20.86 (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.86 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.86 (12) ~ (all_52_7 = e0)
% 141.52/20.86 (13) op(e0, e0) = e0
% 141.52/20.86 (14) op(e0, e3) = all_52_3
% 141.52/20.86 (15) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.86 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.86 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.86 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.86 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.86 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.86 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.86 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.86 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.86 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.86 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.86 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.86 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.86 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.86 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.86 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.86 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.86 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.86 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.86 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.86 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.86 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.86 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.86 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.86 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.86 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.86 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.86 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.86 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.86 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.86 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.86 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.86 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.86 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.86 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.86 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.86 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.86 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.86 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.86 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.86 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.86 (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.52/20.86 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.86 (17) ~ (all_10_2 = e1)
% 141.52/20.86 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.86 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.86 e1)
% 141.52/20.86 (19) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.86 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.86 (20) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.52/20.86 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.86 (21) ~ (e3 = e0)
% 141.52/20.86 (22) op(e3, e1) = all_52_8
% 141.52/20.86 (23) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.86 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.86 (24) ~ (all_52_7 = e2)
% 141.52/20.86 (25) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.86 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.86 e2)
% 141.52/20.86 (26) op(e2, e3) = all_52_1
% 141.52/20.86 (27) ~ (all_52_12 = e0)
% 141.52/20.86 (28) all_57_14 = e1
% 141.52/20.86 (29) ~ (all_52_12 = e1)
% 141.52/20.86 (30) op(e0, e0) = all_10_2
% 141.52/20.86 (31) all_57_11 = e2
% 141.52/20.86 (32) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.86 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.86 (33) ~ (e1 = e0)
% 141.52/20.86 (34) op(e2, e2) = e2
% 141.52/20.86 (35) ~ (all_52_3 = e1)
% 141.52/20.86 (36) ~ (e2 = e0)
% 141.52/20.86 (37) ~ (e3 = e2)
% 141.52/20.86 (38) op(e3, e0) = all_52_12
% 141.52/20.86 (39) ~ (all_52_2 = e1)
% 141.52/20.86 (40) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.86 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.86 (41) op(e3, e3) = e1
% 141.52/20.86 (42) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.52/20.86 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.52/20.86 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.86 (44) ~ (all_52_3 = e0)
% 141.52/20.86 (45) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.86 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.86 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.86 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.86 (46) ~ (all_52_13 = e2)
% 141.52/20.86 (47) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/20.86 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.86 (48) ~ (e3 = e1)
% 141.52/20.86 (49) op(e0, e2) = all_52_7
% 141.52/20.86 (50) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.86 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.86 (51) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.86 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.86 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.52/20.86 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.86 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.86 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.52/20.86 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.52/20.86 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.52/20.86 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.52/20.86 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.52/20.86 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.52/20.86 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.86 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.86 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.86 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.86 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.86 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.86 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.86 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.86 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.86 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.86 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.86 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.86 $i(all_56_14))))
% 141.52/20.86 (52) all_57_15 = e0
% 141.52/20.86 (53) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.86 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.86 (54) op(e3, e3) = all_14_2
% 141.52/20.86 (55) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.86 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.86 (56) op(e2, e0) = all_52_13
% 141.52/20.86 (57) ~ (all_14_2 = e0)
% 141.52/20.86
% 141.52/20.86 Begin of proof
% 141.52/20.86 |
% 141.52/20.86 | BETA: splitting (5) gives:
% 141.52/20.86 |
% 141.52/20.86 | Case 1:
% 141.52/20.86 | |
% 141.52/20.86 | | (58) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/20.86 | |
% 141.52/20.86 | | ALPHA: (58) implies:
% 141.52/20.86 | | (59) all_57_6 = e3
% 141.52/20.86 | |
% 141.52/20.86 | | BETA: splitting (11) gives:
% 141.52/20.86 | |
% 141.52/20.86 | | Case 1:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (60) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.52/20.86 | | | e1)
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (7), (8), (21), (23), (31), (33), (36), (39), (43), (59), (60)
% 141.52/20.86 | | | are inconsistent by sub-proof #305.
% 141.52/20.86 | | |
% 141.52/20.86 | | Case 2:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (61) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.52/20.86 | | | e1)
% 141.52/20.86 | | |
% 141.52/20.86 | | | BETA: splitting (61) gives:
% 141.52/20.86 | | |
% 141.52/20.86 | | | Case 1:
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | (62) all_57_8 = e1 & op(e1, e1) = e1
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | ALPHA: (62) implies:
% 141.52/20.86 | | | | (63) op(e1, e1) = e1
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | REF_CLOSE: (6), (10), (16), (21), (28), (33), (36), (37), (42), (43),
% 141.52/20.86 | | | | (48), (63) are inconsistent by sub-proof #785.
% 141.52/20.86 | | | |
% 141.52/20.86 | | | Case 2:
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | (64) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/20.86 | | | |
% 141.52/20.86 | | | | REF_CLOSE: (10), (31), (64) are inconsistent by sub-proof #862.
% 141.52/20.86 | | | |
% 141.52/20.86 | | | End of split
% 141.52/20.86 | | |
% 141.52/20.86 | | End of split
% 141.52/20.86 | |
% 141.52/20.86 | Case 2:
% 141.52/20.86 | |
% 141.52/20.86 | | (65) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.86 | |
% 141.52/20.86 | | REF_CLOSE: (1), (2), (3), (4), (7), (8), (9), (10), (11), (12), (13), (14),
% 141.52/20.86 | | (15), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 141.52/20.86 | | (27), (29), (30), (32), (33), (34), (35), (36), (37), (38), (39),
% 141.52/20.86 | | (40), (41), (43), (44), (45), (46), (47), (48), (49), (50), (51),
% 141.52/20.86 | | (52), (53), (54), (55), (56), (57), (65) are inconsistent by
% 141.52/20.86 | | sub-proof #287.
% 141.52/20.86 | |
% 141.52/20.86 | End of split
% 141.52/20.86 |
% 141.52/20.86 End of proof
% 141.52/20.86
% 141.52/20.86 Sub-proof #284 shows that the following formulas are inconsistent:
% 141.52/20.86 ----------------------------------------------------------------
% 141.52/20.86 (1) ~ (all_52_7 = e0)
% 141.52/20.86 (2) op(e0, e3) = all_52_3
% 141.52/20.86 (3) all_57_7 = e1
% 141.52/20.86 (4) ~ (e3 = e0)
% 141.52/20.86 (5) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.86 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.86 (6) ~ (e1 = e0)
% 141.52/20.86 (7) op(e2, e2) = e2
% 141.52/20.86 (8) ~ (all_52_3 = e1)
% 141.52/20.86 (9) ~ (e2 = e0)
% 141.52/20.86 (10) ~ (e3 = e2)
% 141.52/20.86 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.86 (12) ~ (e3 = e1)
% 141.52/20.86 (13) op(e0, e2) = all_52_7
% 141.52/20.86 (14) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.86 (15) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.86 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.86
% 141.52/20.86 Begin of proof
% 141.52/20.86 |
% 141.52/20.86 | BETA: splitting (14) gives:
% 141.52/20.86 |
% 141.52/20.86 | Case 1:
% 141.52/20.86 | |
% 141.52/20.86 | | (16) all_57_12 = e1 & op(e0, e3) = e1
% 141.52/20.86 | |
% 141.52/20.86 | | REF_CLOSE: (2), (8), (11), (16) are inconsistent by sub-proof #350.
% 141.52/20.86 | |
% 141.52/20.86 | Case 2:
% 141.52/20.86 | |
% 141.52/20.86 | | (17) all_57_13 = e1 & op(e0, e2) = e1
% 141.52/20.86 | |
% 141.52/20.86 | | ALPHA: (17) implies:
% 141.52/20.86 | | (18) all_57_13 = e1
% 141.52/20.86 | |
% 141.52/20.86 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13), (15),
% 141.52/20.86 | | (18) are inconsistent by sub-proof #285.
% 141.52/20.86 | |
% 141.52/20.86 | End of split
% 141.52/20.86 |
% 141.52/20.86 End of proof
% 141.52/20.86
% 141.52/20.86 Sub-proof #285 shows that the following formulas are inconsistent:
% 141.52/20.86 ----------------------------------------------------------------
% 141.52/20.86 (1) ~ (all_52_7 = e0)
% 141.52/20.86 (2) all_57_7 = e1
% 141.52/20.86 (3) ~ (e3 = e0)
% 141.52/20.86 (4) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.86 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.86 (5) ~ (e1 = e0)
% 141.52/20.86 (6) all_57_13 = e1
% 141.52/20.86 (7) op(e2, e2) = e2
% 141.52/20.86 (8) ~ (e2 = e0)
% 141.52/20.86 (9) ~ (e3 = e2)
% 141.52/20.86 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.86 (11) ~ (e3 = e1)
% 141.52/20.86 (12) op(e0, e2) = all_52_7
% 141.52/20.86 (13) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.86 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.86
% 141.52/20.86 Begin of proof
% 141.52/20.86 |
% 141.52/20.86 | BETA: splitting (13) gives:
% 141.52/20.86 |
% 141.52/20.86 | Case 1:
% 141.52/20.86 | |
% 141.52/20.86 | | (14) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.52/20.86 | | e3)
% 141.52/20.86 | |
% 141.52/20.86 | | BETA: splitting (14) gives:
% 141.52/20.86 | |
% 141.52/20.86 | | Case 1:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (15) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (15) implies:
% 141.52/20.86 | | | (16) all_57_1 = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (10), (12), (16) are
% 141.52/20.86 | | | inconsistent by sub-proof #286.
% 141.52/20.86 | | |
% 141.52/20.86 | | Case 2:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (17) all_57_3 = e3 & op(e2, e2) = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (17) implies:
% 141.52/20.86 | | | (18) op(e2, e2) = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (7), (9), (10), (18) are inconsistent by sub-proof #728.
% 141.52/20.86 | | |
% 141.52/20.86 | | End of split
% 141.52/20.86 | |
% 141.52/20.86 | Case 2:
% 141.52/20.86 | |
% 141.52/20.86 | | (19) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.52/20.86 | | e3)
% 141.52/20.86 | |
% 141.52/20.86 | | BETA: splitting (19) gives:
% 141.52/20.86 | |
% 141.52/20.86 | | Case 1:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (20) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (20) implies:
% 141.52/20.86 | | | (21) all_57_7 = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (2), (11), (21) are inconsistent by sub-proof #915.
% 141.52/20.86 | | |
% 141.52/20.86 | | Case 2:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (22) all_57_13 = e3 & op(e0, e2) = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (22) implies:
% 141.52/20.86 | | | (23) all_57_13 = e3
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (6), (11), (23) are inconsistent by sub-proof #1001.
% 141.52/20.86 | | |
% 141.52/20.86 | | End of split
% 141.52/20.86 | |
% 141.52/20.86 | End of split
% 141.52/20.86 |
% 141.52/20.86 End of proof
% 141.52/20.86
% 141.52/20.86 Sub-proof #286 shows that the following formulas are inconsistent:
% 141.52/20.86 ----------------------------------------------------------------
% 141.52/20.86 (1) ~ (all_52_7 = e0)
% 141.52/20.86 (2) all_57_7 = e1
% 141.52/20.86 (3) ~ (e3 = e0)
% 141.52/20.86 (4) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.86 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.86 (5) ~ (e1 = e0)
% 141.52/20.86 (6) op(e2, e2) = e2
% 141.52/20.86 (7) ~ (e2 = e0)
% 141.52/20.86 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.86 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.86 (9) all_57_1 = e3
% 141.52/20.86 (10) op(e0, e2) = all_52_7
% 141.52/20.86
% 141.52/20.86 Begin of proof
% 141.52/20.86 |
% 141.52/20.86 | BETA: splitting (4) gives:
% 141.52/20.86 |
% 141.52/20.86 | Case 1:
% 141.52/20.86 | |
% 141.52/20.86 | | (11) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 141.52/20.86 | | e0)
% 141.52/20.86 | |
% 141.52/20.86 | | REF_CLOSE: (3), (6), (7), (8), (9), (11) are inconsistent by sub-proof #311.
% 141.52/20.86 | |
% 141.52/20.86 | Case 2:
% 141.52/20.86 | |
% 141.52/20.86 | | (12) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.52/20.86 | | e0)
% 141.52/20.86 | |
% 141.52/20.86 | | BETA: splitting (12) gives:
% 141.52/20.86 | |
% 141.52/20.86 | | Case 1:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (13) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #604.
% 141.52/20.86 | | |
% 141.52/20.86 | | Case 2:
% 141.52/20.86 | | |
% 141.52/20.86 | | | (14) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/20.86 | | |
% 141.52/20.86 | | | ALPHA: (14) implies:
% 141.52/20.86 | | | (15) op(e0, e2) = e0
% 141.52/20.86 | | |
% 141.52/20.86 | | | REF_CLOSE: (1), (8), (10), (15) are inconsistent by sub-proof #977.
% 141.52/20.86 | | |
% 141.52/20.86 | | End of split
% 141.52/20.86 | |
% 141.52/20.86 | End of split
% 141.52/20.86 |
% 141.52/20.86 End of proof
% 141.52/20.86
% 141.52/20.86 Sub-proof #287 shows that the following formulas are inconsistent:
% 141.52/20.86 ----------------------------------------------------------------
% 141.52/20.86 (1) ~ (all_10_2 = e2)
% 141.52/20.86 (2) ~ (all_52_1 = e2)
% 141.52/20.86 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.52/20.86 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.52/20.86 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.86 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.86 (5) op(e1, e3) = all_52_2
% 141.52/20.86 (6) op(e1, e1) = e3
% 141.52/20.86 (7) ~ (all_52_8 = e3)
% 141.52/20.86 (8) ~ (e2 = e1)
% 141.52/20.86 (9) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.86 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.86 (10) ~ (all_52_7 = e0)
% 141.52/20.86 (11) op(e0, e0) = e0
% 141.52/20.86 (12) op(e0, e3) = all_52_3
% 141.52/20.86 (13) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.86 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.86 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.86 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.86 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.86 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.86 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.86 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.86 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.86 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.86 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.86 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.86 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.86 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.86 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.86 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.86 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.86 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.86 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.86 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.86 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.86 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.86 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.86 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.86 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.86 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.86 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.86 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.86 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.86 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.86 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.86 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.86 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.86 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.86 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.86 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.86 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.86 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.86 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.86 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.86 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.86 (14) ~ (all_10_2 = e1)
% 141.52/20.86 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.86 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.86 e1)
% 141.52/20.86 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.86 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.86 (17) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.86 (18) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.52/20.86 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.86 (19) ~ (e3 = e0)
% 141.52/20.86 (20) op(e3, e1) = all_52_8
% 141.52/20.86 (21) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.86 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.86 (22) ~ (all_52_7 = e2)
% 141.52/20.86 (23) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.86 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.86 e2)
% 141.52/20.86 (24) op(e2, e3) = all_52_1
% 141.52/20.86 (25) ~ (all_52_12 = e0)
% 141.52/20.86 (26) ~ (all_52_12 = e1)
% 141.52/20.86 (27) op(e0, e0) = all_10_2
% 141.52/20.86 (28) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.86 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.86 (29) ~ (e1 = e0)
% 141.52/20.86 (30) op(e2, e2) = e2
% 141.52/20.86 (31) ~ (all_52_3 = e1)
% 141.52/20.86 (32) ~ (e2 = e0)
% 141.52/20.86 (33) ~ (e3 = e2)
% 141.52/20.87 (34) op(e3, e0) = all_52_12
% 141.52/20.87 (35) ~ (all_52_2 = e1)
% 141.52/20.87 (36) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.87 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.87 (37) op(e3, e3) = e1
% 141.52/20.87 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.87 (39) ~ (all_52_3 = e0)
% 141.52/20.87 (40) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.87 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.87 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.87 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.87 (41) ~ (all_52_13 = e2)
% 141.52/20.87 (42) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/20.87 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.87 (43) ~ (e3 = e1)
% 141.52/20.87 (44) op(e0, e2) = all_52_7
% 141.52/20.87 (45) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.87 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.87 (46) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.87 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.87 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.52/20.87 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.87 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.87 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.52/20.87 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.52/20.87 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.52/20.87 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.52/20.87 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.52/20.87 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.52/20.87 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.87 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.87 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.87 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.87 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.87 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.87 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.87 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.87 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.87 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.87 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.87 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.87 $i(all_56_14))))
% 141.52/20.87 (47) all_57_15 = e0
% 141.52/20.87 (48) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.87 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.87 (49) op(e3, e3) = all_14_2
% 141.52/20.87 (50) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.87 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.87 (51) op(e2, e0) = all_52_13
% 141.52/20.87 (52) ~ (all_14_2 = e0)
% 141.52/20.87
% 141.52/20.87 Begin of proof
% 141.52/20.87 |
% 141.52/20.87 | ALPHA: (17) implies:
% 141.52/20.87 | (53) all_57_12 = e3
% 141.52/20.87 |
% 141.52/20.87 | BETA: splitting (48) gives:
% 141.52/20.87 |
% 141.52/20.87 | Case 1:
% 141.52/20.87 | |
% 141.52/20.87 | | (54) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 141.52/20.87 | | e2)
% 141.52/20.87 | |
% 141.52/20.87 | | REF_CLOSE: (2), (8), (24), (37), (38), (54) are inconsistent by sub-proof
% 141.52/20.87 | | #288.
% 141.52/20.87 | |
% 141.52/20.87 | Case 2:
% 141.52/20.87 | |
% 141.52/20.87 | | (55) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 141.52/20.87 | | e2)
% 141.52/20.87 | |
% 141.52/20.87 | | BETA: splitting (55) gives:
% 141.52/20.87 | |
% 141.52/20.87 | | Case 1:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (56) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | ALPHA: (56) implies:
% 141.52/20.87 | | | (57) all_57_6 = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.52/20.87 | | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (25),
% 141.52/20.87 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 141.52/20.87 | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 141.52/20.87 | | | (46), (47), (49), (50), (51), (52), (53), (57) are inconsistent
% 141.52/20.87 | | | by sub-proof #290.
% 141.52/20.87 | | |
% 141.52/20.87 | | Case 2:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (58) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | ALPHA: (58) implies:
% 141.52/20.87 | | | (59) all_57_12 = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | REF_CLOSE: (33), (53), (59) are inconsistent by sub-proof #772.
% 141.52/20.87 | | |
% 141.52/20.87 | | End of split
% 141.52/20.87 | |
% 141.52/20.87 | End of split
% 141.52/20.87 |
% 141.52/20.87 End of proof
% 141.52/20.87
% 141.52/20.87 Sub-proof #288 shows that the following formulas are inconsistent:
% 141.52/20.87 ----------------------------------------------------------------
% 141.52/20.87 (1) ~ (all_52_1 = e2)
% 141.52/20.87 (2) ~ (e2 = e1)
% 141.52/20.87 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 141.52/20.87 (4) op(e2, e3) = all_52_1
% 141.52/20.87 (5) op(e3, e3) = e1
% 141.52/20.87 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.87
% 141.52/20.87 Begin of proof
% 141.52/20.87 |
% 141.52/20.87 | BETA: splitting (3) gives:
% 141.52/20.87 |
% 141.52/20.87 | Case 1:
% 141.52/20.87 | |
% 141.52/20.87 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 141.52/20.87 | |
% 141.52/20.87 | | ALPHA: (7) implies:
% 141.52/20.87 | | (8) op(e3, e3) = e2
% 141.52/20.87 | |
% 141.52/20.87 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #818.
% 141.52/20.87 | |
% 141.52/20.87 | Case 2:
% 141.52/20.87 | |
% 141.52/20.87 | | (9) all_57_2 = e2 & op(e2, e3) = e2
% 141.52/20.87 | |
% 141.52/20.87 | | ALPHA: (9) implies:
% 141.52/20.87 | | (10) op(e2, e3) = e2
% 141.52/20.87 | |
% 141.52/20.87 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #882.
% 141.52/20.87 | |
% 141.52/20.87 | End of split
% 141.52/20.87 |
% 141.52/20.87 End of proof
% 141.52/20.87
% 141.52/20.87 Sub-proof #289 shows that the following formulas are inconsistent:
% 141.52/20.87 ----------------------------------------------------------------
% 141.52/20.87 (1) ~ (all_10_2 = e2)
% 141.52/20.87 (2) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.52/20.87 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.52/20.87 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.87 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.87 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.87 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.87 (5) op(e1, e3) = all_52_2
% 141.52/20.87 (6) op(e1, e1) = e3
% 141.52/20.87 (7) ~ (all_52_8 = e3)
% 141.52/20.87 (8) ~ (e2 = e1)
% 141.52/20.87 (9) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.87 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.87 (10) ~ (all_52_7 = e0)
% 141.52/20.87 (11) op(e0, e0) = e0
% 141.52/20.87 (12) op(e0, e3) = all_52_3
% 141.52/20.87 (13) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.87 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.87 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.87 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.87 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.87 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.87 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.87 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.87 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.87 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.87 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.87 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.87 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.87 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.87 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.87 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.87 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.87 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.87 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.87 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.87 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.87 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.87 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.87 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.87 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.87 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.87 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.87 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.87 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.87 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.87 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.87 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.87 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.87 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.87 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.87 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.87 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.87 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.87 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.87 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.87 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.87 (14) ~ (all_10_2 = e1)
% 141.52/20.87 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.87 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.87 e1)
% 141.52/20.87 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.87 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.87 (17) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.52/20.87 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.87 (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.52/20.87 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/20.87 (19) ~ (e3 = e0)
% 141.52/20.87 (20) op(e1, e1) = all_4_2
% 141.52/20.87 (21) op(e3, e1) = all_52_8
% 141.52/20.87 (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.87 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.87 (23) ~ (all_52_7 = e2)
% 141.52/20.87 (24) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.87 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.87 e2)
% 141.52/20.87 (25) ~ (all_52_12 = e0)
% 141.52/20.87 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.87 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.87 (27) ~ (all_52_12 = e1)
% 141.52/20.87 (28) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/20.87 (29) op(e0, e0) = all_10_2
% 141.52/20.87 (30) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.87 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.87 (31) ~ (e1 = e0)
% 141.52/20.87 (32) op(e2, e2) = e2
% 141.52/20.87 (33) ~ (all_52_3 = e1)
% 141.52/20.87 (34) ~ (e2 = e0)
% 141.52/20.87 (35) ~ (e3 = e2)
% 141.52/20.87 (36) op(e3, e0) = all_52_12
% 141.52/20.87 (37) ~ (all_52_2 = e1)
% 141.52/20.87 (38) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.87 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.87 (39) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/20.87 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/20.87 (40) op(e3, e3) = e1
% 141.52/20.87 (41) ~ (all_4_2 = e2)
% 141.52/20.87 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.87 (43) ~ (all_52_3 = e0)
% 141.52/20.87 (44) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.87 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.87 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.87 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.87 (45) ~ (all_52_13 = e2)
% 141.52/20.87 (46) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/20.87 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.87 (47) ~ (e3 = e1)
% 141.52/20.87 (48) op(e0, e2) = all_52_7
% 141.52/20.87 (49) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.87 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.87 (50) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.87 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.87 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.52/20.87 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.87 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.87 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.52/20.87 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.52/20.87 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.52/20.87 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.52/20.87 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.52/20.87 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.52/20.87 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.87 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.87 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.87 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.87 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.87 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.87 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.87 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.87 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.87 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.87 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.87 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.87 $i(all_56_14))))
% 141.52/20.87 (51) all_57_15 = e0
% 141.52/20.87 (52) op(e3, e3) = all_14_2
% 141.52/20.87 (53) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.87 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.87 (54) op(e2, e0) = all_52_13
% 141.52/20.87 (55) ~ (all_14_2 = e0)
% 141.52/20.87 (56) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.87 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.87
% 141.52/20.87 Begin of proof
% 141.52/20.87 |
% 141.52/20.87 | ALPHA: (28) implies:
% 141.52/20.87 | (57) all_57_6 = e2
% 141.52/20.87 |
% 141.52/20.87 | BETA: splitting (18) gives:
% 141.52/20.87 |
% 141.52/20.87 | Case 1:
% 141.52/20.87 | |
% 141.52/20.87 | | (58) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 141.52/20.87 | | e0)
% 141.52/20.87 | |
% 141.52/20.87 | | BETA: splitting (58) gives:
% 141.52/20.87 | |
% 141.52/20.87 | | Case 1:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (59) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.87 | | |
% 141.52/20.87 | | | ALPHA: (59) implies:
% 141.52/20.87 | | | (60) op(e3, e3) = e0
% 141.52/20.87 | | |
% 141.52/20.87 | | | REF_CLOSE: (31), (40), (42), (60) are inconsistent by sub-proof #840.
% 141.52/20.87 | | |
% 141.52/20.87 | | Case 2:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (61) all_57_2 = e0 & op(e2, e3) = e0
% 141.52/20.87 | | |
% 141.52/20.87 | | | ALPHA: (61) implies:
% 141.52/20.87 | | | (62) all_57_2 = e0
% 141.52/20.87 | | |
% 141.52/20.87 | | | BETA: splitting (26) gives:
% 141.52/20.87 | | |
% 141.52/20.87 | | | Case 1:
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | (63) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 141.52/20.87 | | | | = e3)
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | REF_CLOSE: (19), (40), (42), (47), (62), (63) are inconsistent by
% 141.52/20.87 | | | | sub-proof #313.
% 141.52/20.87 | | | |
% 141.52/20.87 | | | Case 2:
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | (64) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 141.52/20.87 | | | | = e3)
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | BETA: splitting (64) gives:
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | Case 1:
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | (65) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | REF_CLOSE: (3), (5), (6), (8), (9), (19), (20), (22), (30), (31),
% 141.52/20.87 | | | | | (32), (34), (35), (37), (39), (41), (42), (47), (56), (65)
% 141.52/20.87 | | | | | are inconsistent by sub-proof #302.
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | Case 2:
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | (66) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | ALPHA: (66) implies:
% 141.52/20.87 | | | | | (67) all_57_12 = e3
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 141.52/20.87 | | | | | (13), (14), (15), (16), (17), (19), (21), (22), (23), (24),
% 141.52/20.87 | | | | | (25), (27), (29), (30), (31), (32), (33), (34), (35), (36),
% 141.52/20.87 | | | | | (37), (38), (40), (42), (43), (44), (45), (46), (47), (48),
% 141.52/20.87 | | | | | (49), (50), (51), (52), (53), (54), (55), (57), (67) are
% 141.52/20.87 | | | | | inconsistent by sub-proof #290.
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | End of split
% 141.52/20.87 | | | |
% 141.52/20.87 | | | End of split
% 141.52/20.87 | | |
% 141.52/20.87 | | End of split
% 141.52/20.87 | |
% 141.52/20.87 | Case 2:
% 141.52/20.87 | |
% 141.52/20.87 | | (68) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 141.52/20.87 | | e0)
% 141.52/20.87 | |
% 141.52/20.87 | | REF_CLOSE: (12), (34), (42), (43), (57), (68) are inconsistent by sub-proof
% 141.52/20.87 | | #985.
% 141.52/20.87 | |
% 141.52/20.87 | End of split
% 141.52/20.87 |
% 141.52/20.87 End of proof
% 141.52/20.87
% 141.52/20.87 Sub-proof #290 shows that the following formulas are inconsistent:
% 141.52/20.87 ----------------------------------------------------------------
% 141.52/20.87 (1) ~ (all_10_2 = e2)
% 141.52/20.87 (2) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.52/20.87 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.52/20.87 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.87 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.87 (4) op(e1, e3) = all_52_2
% 141.52/20.87 (5) op(e1, e1) = e3
% 141.52/20.87 (6) ~ (all_52_8 = e3)
% 141.52/20.87 (7) ~ (e2 = e1)
% 141.52/20.87 (8) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.87 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.87 (9) ~ (all_52_7 = e0)
% 141.52/20.87 (10) op(e0, e0) = e0
% 141.52/20.87 (11) op(e0, e3) = all_52_3
% 141.52/20.87 (12) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.87 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.87 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.87 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.87 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.87 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.87 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.87 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.87 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.87 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.87 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.87 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.87 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.87 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.87 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.87 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.87 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.87 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.87 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.87 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.87 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.87 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.87 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.87 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.87 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.87 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.87 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.87 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.87 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.87 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.87 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.87 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.87 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.87 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.87 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.87 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.87 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.87 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.87 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.87 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.87 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.87 (13) ~ (all_10_2 = e1)
% 141.52/20.87 (14) all_57_12 = e3
% 141.52/20.87 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.87 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.52/20.87 e1)
% 141.52/20.87 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.87 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.87 (17) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.52/20.87 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.87 (18) ~ (e3 = e0)
% 141.52/20.87 (19) op(e3, e1) = all_52_8
% 141.52/20.87 (20) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.87 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.87 (21) ~ (all_52_7 = e2)
% 141.52/20.87 (22) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.87 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.87 e2)
% 141.52/20.87 (23) ~ (all_52_12 = e0)
% 141.52/20.87 (24) ~ (all_52_12 = e1)
% 141.52/20.87 (25) op(e0, e0) = all_10_2
% 141.52/20.87 (26) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.87 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.87 (27) ~ (e1 = e0)
% 141.52/20.87 (28) op(e2, e2) = e2
% 141.52/20.87 (29) ~ (all_52_3 = e1)
% 141.52/20.87 (30) ~ (e2 = e0)
% 141.52/20.87 (31) all_57_6 = e2
% 141.52/20.87 (32) ~ (e3 = e2)
% 141.52/20.87 (33) op(e3, e0) = all_52_12
% 141.52/20.87 (34) ~ (all_52_2 = e1)
% 141.52/20.87 (35) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.87 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.87 (36) op(e3, e3) = e1
% 141.52/20.87 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.87 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.87 (38) ~ (all_52_3 = e0)
% 141.52/20.87 (39) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.87 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.87 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.87 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.87 (40) ~ (all_52_13 = e2)
% 141.52/20.87 (41) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/20.87 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.87 (42) ~ (e3 = e1)
% 141.52/20.87 (43) op(e0, e2) = all_52_7
% 141.52/20.87 (44) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.87 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.87 (45) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.87 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.87 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.52/20.87 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.87 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.87 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.52/20.87 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.52/20.87 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.52/20.87 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.52/20.87 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.52/20.87 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.52/20.87 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.87 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.87 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.87 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.87 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.87 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.87 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.87 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.87 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.87 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.87 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.87 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.87 $i(all_56_14))))
% 141.52/20.87 (46) all_57_15 = e0
% 141.52/20.87 (47) op(e3, e3) = all_14_2
% 141.52/20.87 (48) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.87 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.87 (49) op(e2, e0) = all_52_13
% 141.52/20.87 (50) ~ (all_14_2 = e0)
% 141.52/20.87
% 141.52/20.87 Begin of proof
% 141.52/20.87 |
% 141.52/20.87 | BETA: splitting (22) gives:
% 141.52/20.87 |
% 141.52/20.87 | Case 1:
% 141.52/20.87 | |
% 141.52/20.87 | | (51) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 141.52/20.87 | | e2)
% 141.52/20.87 | |
% 141.52/20.87 | | BETA: splitting (51) gives:
% 141.52/20.87 | |
% 141.52/20.87 | | Case 1:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (52) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | ALPHA: (52) implies:
% 141.52/20.87 | | | (53) all_57_12 = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | REF_CLOSE: (14), (32), (53) are inconsistent by sub-proof #772.
% 141.52/20.87 | | |
% 141.52/20.87 | | Case 2:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (54) all_57_13 = e2 & op(e0, e2) = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | REF_CLOSE: (21), (37), (43), (54) are inconsistent by sub-proof #446.
% 141.52/20.87 | | |
% 141.52/20.87 | | End of split
% 141.52/20.87 | |
% 141.52/20.87 | Case 2:
% 141.52/20.87 | |
% 141.52/20.87 | | (55) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.87 | | e2)
% 141.52/20.87 | |
% 141.52/20.87 | | BETA: splitting (55) gives:
% 141.52/20.87 | |
% 141.52/20.87 | | Case 1:
% 141.52/20.87 | | |
% 141.52/20.87 | | | (56) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | ALPHA: (56) implies:
% 141.52/20.87 | | | (57) all_57_14 = e2
% 141.52/20.87 | | |
% 141.52/20.87 | | | BETA: splitting (41) gives:
% 141.52/20.87 | | |
% 141.52/20.87 | | | Case 1:
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | (58) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 141.52/20.87 | | | | = e1)
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | BETA: splitting (58) gives:
% 141.52/20.87 | | | |
% 141.52/20.87 | | | | Case 1:
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | (59) all_57_9 = e1 & op(e3, e0) = e1
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | REF_CLOSE: (24), (33), (37), (59) are inconsistent by sub-proof #461.
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | Case 2:
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | (60) all_57_10 = e1 & op(e2, e0) = e1
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | ALPHA: (60) implies:
% 141.52/20.87 | | | | | (61) all_57_10 = e1
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | BETA: splitting (35) gives:
% 141.52/20.87 | | | | |
% 141.52/20.87 | | | | | Case 1:
% 141.52/20.87 | | | | | |
% 141.52/20.87 | | | | | | (62) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 141.52/20.87 | | | | | | e0) = e3)
% 141.52/20.87 | | | | | |
% 141.52/20.87 | | | | | | BETA: splitting (62) gives:
% 141.52/20.87 | | | | | |
% 141.52/20.87 | | | | | | Case 1:
% 141.52/20.87 | | | | | | |
% 141.52/20.87 | | | | | | | (63) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.87 | | | | | | |
% 141.52/20.87 | | | | | | | ALPHA: (63) implies:
% 141.52/20.87 | | | | | | | (64) all_57_9 = e3
% 141.52/20.87 | | | | | | |
% 141.52/20.87 | | | | | | | BETA: splitting (20) gives:
% 141.52/20.87 | | | | | | |
% 141.52/20.87 | | | | | | | Case 1:
% 141.52/20.87 | | | | | | | |
% 141.52/20.87 | | | | | | | | (65) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 &
% 141.52/20.87 | | | | | | | | op(e1, e2) = e0)
% 141.52/20.87 | | | | | | | |
% 141.52/20.87 | | | | | | | | BETA: splitting (65) gives:
% 141.52/20.87 | | | | | | | |
% 141.52/20.87 | | | | | | | | Case 1:
% 141.52/20.87 | | | | | | | | |
% 141.52/20.87 | | | | | | | | | (66) all_57_6 = e0 & op(e1, e3) = e0
% 141.52/20.87 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | REF_CLOSE: (30), (31), (66) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | | #994.
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | (67) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | ALPHA: (67) implies:
% 141.52/20.88 | | | | | | | | | (68) all_57_7 = e0
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | BETA: splitting (8) gives:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | (69) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 141.52/20.88 | | | | | | | | | | op(e1, e2) = e1)
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | BETA: splitting (69) gives:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (70) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (70) implies:
% 141.52/20.88 | | | | | | | | | | | (71) op(e1, e3) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (4), (34), (37), (71) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | sub-proof #332.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (72) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (72) implies:
% 141.52/20.88 | | | | | | | | | | | (73) all_57_7 = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | COMBINE_EQS: (68), (73) imply:
% 141.52/20.88 | | | | | | | | | | | (74) e1 = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REDUCE: (27), (74) imply:
% 141.52/20.88 | | | | | | | | | | | (75) $false
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | CLOSE: (75) is inconsistent.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | (76) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1
% 141.52/20.88 | | | | | | | | | | & op(e1, e0) = e1)
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | BETA: splitting (76) gives:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (77) all_57_8 = e1 & op(e1, e1) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (77) implies:
% 141.52/20.88 | | | | | | | | | | | (78) op(e1, e1) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (5), (37), (42), (78) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | sub-proof #1096.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (79) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (79) implies:
% 141.52/20.88 | | | | | | | | | | | (80) all_57_11 = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (3), (7), (15), (16), (18), (27), (30), (32),
% 141.52/20.88 | | | | | | | | | | | (37), (39), (40), (42), (49), (57), (64), (80) are
% 141.52/20.88 | | | | | | | | | | | inconsistent by sub-proof #300.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | End of split
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | (81) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 &
% 141.52/20.88 | | | | | | | | op(e1, e0) = e0)
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | REF_CLOSE: (3), (5), (7), (9), (14), (15), (16), (18), (22),
% 141.52/20.88 | | | | | | | | (27), (30), (32), (35), (37), (39), (40), (42), (43),
% 141.52/20.88 | | | | | | | | (49), (57), (61), (81) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | #299.
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | End of split
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | Case 2:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (82) all_57_10 = e3 & op(e2, e0) = e3
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | ALPHA: (82) implies:
% 141.52/20.88 | | | | | | | (83) all_57_10 = e3
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | COMBINE_EQS: (61), (83) imply:
% 141.52/20.88 | | | | | | | (84) e3 = e1
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | REDUCE: (42), (84) imply:
% 141.52/20.88 | | | | | | | (85) $false
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | CLOSE: (85) is inconsistent.
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | End of split
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | Case 2:
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | (86) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 141.52/20.88 | | | | | | op(e0, e0) = e3)
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | BETA: splitting (86) gives:
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | Case 1:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (87) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | ALPHA: (87) implies:
% 141.52/20.88 | | | | | | | (88) all_57_11 = e3
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | BETA: splitting (20) gives:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | (89) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 &
% 141.52/20.88 | | | | | | | | op(e1, e2) = e0)
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | BETA: splitting (89) gives:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | (90) all_57_6 = e0 & op(e1, e3) = e0
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | REF_CLOSE: (30), (31), (90) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | | #994.
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | (91) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | ALPHA: (91) implies:
% 141.52/20.88 | | | | | | | | | (92) all_57_7 = e0
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | BETA: splitting (8) gives:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | (93) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 &
% 141.52/20.88 | | | | | | | | | | op(e1, e2) = e1)
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | BETA: splitting (93) gives:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (94) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (94) implies:
% 141.52/20.88 | | | | | | | | | | | (95) op(e1, e3) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (4), (34), (37), (95) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | sub-proof #332.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (96) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (96) implies:
% 141.52/20.88 | | | | | | | | | | | (97) all_57_7 = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (27), (92), (97) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | | | | #712.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | (98) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1
% 141.52/20.88 | | | | | | | | | | & op(e1, e0) = e1)
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | BETA: splitting (98) gives:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (99) all_57_8 = e1 & op(e1, e1) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (99) implies:
% 141.52/20.88 | | | | | | | | | | | (100) op(e1, e1) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (5), (37), (42), (100) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | sub-proof #1096.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (101) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (42), (88), (101) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | | | | #1033.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | End of split
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | (102) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 &
% 141.52/20.88 | | | | | | | | op(e1, e0) = e0)
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | REF_CLOSE: (3), (5), (7), (9), (14), (15), (16), (18), (22),
% 141.52/20.88 | | | | | | | | (27), (30), (32), (35), (37), (39), (40), (42), (43),
% 141.52/20.88 | | | | | | | | (49), (57), (61), (102) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | #299.
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | End of split
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | Case 2:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (103) all_57_15 = e3 & op(e0, e0) = e3
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | REF_CLOSE: (7), (9), (14), (15), (18), (22), (27), (30), (32),
% 141.52/20.88 | | | | | | | (37), (39), (42), (43), (103) are inconsistent by
% 141.52/20.88 | | | | | | | sub-proof #467.
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | End of split
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | End of split
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | End of split
% 141.52/20.88 | | | |
% 141.52/20.88 | | | Case 2:
% 141.52/20.88 | | | |
% 141.52/20.88 | | | | (104) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 141.52/20.88 | | | | e0) = e1)
% 141.52/20.88 | | | |
% 141.52/20.88 | | | | BETA: splitting (104) gives:
% 141.52/20.88 | | | |
% 141.52/20.88 | | | | Case 1:
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | (105) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | ALPHA: (105) implies:
% 141.52/20.88 | | | | | (106) all_57_11 = e1
% 141.52/20.88 | | | | | (107) op(e1, e0) = e1
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | BETA: splitting (16) gives:
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | Case 1:
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | (108) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 141.52/20.88 | | | | | | op(e2, e0) = e2)
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | BETA: splitting (108) gives:
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | Case 1:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (109) all_57_9 = e2 & op(e3, e0) = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | ALPHA: (109) implies:
% 141.52/20.88 | | | | | | | (110) all_57_9 = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | BETA: splitting (44) gives:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | (111) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 141.52/20.88 | | | | | | | | op(e3, e2) = e3)
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | BETA: splitting (111) gives:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | (112) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | ALPHA: (112) implies:
% 141.52/20.88 | | | | | | | | | (113) op(e3, e3) = e3
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | REF_CLOSE: (36), (37), (42), (113) are inconsistent by
% 141.52/20.88 | | | | | | | | | sub-proof #838.
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | (114) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | ALPHA: (114) implies:
% 141.52/20.88 | | | | | | | | | (115) all_57_1 = e3
% 141.52/20.88 | | | | | | | | | (116) op(e3, e2) = e3
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | BETA: splitting (48) gives:
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | (117) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0
% 141.52/20.88 | | | | | | | | | | & op(e3, e2) = e0)
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | BETA: splitting (117) gives:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (118) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (118) implies:
% 141.52/20.88 | | | | | | | | | | | (119) op(e3, e3) = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (27), (36), (37), (119) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | sub-proof #840.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (120) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (18), (115), (120) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | | | | #312.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | (121) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0
% 141.52/20.88 | | | | | | | | | | & op(e3, e0) = e0)
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | BETA: splitting (121) gives:
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (122) all_57_4 = e0 & op(e3, e1) = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (122) implies:
% 141.52/20.88 | | | | | | | | | | | (123) all_57_4 = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | BETA: splitting (26) gives:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | (124) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 141.52/20.88 | | | | | | | | | | | | & op(e2, e2) = e0)
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | REF_CLOSE: (18), (28), (30), (37), (115), (124) are
% 141.52/20.88 | | | | | | | | | | | | inconsistent by sub-proof #311.
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | (125) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 141.52/20.88 | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | BETA: splitting (125) gives:
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | (126) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | ALPHA: (126) implies:
% 141.52/20.88 | | | | | | | | | | | | | (127) all_57_7 = e0
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | BETA: splitting (15) gives:
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | (128) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 141.52/20.88 | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | BETA: splitting (128) gives:
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | (129) all_57_12 = e1 & op(e0, e3) = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | REF_CLOSE: (11), (29), (37), (129) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | | | sub-proof #350.
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | (130) all_57_13 = e1 & op(e0, e2) = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | (131) all_57_13 = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | BETA: splitting (12) gives:
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | (132) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 141.52/20.88 | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 141.52/20.88 | | | | | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 141.52/20.88 | | | | | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | BETA: splitting (132) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | (133) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 141.52/20.88 | | | | | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 141.52/20.88 | | | | | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 141.52/20.88 | | | | | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.52/20.88 | | | | | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | ALPHA: (133) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | (134) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | $i(all_56_15))
% 141.52/20.88 | | | | | | | | | | | | | | | | | (135) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13
% 141.52/20.88 | | | | | | | | | | | | | | | | | = e3) & op(e1, e1) = all_56_13 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | $i(all_56_13))
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | (136) all_56_6 = e1 & op(e1, e3) = e1
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | (137) op(e1, e3) = e1
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (34), (37), (137) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | | | | | | sub-proof #332.
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | (138) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | $i(all_56_13)
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | ALPHA: (138) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | (139) ~ (all_56_13 = e3)
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | BETA: splitting (45) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (140) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e3) = all_56_6 & op(e1, e1) = e3 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | $i(all_56_6))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | BETA: splitting (140) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (141) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e2 & op(e3, e2) = all_56_0
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e2 & all_56_11 = e3 & ~ (all_56_3 = e2) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e2) = e3 & $i(all_56_3))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (37), (141) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | sub-proof #298.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (142) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e3 & ~ (all_56_6 = e1) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e1) = e3 & $i(all_56_6))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (139), (142) are inconsistent by sub-proof #297.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (143) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e0) = all_56_5 & op(e0, e0) = e2 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | BETA: splitting (143) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (144) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e1) = e2 & $i(all_56_4))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | BETA: splitting (144) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (145) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e3 & $i(all_56_2)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | ALPHA: (145) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (146) op(e0, e0) = e3
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (11), (37), (38), (134), (146) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | sub-proof #739.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (147) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_4)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | ALPHA: (147) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (148) op(e2, e2) = e1
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (30), (32), (37), (115), (127), (131),
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (148) are inconsistent by sub-proof #520.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (149) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | BETA: splitting (149) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (150) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | e1) & op(e2, e2) = e1 & op(e1, e2) = all_56_7 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | op(e1, e1) = e2 & $i(all_56_7)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | ALPHA: (150) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (151) op(e2, e2) = e1
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (17), (30), (32), (37), (115), (127), (131),
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (151) are inconsistent by sub-proof #520.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (152) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14))))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (152) gives:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (153) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | op(e0, e0) = e2 & $i(all_56_5)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (153) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (154) op(e0, e0) = e2
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (3), (7), (15), (18), (27), (30), (32), (37),
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (39), (42), (57), (154) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | sub-proof #767.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (155) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | all_56_14 & $i(all_56_14)))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (155) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (156) op(e0, e0) = all_56_15
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (157) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (25), (37), (47), (50), (156), (157)
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #1114.
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | (158) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 141.52/20.88 | | | | | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 141.52/20.88 | | | | | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 141.52/20.88 | | | | | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 141.52/20.88 | | | | | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.52/20.88 | | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.52/20.88 | | | | | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 141.52/20.88 | | | | | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 141.52/20.88 | | | | | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | | | (159) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0
% 141.52/20.88 | | | | | | | | | | | | | | | | | = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (36), (37), (116), (159) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | | | | | sub-proof #296.
% 141.52/20.88 | | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | (160) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 141.52/20.88 | | | | | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 141.52/20.88 | | | | | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/20.88 | | | | | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.52/20.88 | | | | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.88 | | | | | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.52/20.88 | | | | | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 141.52/20.88 | | | | | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.52/20.88 | | | | | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | | REF_CLOSE: (5), (6), (18), (19), (36), (37), (107), (160) are
% 141.52/20.88 | | | | | | | | | | | | | | | | inconsistent by sub-proof #293.
% 141.52/20.88 | | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | (161) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 141.52/20.88 | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | BETA: splitting (161) gives:
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | Case 1:
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | (162) all_57_14 = e1 & op(e0, e1) = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | ALPHA: (162) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | (163) all_57_14 = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | COMBINE_EQS: (57), (163) imply:
% 141.52/20.88 | | | | | | | | | | | | | | | (164) e2 = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | SIMP: (164) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | (165) e2 = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | COMBINE_EQS: (110), (165) imply:
% 141.52/20.88 | | | | | | | | | | | | | | | (166) all_57_9 = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | REF_CLOSE: (2), (7), (18), (30), (32), (36), (37), (42),
% 141.52/20.88 | | | | | | | | | | | | | | | (44), (123), (166) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | | | | | | | | | #814.
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | (167) all_57_15 = e1 & op(e0, e0) = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | ALPHA: (167) implies:
% 141.52/20.88 | | | | | | | | | | | | | | | (168) all_57_15 = e1
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | COMBINE_EQS: (46), (168) imply:
% 141.52/20.88 | | | | | | | | | | | | | | | (169) e1 = e0
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | REDUCE: (27), (169) imply:
% 141.52/20.88 | | | | | | | | | | | | | | | (170) $false
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | | CLOSE: (170) is inconsistent.
% 141.52/20.88 | | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | (171) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | ALPHA: (171) implies:
% 141.52/20.88 | | | | | | | | | | | | | (172) op(e0, e2) = e0
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | | REF_CLOSE: (9), (37), (43), (172) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | | | sub-proof #977.
% 141.52/20.88 | | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | (173) all_57_9 = e0 & op(e3, e0) = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | ALPHA: (173) implies:
% 141.52/20.88 | | | | | | | | | | | (174) op(e3, e0) = e0
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | | REF_CLOSE: (23), (33), (37), (174) are inconsistent by
% 141.52/20.88 | | | | | | | | | | | sub-proof #941.
% 141.52/20.88 | | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | | |
% 141.52/20.88 | | | | | | | | | End of split
% 141.52/20.88 | | | | | | | | |
% 141.52/20.88 | | | | | | | | End of split
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | Case 2:
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | (175) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 141.52/20.88 | | | | | | | | op(e3, e0) = e3)
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | | REF_CLOSE: (3), (6), (7), (15), (16), (18), (19), (27), (30),
% 141.52/20.88 | | | | | | | | (32), (37), (39), (40), (42), (49), (57), (106),
% 141.52/20.88 | | | | | | | | (175) are inconsistent by sub-proof #292.
% 141.52/20.88 | | | | | | | |
% 141.52/20.88 | | | | | | | End of split
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | Case 2:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (176) all_57_10 = e2 & op(e2, e0) = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | ALPHA: (176) implies:
% 141.52/20.88 | | | | | | | (177) op(e2, e0) = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | REF_CLOSE: (37), (40), (49), (177) are inconsistent by sub-proof
% 141.52/20.88 | | | | | | | #1030.
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | End of split
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | Case 2:
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | (178) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 141.52/20.88 | | | | | | op(e0, e0) = e2)
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | BETA: splitting (178) gives:
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | | Case 1:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (179) all_57_11 = e2 & op(e1, e0) = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | REF_CLOSE: (7), (106), (179) are inconsistent by sub-proof #913.
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | Case 2:
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | (180) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | ALPHA: (180) implies:
% 141.52/20.88 | | | | | | | (181) op(e0, e0) = e2
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | | REF_CLOSE: (3), (7), (15), (18), (27), (30), (32), (37), (39),
% 141.52/20.88 | | | | | | | (42), (57), (181) are inconsistent by sub-proof #767.
% 141.52/20.88 | | | | | | |
% 141.52/20.88 | | | | | | End of split
% 141.52/20.88 | | | | | |
% 141.52/20.88 | | | | | End of split
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | Case 2:
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | (182) all_57_15 = e1 & op(e0, e0) = e1
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | ALPHA: (182) implies:
% 141.52/20.88 | | | | | (183) all_57_15 = e1
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | | REF_CLOSE: (27), (46), (183) are inconsistent by sub-proof #291.
% 141.52/20.88 | | | | |
% 141.52/20.88 | | | | End of split
% 141.52/20.88 | | | |
% 141.52/20.88 | | | End of split
% 141.52/20.88 | | |
% 141.52/20.88 | | Case 2:
% 141.52/20.88 | | |
% 141.52/20.88 | | | (184) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.88 | | |
% 141.52/20.88 | | | ALPHA: (184) implies:
% 141.52/20.88 | | | (185) op(e0, e0) = e2
% 141.52/20.88 | | |
% 141.52/20.88 | | | REF_CLOSE: (10), (30), (37), (185) are inconsistent by sub-proof #1094.
% 141.52/20.88 | | |
% 141.52/20.88 | | End of split
% 141.52/20.88 | |
% 141.52/20.88 | End of split
% 141.52/20.88 |
% 141.52/20.88 End of proof
% 141.52/20.88
% 141.52/20.88 Sub-proof #291 shows that the following formulas are inconsistent:
% 141.52/20.88 ----------------------------------------------------------------
% 141.52/20.88 (1) all_57_15 = e1
% 141.52/20.88 (2) all_57_15 = e0
% 141.52/20.88 (3) ~ (e1 = e0)
% 141.52/20.88
% 141.52/20.88 Begin of proof
% 141.52/20.88 |
% 141.52/20.88 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.88 | (4) e1 = e0
% 141.52/20.88 |
% 141.52/20.88 | SIMP: (4) implies:
% 141.52/20.88 | (5) e1 = e0
% 141.52/20.88 |
% 141.52/20.88 | REDUCE: (3), (5) imply:
% 141.52/20.88 | (6) $false
% 141.52/20.88 |
% 141.52/20.88 | CLOSE: (6) is inconsistent.
% 141.52/20.88 |
% 141.52/20.88 End of proof
% 141.52/20.88
% 141.52/20.88 Sub-proof #292 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.89 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.89 (2) ~ (all_52_8 = e3)
% 141.52/20.89 (3) ~ (e2 = e1)
% 141.52/20.89 (4) all_57_14 = e2
% 141.52/20.89 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.52/20.89 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.89 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.89 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.89 (7) ~ (e3 = e0)
% 141.52/20.89 (8) op(e3, e1) = all_52_8
% 141.52/20.89 (9) ~ (e1 = e0)
% 141.52/20.89 (10) ~ (e2 = e0)
% 141.52/20.89 (11) ~ (e3 = e2)
% 141.52/20.89 (12) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.89 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.89 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.89 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.89 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.89 (15) ~ (all_52_13 = e2)
% 141.52/20.89 (16) ~ (e3 = e1)
% 141.52/20.89 (17) all_57_11 = e1
% 141.52/20.89 (18) op(e2, e0) = all_52_13
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (12) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (19) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (19) implies:
% 141.52/20.89 | | (20) op(e3, e1) = e3
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (2), (8), (13), (20) are inconsistent by sub-proof #1106.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (21) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (21) implies:
% 141.52/20.89 | | (22) all_57_9 = e3
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14), (15),
% 141.52/20.89 | | (16), (17), (18), (22) are inconsistent by sub-proof #300.
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #293 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) op(e1, e1) = e3
% 141.52/20.89 (2) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.89 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.89 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.89 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.89 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.89 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.89 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.89 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.52/20.89 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.52/20.89 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.52/20.89 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.52/20.89 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.89 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/20.89 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.52/20.89 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.89 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/20.89 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.89 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.89 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.52/20.89 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.89 (3) ~ (all_52_8 = e3)
% 141.52/20.89 (4) ~ (e3 = e0)
% 141.52/20.89 (5) op(e3, e1) = all_52_8
% 141.52/20.89 (6) op(e3, e3) = e1
% 141.52/20.89 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (8) op(e1, e0) = e1
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (2) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (9) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1)
% 141.52/20.89 | | = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/20.89 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.52/20.89 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.89 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1)
% 141.52/20.89 | | = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1)
% 141.52/20.89 | | | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.89 | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.89 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.89 | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.89 | | $i(all_56_14)))
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (9) implies:
% 141.52/20.89 | | (10) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3)
% 141.52/20.89 | | = all_56_9 & $i(all_56_9))
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (3), (5), (6), (7), (10) are inconsistent by sub-proof #295.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (11) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.52/20.89 | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.52/20.89 | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.52/20.89 | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.89 | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.52/20.89 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.52/20.89 | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.52/20.89 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.52/20.89 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.52/20.89 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.52/20.89 | | e0) = all_56_8 & $i(all_56_8)))
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (11) implies:
% 141.52/20.89 | | (12) (all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.52/20.89 | | e0) = all_56_8 & $i(all_56_8))
% 141.52/20.89 | |
% 141.52/20.89 | | BETA: splitting (12) gives:
% 141.52/20.89 | |
% 141.52/20.89 | | Case 1:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (13) all_56_13 = e0 & op(e1, e1) = e0
% 141.52/20.89 | | |
% 141.52/20.89 | | | ALPHA: (13) implies:
% 141.52/20.89 | | | (14) op(e1, e1) = e0
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (1), (4), (7), (14) are inconsistent by sub-proof #308.
% 141.52/20.89 | | |
% 141.52/20.89 | | Case 2:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (15) ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8)
% 141.52/20.89 | | |
% 141.52/20.89 | | | ALPHA: (15) implies:
% 141.52/20.89 | | | (16) ~ (all_56_8 = e1)
% 141.52/20.89 | | | (17) op(e1, e0) = all_56_8
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (7), (8), (16), (17) are inconsistent by sub-proof #294.
% 141.52/20.89 | | |
% 141.52/20.89 | | End of split
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #294 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (2) op(e1, e0) = all_56_8
% 141.52/20.89 (3) op(e1, e0) = e1
% 141.52/20.89 (4) ~ (all_56_8 = e1)
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | GROUND_INST: instantiating (1) with e1, all_56_8, e0, e1, simplifying with
% 141.52/20.89 | (2), (3) gives:
% 141.52/20.89 | (5) all_56_8 = e1
% 141.52/20.89 |
% 141.52/20.89 | REDUCE: (4), (5) imply:
% 141.52/20.89 | (6) $false
% 141.52/20.89 |
% 141.52/20.89 | CLOSE: (6) is inconsistent.
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #295 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) ~ (all_52_8 = e3)
% 141.52/20.89 (2) op(e3, e1) = all_52_8
% 141.52/20.89 (3) op(e3, e3) = e1
% 141.52/20.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (5) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.52/20.89 all_56_9 & $i(all_56_9))
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (5) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (6) all_56_1 = e3 & op(e3, e1) = e3
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (6) implies:
% 141.52/20.89 | | (7) op(e3, e1) = e3
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #1106.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (8) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (8) implies:
% 141.52/20.89 | | (9) ~ (all_56_9 = e1)
% 141.52/20.89 | | (10) op(e3, e3) = all_56_9
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (3), (4), (9), (10) are inconsistent by sub-proof #758.
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #296 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) ~ (e2 = e1)
% 141.52/20.89 (2) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 141.52/20.89 all_56_0 & $i(all_56_0))
% 141.52/20.89 (3) op(e3, e3) = e1
% 141.52/20.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (5) op(e3, e2) = e3
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (2) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (6) all_56_9 = e2 & op(e3, e3) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (6) implies:
% 141.52/20.89 | | (7) op(e3, e3) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (1), (3), (4), (7) are inconsistent by sub-proof #818.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (8) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0)
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (8) implies:
% 141.52/20.89 | | (9) ~ (all_56_0 = e3)
% 141.52/20.89 | | (10) op(e3, e2) = all_56_0
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (4), (5), (9), (10) are inconsistent by sub-proof #670.
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #297 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 &
% 141.52/20.89 op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 141.52/20.89 e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3)
% 141.52/20.89 = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.52/20.89 (2) ~ (all_56_13 = e3)
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (1) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (3) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1
% 141.52/20.89 | | & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (3) implies:
% 141.52/20.89 | | (4) all_56_13 = e3
% 141.52/20.89 | |
% 141.52/20.89 | | REDUCE: (2), (4) imply:
% 141.52/20.89 | | (5) $false
% 141.52/20.89 | |
% 141.52/20.89 | | CLOSE: (5) is inconsistent.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (6) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1
% 141.52/20.89 | | & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (6) implies:
% 141.52/20.89 | | (7) all_56_13 = e3
% 141.52/20.89 | |
% 141.52/20.89 | | REDUCE: (2), (7) imply:
% 141.52/20.89 | | (8) $false
% 141.52/20.89 | |
% 141.52/20.89 | | CLOSE: (8) is inconsistent.
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #298 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.89 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.89 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.52/20.89 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.52/20.89 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (3) op(e3, e3) = e1
% 141.52/20.89 (4) ~ (e2 = e1)
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (1) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (5) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2
% 141.52/20.89 | | & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (5) implies:
% 141.52/20.89 | | (6) op(e3, e3) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #818.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (7) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2
% 141.52/20.89 | | & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (7) implies:
% 141.52/20.89 | | (8) op(e3, e3) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #818.
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #299 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.89 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.89 (2) op(e1, e1) = e3
% 141.52/20.89 (3) ~ (e2 = e1)
% 141.52/20.89 (4) ~ (all_52_7 = e0)
% 141.52/20.89 (5) all_57_14 = e2
% 141.52/20.89 (6) all_57_12 = e3
% 141.52/20.89 (7) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.89 (8) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.52/20.89 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.89 (9) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.89 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.89 (10) ~ (e3 = e0)
% 141.52/20.89 (11) all_57_10 = e1
% 141.52/20.89 (12) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.89 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.89 e2)
% 141.52/20.89 (13) ~ (e1 = e0)
% 141.52/20.89 (14) ~ (e2 = e0)
% 141.52/20.89 (15) ~ (e3 = e2)
% 141.52/20.89 (16) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.89 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.89 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (18) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.89 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.89 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.89 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.89 (19) ~ (all_52_13 = e2)
% 141.52/20.89 (20) ~ (e3 = e1)
% 141.52/20.89 (21) op(e0, e2) = all_52_7
% 141.52/20.89 (22) op(e2, e0) = all_52_13
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (7) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (23) all_57_8 = e0 & op(e1, e1) = e0
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (23) implies:
% 141.52/20.89 | | (24) op(e1, e1) = e0
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (2), (10), (17), (24) are inconsistent by sub-proof #308.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (25) all_57_11 = e0 & op(e1, e0) = e0
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (25) implies:
% 141.52/20.89 | | (26) all_57_11 = e0
% 141.52/20.89 | |
% 141.52/20.89 | | BETA: splitting (9) gives:
% 141.52/20.89 | |
% 141.52/20.89 | | Case 1:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (27) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 141.52/20.89 | | | e2)
% 141.52/20.89 | | |
% 141.52/20.89 | | | BETA: splitting (27) gives:
% 141.52/20.89 | | |
% 141.52/20.89 | | | Case 1:
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | (28) all_57_9 = e2 & op(e3, e0) = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | ALPHA: (28) implies:
% 141.52/20.89 | | | | (29) all_57_9 = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | REF_CLOSE: (3), (4), (6), (8), (10), (11), (12), (13), (14), (15), (16),
% 141.52/20.89 | | | | (17), (18), (20), (21), (26), (29) are inconsistent by
% 141.52/20.89 | | | | sub-proof #466.
% 141.52/20.89 | | | |
% 141.52/20.89 | | | Case 2:
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | (30) all_57_10 = e2 & op(e2, e0) = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | ALPHA: (30) implies:
% 141.52/20.89 | | | | (31) op(e2, e0) = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | REF_CLOSE: (17), (19), (22), (31) are inconsistent by sub-proof #1030.
% 141.52/20.89 | | | |
% 141.52/20.89 | | | End of split
% 141.52/20.89 | | |
% 141.52/20.89 | | Case 2:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (32) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0)
% 141.52/20.89 | | | = e2)
% 141.52/20.89 | | |
% 141.52/20.89 | | | BETA: splitting (32) gives:
% 141.52/20.89 | | |
% 141.52/20.89 | | | Case 1:
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | (33) all_57_11 = e2 & op(e1, e0) = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | ALPHA: (33) implies:
% 141.52/20.89 | | | | (34) all_57_11 = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | REF_CLOSE: (14), (26), (34) are inconsistent by sub-proof #996.
% 141.52/20.89 | | | |
% 141.52/20.89 | | | Case 2:
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | (35) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | ALPHA: (35) implies:
% 141.52/20.89 | | | | (36) op(e0, e0) = e2
% 141.52/20.89 | | | |
% 141.52/20.89 | | | | REF_CLOSE: (1), (3), (5), (8), (10), (13), (14), (15), (17), (18), (20),
% 141.52/20.89 | | | | (36) are inconsistent by sub-proof #767.
% 141.52/20.89 | | | |
% 141.52/20.89 | | | End of split
% 141.52/20.89 | | |
% 141.52/20.89 | | End of split
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #300 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.89 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.89 (2) ~ (e2 = e1)
% 141.52/20.89 (3) all_57_14 = e2
% 141.52/20.89 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.52/20.89 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/20.89 (5) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.52/20.89 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.89 (6) ~ (e3 = e0)
% 141.52/20.89 (7) ~ (e1 = e0)
% 141.52/20.89 (8) ~ (e2 = e0)
% 141.52/20.89 (9) ~ (e3 = e2)
% 141.52/20.89 (10) all_57_9 = e3
% 141.52/20.89 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.89 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.89 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.89 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.89 (13) ~ (all_52_13 = e2)
% 141.52/20.89 (14) ~ (e3 = e1)
% 141.52/20.89 (15) all_57_11 = e1
% 141.52/20.89 (16) op(e2, e0) = all_52_13
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (5) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (17) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 141.52/20.89 | | e2)
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (9), (10), (11), (13), (16), (17) are inconsistent by sub-proof
% 141.52/20.89 | | #301.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (18) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.89 | | e2)
% 141.52/20.89 | |
% 141.52/20.89 | | BETA: splitting (18) gives:
% 141.52/20.89 | |
% 141.52/20.89 | | Case 1:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (19) all_57_11 = e2 & op(e1, e0) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | ALPHA: (19) implies:
% 141.52/20.89 | | | (20) all_57_11 = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (2), (15), (20) are inconsistent by sub-proof #810.
% 141.52/20.89 | | |
% 141.52/20.89 | | Case 2:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (21) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | ALPHA: (21) implies:
% 141.52/20.89 | | | (22) op(e0, e0) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (14), (22)
% 141.52/20.89 | | | are inconsistent by sub-proof #767.
% 141.52/20.89 | | |
% 141.52/20.89 | | End of split
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #301 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) ~ (e3 = e2)
% 141.52/20.89 (2) all_57_9 = e3
% 141.52/20.89 (3) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.52/20.89 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (5) ~ (all_52_13 = e2)
% 141.52/20.89 (6) op(e2, e0) = all_52_13
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (3) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (7) all_57_9 = e2 & op(e3, e0) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #598.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (8) all_57_10 = e2 & op(e2, e0) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | ALPHA: (8) implies:
% 141.52/20.89 | | (9) op(e2, e0) = e2
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1030.
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #302 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.89 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.89 (2) op(e1, e3) = all_52_2
% 141.52/20.89 (3) op(e1, e1) = e3
% 141.52/20.89 (4) ~ (e2 = e1)
% 141.52/20.89 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.89 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.89 (6) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/20.89 (7) ~ (e3 = e0)
% 141.52/20.89 (8) op(e1, e1) = all_4_2
% 141.52/20.89 (9) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.89 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.89 (10) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.89 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.89 (11) ~ (e1 = e0)
% 141.52/20.89 (12) op(e2, e2) = e2
% 141.52/20.89 (13) ~ (e2 = e0)
% 141.52/20.89 (14) ~ (e3 = e2)
% 141.52/20.89 (15) ~ (all_52_2 = e1)
% 141.52/20.89 (16) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/20.89 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/20.89 (17) ~ (all_4_2 = e2)
% 141.52/20.89 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (19) ~ (e3 = e1)
% 141.52/20.89 (20) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.89 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | ALPHA: (6) implies:
% 141.52/20.89 | (21) all_57_6 = e3
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (16) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (22) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 141.52/20.89 | | e2)
% 141.52/20.89 | |
% 141.52/20.89 | | BETA: splitting (22) gives:
% 141.52/20.89 | |
% 141.52/20.89 | | Case 1:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (23) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (14), (21), (23) are inconsistent by sub-proof #998.
% 141.52/20.89 | | |
% 141.52/20.89 | | Case 2:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (24) all_57_7 = e2 & op(e1, e2) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (1), (4), (7), (10), (11), (12), (13), (14), (18), (19), (20),
% 141.52/20.89 | | | (24) are inconsistent by sub-proof #309.
% 141.52/20.89 | | |
% 141.52/20.89 | | End of split
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (25) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 141.52/20.89 | | e2)
% 141.52/20.89 | |
% 141.52/20.89 | | BETA: splitting (25) gives:
% 141.52/20.89 | |
% 141.52/20.89 | | Case 1:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (26) all_57_8 = e2 & op(e1, e1) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | ALPHA: (26) implies:
% 141.52/20.89 | | | (27) op(e1, e1) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (8), (17), (18), (27) are inconsistent by sub-proof #1124.
% 141.52/20.89 | | |
% 141.52/20.89 | | Case 2:
% 141.52/20.89 | | |
% 141.52/20.89 | | | (28) all_57_11 = e2 & op(e1, e0) = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | ALPHA: (28) implies:
% 141.52/20.89 | | | (29) all_57_11 = e2
% 141.52/20.89 | | |
% 141.52/20.89 | | | REF_CLOSE: (2), (3), (4), (5), (7), (9), (11), (13), (15), (18), (19),
% 141.52/20.89 | | | (21), (29) are inconsistent by sub-proof #303.
% 141.52/20.89 | | |
% 141.52/20.89 | | End of split
% 141.52/20.89 | |
% 141.52/20.89 | End of split
% 141.52/20.89 |
% 141.52/20.89 End of proof
% 141.52/20.89
% 141.52/20.89 Sub-proof #303 shows that the following formulas are inconsistent:
% 141.52/20.89 ----------------------------------------------------------------
% 141.52/20.89 (1) op(e1, e3) = all_52_2
% 141.52/20.89 (2) op(e1, e1) = e3
% 141.52/20.89 (3) all_57_6 = e3
% 141.52/20.89 (4) ~ (e2 = e1)
% 141.52/20.89 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.89 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.89 (6) ~ (e3 = e0)
% 141.52/20.89 (7) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.89 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.89 (8) all_57_11 = e2
% 141.52/20.89 (9) ~ (e1 = e0)
% 141.52/20.89 (10) ~ (e2 = e0)
% 141.52/20.89 (11) ~ (all_52_2 = e1)
% 141.52/20.89 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.89 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.89 (13) ~ (e3 = e1)
% 141.52/20.89
% 141.52/20.89 Begin of proof
% 141.52/20.89 |
% 141.52/20.89 | BETA: splitting (5) gives:
% 141.52/20.89 |
% 141.52/20.89 | Case 1:
% 141.52/20.89 | |
% 141.52/20.89 | | (14) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.52/20.89 | | e1)
% 141.52/20.89 | |
% 141.52/20.89 | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (14) are
% 141.52/20.89 | | inconsistent by sub-proof #305.
% 141.52/20.89 | |
% 141.52/20.89 | Case 2:
% 141.52/20.89 | |
% 141.52/20.89 | | (15) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.52/20.90 | | e1)
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (4), (8), (12), (13), (15) are inconsistent by sub-proof
% 141.52/20.90 | | #304.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #304 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) op(e1, e1) = e3
% 141.52/20.90 (2) ~ (e2 = e1)
% 141.52/20.90 (3) all_57_11 = e2
% 141.52/20.90 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (5) ~ (e3 = e1)
% 141.52/20.90 (6) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (6) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (7) implies:
% 141.52/20.90 | | (8) op(e1, e1) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1096.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (9) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (9) are inconsistent by sub-proof #862.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #305 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) op(e1, e3) = all_52_2
% 141.52/20.90 (2) op(e1, e1) = e3
% 141.52/20.90 (3) all_57_6 = e3
% 141.52/20.90 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1)
% 141.52/20.90 (5) ~ (e3 = e0)
% 141.52/20.90 (6) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.90 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.90 (7) all_57_11 = e2
% 141.52/20.90 (8) ~ (e1 = e0)
% 141.52/20.90 (9) ~ (e2 = e0)
% 141.52/20.90 (10) ~ (all_52_2 = e1)
% 141.52/20.90 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (4) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (12) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (12) implies:
% 141.52/20.90 | | (13) op(e1, e3) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (10), (11), (13) are inconsistent by sub-proof #332.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (14) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (14) implies:
% 141.52/20.90 | | (15) all_57_7 = e1
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (11), (15) are inconsistent by
% 141.52/20.90 | | sub-proof #306.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #306 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) op(e1, e1) = e3
% 141.52/20.90 (2) all_57_6 = e3
% 141.52/20.90 (3) all_57_7 = e1
% 141.52/20.90 (4) ~ (e3 = e0)
% 141.52/20.90 (5) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 141.52/20.90 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.90 (6) all_57_11 = e2
% 141.52/20.90 (7) ~ (e1 = e0)
% 141.52/20.90 (8) ~ (e2 = e0)
% 141.52/20.90 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (5) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (10) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 141.52/20.90 | | e0)
% 141.52/20.90 | |
% 141.52/20.90 | | BETA: splitting (10) gives:
% 141.52/20.90 | |
% 141.52/20.90 | | Case 1:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (11) all_57_6 = e0 & op(e1, e3) = e0
% 141.52/20.90 | | |
% 141.52/20.90 | | | ALPHA: (11) implies:
% 141.52/20.90 | | | (12) all_57_6 = e0
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (2), (4), (12) are inconsistent by sub-proof #873.
% 141.52/20.90 | | |
% 141.52/20.90 | | Case 2:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (13) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/20.90 | | |
% 141.52/20.90 | | | ALPHA: (13) implies:
% 141.52/20.90 | | | (14) all_57_7 = e0
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (3), (7), (14) are inconsistent by sub-proof #712.
% 141.52/20.90 | | |
% 141.52/20.90 | | End of split
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (15) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 141.52/20.90 | | e0)
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (4), (6), (8), (9), (15) are inconsistent by sub-proof #307.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #307 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) op(e1, e1) = e3
% 141.52/20.90 (2) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.90 (3) ~ (e3 = e0)
% 141.52/20.90 (4) all_57_11 = e2
% 141.52/20.90 (5) ~ (e2 = e0)
% 141.52/20.90 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (2) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (7) implies:
% 141.52/20.90 | | (8) op(e1, e1) = e0
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (3), (6), (8) are inconsistent by sub-proof #308.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (9) all_57_11 = e0 & op(e1, e0) = e0
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #992.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #308 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (2) op(e1, e1) = e3
% 141.52/20.90 (3) op(e1, e1) = e0
% 141.52/20.90 (4) ~ (e3 = e0)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | GROUND_INST: instantiating (1) with e3, e0, e1, e1, simplifying with (2), (3)
% 141.52/20.90 | gives:
% 141.52/20.90 | (5) e3 = e0
% 141.52/20.90 |
% 141.52/20.90 | REDUCE: (4), (5) imply:
% 141.52/20.90 | (6) $false
% 141.52/20.90 |
% 141.52/20.90 | CLOSE: (6) is inconsistent.
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #309 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.90 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.90 (2) ~ (e2 = e1)
% 141.52/20.90 (3) ~ (e3 = e0)
% 141.52/20.90 (4) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.90 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.90 (5) ~ (e1 = e0)
% 141.52/20.90 (6) op(e2, e2) = e2
% 141.52/20.90 (7) ~ (e2 = e0)
% 141.52/20.90 (8) ~ (e3 = e2)
% 141.52/20.90 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (10) ~ (e3 = e1)
% 141.52/20.90 (11) all_57_7 = e2 & op(e1, e2) = e2
% 141.52/20.90 (12) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.90 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | ALPHA: (11) implies:
% 141.52/20.90 | (13) all_57_7 = e2
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (1) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (14) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 141.52/20.90 | | e1)
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13), (14)
% 141.52/20.90 | | are inconsistent by sub-proof #415.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (15) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 141.52/20.90 | | e1)
% 141.52/20.90 | |
% 141.52/20.90 | | BETA: splitting (15) gives:
% 141.52/20.90 | |
% 141.52/20.90 | | Case 1:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (16) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (2), (13), (16) are inconsistent by sub-proof #864.
% 141.52/20.90 | | |
% 141.52/20.90 | | Case 2:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (17) all_57_13 = e1 & op(e0, e2) = e1
% 141.52/20.90 | | |
% 141.52/20.90 | | | ALPHA: (17) implies:
% 141.52/20.90 | | | (18) all_57_13 = e1
% 141.52/20.90 | | |
% 141.52/20.90 | | | BETA: splitting (12) gives:
% 141.52/20.90 | | |
% 141.52/20.90 | | | Case 1:
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | (19) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 141.52/20.90 | | | | = e3)
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | BETA: splitting (19) gives:
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | Case 1:
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | | (20) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | | ALPHA: (20) implies:
% 141.52/20.90 | | | | | (21) all_57_1 = e3
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 141.52/20.90 | | | | | (13), (21) are inconsistent by sub-proof #310.
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | Case 2:
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | | (22) all_57_3 = e3 & op(e2, e2) = e3
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | | ALPHA: (22) implies:
% 141.52/20.90 | | | | | (23) op(e2, e2) = e3
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | | REF_CLOSE: (6), (8), (9), (23) are inconsistent by sub-proof #728.
% 141.52/20.90 | | | | |
% 141.52/20.90 | | | | End of split
% 141.52/20.90 | | | |
% 141.52/20.90 | | | Case 2:
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | (24) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 141.52/20.90 | | | | = e3)
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | REF_CLOSE: (8), (10), (13), (18), (24) are inconsistent by sub-proof
% 141.52/20.90 | | | | #770.
% 141.52/20.90 | | | |
% 141.52/20.90 | | | End of split
% 141.52/20.90 | | |
% 141.52/20.90 | | End of split
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #310 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.90 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.90 (2) ~ (e2 = e1)
% 141.52/20.90 (3) all_57_7 = e2
% 141.52/20.90 (4) ~ (e3 = e0)
% 141.52/20.90 (5) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.90 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.90 (6) ~ (e1 = e0)
% 141.52/20.90 (7) op(e2, e2) = e2
% 141.52/20.90 (8) ~ (e2 = e0)
% 141.52/20.90 (9) ~ (e3 = e2)
% 141.52/20.90 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (11) all_57_1 = e3
% 141.52/20.90 (12) ~ (e3 = e1)
% 141.52/20.90 (13) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.90 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (5) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (14) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 141.52/20.90 | | e0)
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (4), (7), (8), (10), (11), (14) are inconsistent by sub-proof
% 141.52/20.90 | | #311.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (15) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.52/20.90 | | e0)
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (15)
% 141.52/20.90 | | are inconsistent by sub-proof #682.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #311 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) ~ (e3 = e0)
% 141.52/20.90 (2) op(e2, e2) = e2
% 141.52/20.90 (3) ~ (e2 = e0)
% 141.52/20.90 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (5) all_57_1 = e3
% 141.52/20.90 (6) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (6) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (7) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #312.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (8) implies:
% 141.52/20.90 | | (9) op(e2, e2) = e0
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1076.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #312 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.90 (2) all_57_1 = e3
% 141.52/20.90 (3) ~ (e3 = e0)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | ALPHA: (1) implies:
% 141.52/20.90 | (4) all_57_1 = e0
% 141.52/20.90 |
% 141.52/20.90 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.90 | (5) e3 = e0
% 141.52/20.90 |
% 141.52/20.90 | REDUCE: (3), (5) imply:
% 141.52/20.90 | (6) $false
% 141.52/20.90 |
% 141.52/20.90 | CLOSE: (6) is inconsistent.
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #313 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) ~ (e3 = e0)
% 141.52/20.90 (2) op(e3, e3) = e1
% 141.52/20.90 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (4) ~ (e3 = e1)
% 141.52/20.90 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 141.52/20.90 (6) all_57_2 = e0
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (5) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (7) implies:
% 141.52/20.90 | | (8) op(e3, e3) = e3
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #838.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (9) all_57_2 = e3 & op(e2, e3) = e3
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (9) implies:
% 141.52/20.90 | | (10) all_57_2 = e3
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #879.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #314 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) ~ (e2 = e1)
% 141.52/20.90 (2) ~ (all_10_2 = e1)
% 141.52/20.90 (3) ~ (all_14_2 = e1)
% 141.52/20.90 (4) op(e0, e0) = all_10_2
% 141.52/20.90 (5) op(e2, e2) = e2
% 141.52/20.90 (6) ~ (e2 = e0)
% 141.52/20.90 (7) ~ (e3 = e2)
% 141.52/20.90 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (9) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.90 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.90 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.52/20.90 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.52/20.90 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.52/20.90 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 141.52/20.90 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 141.52/20.90 op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 & all_56_15 = e3 & ~
% 141.52/20.90 (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 141.52/20.90 = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4
% 141.52/20.90 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 141.52/20.90 $i(all_56_4)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 141.52/20.90 op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 141.52/20.90 $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 141.52/20.90 op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 141.52/20.90 $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 141.52/20.90 e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.90 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.90 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 141.52/20.90 = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 141.52/20.90 ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.52/20.90 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 141.52/20.90 e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.52/20.90 (10) op(e2, e2) = all_6_2
% 141.52/20.90 (11) op(e3, e3) = all_14_2
% 141.52/20.90 (12) ~ (all_14_2 = e0)
% 141.52/20.90 (13) ~ (all_6_2 = e0)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (9) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (14) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 141.52/20.90 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.52/20.90 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 141.52/20.90 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 141.52/20.90 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 141.52/20.90 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.52/20.90 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 141.52/20.90 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.52/20.90 | |
% 141.52/20.90 | | BETA: splitting (14) gives:
% 141.52/20.90 | |
% 141.52/20.90 | | Case 1:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (15) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 141.52/20.90 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 141.52/20.90 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 141.52/20.90 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (5), (7), (8), (15) are inconsistent by sub-proof #317.
% 141.52/20.90 | | |
% 141.52/20.90 | | Case 2:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (16) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 141.52/20.90 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 141.52/20.90 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 141.52/20.90 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (3), (8), (11), (16) are inconsistent by sub-proof #316.
% 141.52/20.90 | | |
% 141.52/20.90 | | End of split
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (17) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.52/20.90 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.52/20.90 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.52/20.90 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 141.52/20.90 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.52/20.90 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.52/20.90 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.52/20.90 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.52/20.90 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.90 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.90 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.90 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/20.90 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.90 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.52/20.90 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.52/20.90 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.52/20.90 | | all_56_14 & $i(all_56_14))))
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (10), (11), (12), (13), (17) are
% 141.52/20.90 | | inconsistent by sub-proof #315.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #315 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) ~ (e2 = e1)
% 141.52/20.90 (2) ~ (all_10_2 = e1)
% 141.52/20.90 (3) op(e0, e0) = all_10_2
% 141.52/20.90 (4) op(e2, e2) = e2
% 141.52/20.90 (5) ~ (e2 = e0)
% 141.52/20.90 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (7) op(e2, e2) = all_6_2
% 141.52/20.90 (8) op(e3, e3) = all_14_2
% 141.52/20.90 (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.52/20.90 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.52/20.90 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.52/20.90 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.52/20.90 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.52/20.90 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.52/20.90 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.52/20.90 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.52/20.90 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.52/20.90 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.90 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.52/20.90 e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.90 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.52/20.90 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.90 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/20.90 $i(all_56_14))))
% 141.52/20.90 (10) ~ (all_14_2 = e0)
% 141.52/20.90 (11) ~ (all_6_2 = e0)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (9) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (12) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.52/20.90 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 141.52/20.90 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.52/20.90 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.52/20.90 | |
% 141.52/20.90 | | BETA: splitting (12) gives:
% 141.52/20.90 | |
% 141.52/20.90 | | Case 1:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (13) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 141.52/20.90 | | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.52/20.90 | | |
% 141.52/20.90 | | | ALPHA: (13) implies:
% 141.52/20.90 | | | (14) op(e3, e3) = e0
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (6), (8), (10), (14) are inconsistent by sub-proof #1125.
% 141.52/20.90 | | |
% 141.52/20.90 | | Case 2:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (15) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 141.52/20.90 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 141.52/20.90 | | |
% 141.52/20.90 | | | ALPHA: (15) implies:
% 141.52/20.90 | | | (16) op(e2, e2) = e1
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (1), (4), (6), (16) are inconsistent by sub-proof #749.
% 141.52/20.90 | | |
% 141.52/20.90 | | End of split
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (17) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 141.52/20.90 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 141.52/20.90 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 141.52/20.90 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.52/20.90 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.90 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.90 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.90 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/20.90 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.90 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 141.52/20.90 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 141.52/20.90 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 141.52/20.90 | | all_56_14 & $i(all_56_14))))
% 141.52/20.90 | |
% 141.52/20.90 | | BETA: splitting (17) gives:
% 141.52/20.90 | |
% 141.52/20.90 | | Case 1:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (18) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 141.52/20.90 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)
% 141.52/20.90 | | |
% 141.52/20.90 | | | ALPHA: (18) implies:
% 141.52/20.90 | | | (19) op(e2, e2) = e1
% 141.52/20.90 | | |
% 141.52/20.90 | | | REF_CLOSE: (1), (4), (6), (19) are inconsistent by sub-proof #749.
% 141.52/20.90 | | |
% 141.52/20.90 | | Case 2:
% 141.52/20.90 | | |
% 141.52/20.90 | | | (20) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 141.52/20.90 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 141.52/20.90 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.90 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.90 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.90 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/20.90 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.90 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.52/20.90 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.90 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.52/20.90 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 141.52/20.90 | | |
% 141.52/20.90 | | | BETA: splitting (20) gives:
% 141.52/20.90 | | |
% 141.52/20.90 | | | Case 1:
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | (21) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 141.52/20.90 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 141.52/20.90 | | | | $i(all_56_5)
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | ALPHA: (21) implies:
% 141.52/20.90 | | | | (22) op(e2, e2) = e0
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | REF_CLOSE: (4), (5), (6), (22) are inconsistent by sub-proof #1076.
% 141.52/20.90 | | | |
% 141.52/20.90 | | | Case 2:
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | (23) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 141.52/20.90 | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.90 | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.90 | | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/20.90 | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.52/20.90 | | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.52/20.90 | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.90 | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 141.52/20.90 | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | ALPHA: (23) implies:
% 141.52/20.90 | | | | (24) op(e0, e0) = all_56_15
% 141.52/20.90 | | | | (25) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.52/20.90 | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.90 | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/20.90 | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 141.52/20.90 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.52/20.90 | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.90 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 141.52/20.90 | | | | e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/20.90 | | | |
% 141.52/20.90 | | | | REF_CLOSE: (2), (3), (6), (7), (8), (10), (11), (24), (25) are
% 141.52/20.90 | | | | inconsistent by sub-proof #1120.
% 141.52/20.90 | | | |
% 141.52/20.90 | | | End of split
% 141.52/20.90 | | |
% 141.52/20.90 | | End of split
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #316 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 &
% 141.52/20.90 op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 =
% 141.52/20.90 e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3)
% 141.52/20.90 = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 141.52/20.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (3) op(e3, e3) = all_14_2
% 141.52/20.90 (4) ~ (all_14_2 = e1)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (1) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (5) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1
% 141.52/20.90 | | & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (5) implies:
% 141.52/20.90 | | (6) op(e3, e3) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #365.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (7) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1
% 141.52/20.90 | | & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (7) implies:
% 141.52/20.90 | | (8) op(e3, e3) = e1
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #365.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #317 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.52/20.90 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.52/20.90 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 141.52/20.90 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 141.52/20.90 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.90 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.90 (3) op(e2, e2) = e2
% 141.52/20.90 (4) ~ (e3 = e2)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | BETA: splitting (1) gives:
% 141.52/20.90 |
% 141.52/20.90 | Case 1:
% 141.52/20.90 | |
% 141.52/20.90 | | (5) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2
% 141.52/20.90 | | & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (5) implies:
% 141.52/20.90 | | (6) op(e2, e2) = e3
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #728.
% 141.52/20.90 | |
% 141.52/20.90 | Case 2:
% 141.52/20.90 | |
% 141.52/20.90 | | (7) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2
% 141.52/20.90 | | & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 141.52/20.90 | |
% 141.52/20.90 | | ALPHA: (7) implies:
% 141.52/20.90 | | (8) op(e2, e2) = e3
% 141.52/20.90 | |
% 141.52/20.90 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #728.
% 141.52/20.90 | |
% 141.52/20.90 | End of split
% 141.52/20.90 |
% 141.52/20.90 End of proof
% 141.52/20.90
% 141.52/20.90 Sub-proof #318 shows that the following formulas are inconsistent:
% 141.52/20.90 ----------------------------------------------------------------
% 141.52/20.90 (1) all_54_5 = all_6_2
% 141.52/20.90 (2) all_54_5 = e3
% 141.52/20.90 (3) ~ (all_6_2 = e3)
% 141.52/20.90
% 141.52/20.90 Begin of proof
% 141.52/20.90 |
% 141.52/20.90 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.90 | (4) all_6_2 = e3
% 141.52/20.91 |
% 141.52/20.91 | SIMP: (4) implies:
% 141.52/20.91 | (5) all_6_2 = e3
% 141.52/20.91 |
% 141.52/20.91 | REDUCE: (3), (5) imply:
% 141.52/20.91 | (6) $false
% 141.52/20.91 |
% 141.52/20.91 | CLOSE: (6) is inconsistent.
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #319 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 141.52/20.91 (2) ~ (all_52_8 = e3)
% 141.52/20.91 (3) op(e3, e1) = all_52_8
% 141.52/20.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (5) ~ (all_52_9 = e3)
% 141.52/20.91 (6) op(e2, e1) = all_52_9
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (1) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (7) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (7) implies:
% 141.52/20.91 | | (8) op(e3, e1) = e3
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1106.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (9) all_57_5 = e3 & op(e2, e1) = e3
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #320.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #320 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) all_57_5 = e3 & op(e2, e1) = e3
% 141.52/20.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (3) op(e2, e1) = all_52_9
% 141.52/20.91 (4) ~ (all_52_9 = e3)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | ALPHA: (1) implies:
% 141.52/20.91 | (5) op(e2, e1) = e3
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (2) with all_52_9, e3, e1, e2, simplifying with
% 141.52/20.91 | (3), (5) gives:
% 141.52/20.91 | (6) all_52_9 = e3
% 141.52/20.91 |
% 141.52/20.91 | REDUCE: (4), (6) imply:
% 141.52/20.91 | (7) $false
% 141.52/20.91 |
% 141.52/20.91 | CLOSE: (7) is inconsistent.
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #321 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (all_52_4 = e0)
% 141.52/20.91 (2) ~ (e2 = e1)
% 141.52/20.91 (3) op(e0, e3) = all_52_3
% 141.52/20.91 (4) ~ (e3 = e0)
% 141.52/20.91 (5) op(e3, e1) = all_52_8
% 141.52/20.91 (6) all_57_6 = e0
% 141.52/20.91 (7) ~ (all_52_12 = e0)
% 141.52/20.91 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.91 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.91 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.52/20.91 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.52/20.91 (10) ~ (e1 = e0)
% 141.52/20.91 (11) ~ (all_52_3 = e1)
% 141.52/20.91 (12) op(e3, e2) = all_52_4
% 141.52/20.91 (13) ~ (e2 = e0)
% 141.52/20.91 (14) ~ (e3 = e2)
% 141.52/20.91 (15) op(e3, e0) = all_52_12
% 141.52/20.91 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (17) ~ (all_52_8 = e0)
% 141.52/20.91 (18) ~ (e3 = e1)
% 141.52/20.91 (19) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.91 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.91 (20) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.91 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (20) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (21) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 141.52/20.91 | | e0)
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (21) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (22) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (22) implies:
% 141.52/20.91 | | | (23) all_57_0 = e0
% 141.52/20.91 | | | (24) op(e3, e3) = e0
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (13), (14), (16),
% 141.52/20.91 | | | (18), (19), (23), (24) are inconsistent by sub-proof #322.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (25) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (1), (12), (16), (25) are inconsistent by sub-proof #1102.
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (26) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 141.52/20.91 | | e0)
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (5), (7), (15), (16), (17), (26) are inconsistent by sub-proof
% 141.52/20.91 | | #463.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #322 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (e2 = e1)
% 141.52/20.91 (2) op(e0, e3) = all_52_3
% 141.52/20.91 (3) ~ (e3 = e0)
% 141.52/20.91 (4) all_57_6 = e0
% 141.52/20.91 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.91 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.91 (6) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.52/20.91 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.52/20.91 (7) ~ (e1 = e0)
% 141.52/20.91 (8) ~ (all_52_3 = e1)
% 141.52/20.91 (9) ~ (e2 = e0)
% 141.52/20.91 (10) ~ (e3 = e2)
% 141.52/20.91 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (12) ~ (e3 = e1)
% 141.52/20.91 (13) all_57_0 = e0
% 141.52/20.91 (14) op(e3, e3) = e0
% 141.52/20.91 (15) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.91 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (6) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (16) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 141.52/20.91 | | e1)
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (16) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (17) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (17) implies:
% 141.52/20.91 | | | (18) op(e3, e3) = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (7), (11), (14), (18) are inconsistent by sub-proof #840.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (19) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (19) implies:
% 141.52/20.91 | | | (20) all_57_2 = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (13),
% 141.52/20.91 | | | (14), (15), (20) are inconsistent by sub-proof #323.
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (21) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 141.52/20.91 | | e1)
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (21) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (22) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (22) implies:
% 141.52/20.91 | | | (23) all_57_6 = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (4), (7), (23) are inconsistent by sub-proof #1026.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (24) all_57_12 = e1 & op(e0, e3) = e1
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (2), (8), (11), (24) are inconsistent by sub-proof #350.
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #323 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (e2 = e1)
% 141.52/20.91 (2) ~ (e3 = e0)
% 141.52/20.91 (3) all_57_6 = e0
% 141.52/20.91 (4) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.91 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.91 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.52/20.91 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.52/20.91 (6) ~ (e1 = e0)
% 141.52/20.91 (7) ~ (e2 = e0)
% 141.52/20.91 (8) ~ (e3 = e2)
% 141.52/20.91 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (10) ~ (e3 = e1)
% 141.52/20.91 (11) all_57_2 = e1
% 141.52/20.91 (12) all_57_0 = e0
% 141.52/20.91 (13) op(e3, e3) = e0
% 141.52/20.91 (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.91 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (14) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (15) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 141.52/20.91 | | e2)
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (1), (7), (9), (11), (13), (15) are inconsistent by sub-proof
% 141.52/20.91 | | #638.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (16) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 141.52/20.91 | | e2)
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (16) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (17) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (3), (7), (17) are inconsistent by sub-proof #783.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (18) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (18) implies:
% 141.52/20.91 | | | (19) all_57_12 = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (12), (13), (19)
% 141.52/20.91 | | | are inconsistent by sub-proof #771.
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #324 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (all_56_5 = e2)
% 141.52/20.91 (2) ~ (all_56_13 = e0)
% 141.52/20.91 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.91 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.91 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.91 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.91 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.91 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.91 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.91 (4) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.52/20.91 all_56_11 & $i(all_56_11))
% 141.52/20.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (6) ~ (e3 = e1)
% 141.52/20.91 (7) all_56_15 = e1
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (4) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (8) all_56_5 = e2 & op(e2, e0) = e2
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (8) implies:
% 141.52/20.91 | | (9) all_56_5 = e2
% 141.52/20.91 | |
% 141.52/20.91 | | REDUCE: (1), (9) imply:
% 141.52/20.91 | | (10) $false
% 141.52/20.91 | |
% 141.52/20.91 | | CLOSE: (10) is inconsistent.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (11) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (11) implies:
% 141.52/20.91 | | (12) ~ (all_56_11 = e0)
% 141.52/20.91 | | (13) op(e2, e2) = all_56_11
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (2), (3), (5), (6), (7), (12), (13) are inconsistent by sub-proof
% 141.52/20.91 | | #326.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #325 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (all_52_1 = e1)
% 141.52/20.91 (2) op(e2, e3) = all_52_1
% 141.52/20.91 (3) ~ (e1 = e0)
% 141.52/20.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (5) op(e3, e3) = e0
% 141.52/20.91 (6) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (6) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (7) implies:
% 141.52/20.91 | | (8) op(e3, e3) = e1
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #840.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (9) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (1), (2), (4), (9) are inconsistent by sub-proof #846.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #326 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (all_56_13 = e0)
% 141.52/20.91 (2) op(e2, e2) = all_56_11
% 141.52/20.91 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.91 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.91 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.91 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.91 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.91 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.91 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.91 (4) ~ (all_56_11 = e0)
% 141.52/20.91 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (6) ~ (e3 = e1)
% 141.52/20.91 (7) all_56_15 = e1
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (3) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (8) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.91 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.91 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 141.52/20.91 | | = all_56_12 & $i(all_56_12))
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (8) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (9) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.91 | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (6), (7), (9) are inconsistent by sub-proof #335.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (10) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.91 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (10) implies:
% 141.52/20.91 | | | (11) op(e2, e2) = e0
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (2), (4), (5), (11) are inconsistent by sub-proof #857.
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (12) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/20.91 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.91 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.91 | | e1) = all_56_14 & $i(all_56_14))
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (1), (12) are inconsistent by sub-proof #947.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #327 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (2) op(e2, e3) = all_14_0
% 141.52/20.91 (3) op(e2, e3) = e1
% 141.52/20.91 (4) ~ (all_14_0 = e1)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (1) with e1, all_14_0, e3, e2, simplifying with
% 141.52/20.91 | (2), (3) gives:
% 141.52/20.91 | (5) all_14_0 = e1
% 141.52/20.91 |
% 141.52/20.91 | REDUCE: (4), (5) imply:
% 141.52/20.91 | (6) $false
% 141.52/20.91 |
% 141.52/20.91 | CLOSE: (6) is inconsistent.
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #328 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 & $i(all_14_1)
% 141.52/20.91 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (3) op(e3, e0) = all_28_1
% 141.52/20.91 (4) op(e3, e0) = e2
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | ALPHA: (1) implies:
% 141.52/20.91 | (5) ~ (all_14_1 = e2)
% 141.52/20.91 | (6) op(e3, e0) = all_14_1
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (2) with e2, all_28_1, e0, e3, simplifying with
% 141.52/20.91 | (3), (4) gives:
% 141.52/20.91 | (7) all_28_1 = e2
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (2) with all_14_1, all_28_1, e0, e3, simplifying
% 141.52/20.91 | with (3), (6) gives:
% 141.52/20.91 | (8) all_28_1 = all_14_1
% 141.52/20.91 |
% 141.52/20.91 | COMBINE_EQS: (7), (8) imply:
% 141.52/20.91 | (9) all_14_1 = e2
% 141.52/20.91 |
% 141.52/20.91 | SIMP: (9) implies:
% 141.52/20.91 | (10) all_14_1 = e2
% 141.52/20.91 |
% 141.52/20.91 | REDUCE: (5), (10) imply:
% 141.52/20.91 | (11) $false
% 141.52/20.91 |
% 141.52/20.91 | CLOSE: (11) is inconsistent.
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #329 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) op(e2, e3) = e1
% 141.52/20.91 (2) ~ (all_14_0 = e1)
% 141.52/20.91 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (4) op(e2, e3) = all_28_0
% 141.52/20.91 (5) op(e2, e3) = all_14_0
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (3) with e1, all_28_0, e3, e2, simplifying with
% 141.52/20.91 | (1), (4) gives:
% 141.52/20.91 | (6) all_28_0 = e1
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (3) with all_14_0, all_28_0, e3, e2, simplifying
% 141.52/20.91 | with (4), (5) gives:
% 141.52/20.91 | (7) all_28_0 = all_14_0
% 141.52/20.91 |
% 141.52/20.91 | COMBINE_EQS: (6), (7) imply:
% 141.52/20.91 | (8) all_14_0 = e1
% 141.52/20.91 |
% 141.52/20.91 | REDUCE: (2), (8) imply:
% 141.52/20.91 | (9) $false
% 141.52/20.91 |
% 141.52/20.91 | CLOSE: (9) is inconsistent.
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #330 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.91 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.91 (2) ~ (e2 = e1)
% 141.52/20.91 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.91 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.91 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.91 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.91 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.91 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.91 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.91 (4) all_57_15 = e1
% 141.52/20.91 (5) ~ (e3 = e0)
% 141.52/20.91 (6) op(e1, e1) = all_4_2
% 141.52/20.91 (7) ~ (all_52_7 = e2)
% 141.52/20.91 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.52/20.91 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.91 (9) op(e0, e0) = e1
% 141.52/20.91 (10) ~ (all_4_2 = e3)
% 141.52/20.91 (11) ~ (e1 = e0)
% 141.52/20.91 (12) op(e2, e2) = e2
% 141.52/20.91 (13) ~ (e2 = e0)
% 141.52/20.91 (14) ~ (e3 = e2)
% 141.52/20.91 (15) ~ (all_4_2 = e2)
% 141.52/20.91 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (17) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.91 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.91 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.91 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.91 (18) ~ (e3 = e1)
% 141.52/20.91 (19) op(e0, e2) = all_52_7
% 141.52/20.91 (20) op(e0, e0) = all_56_15
% 141.52/20.91 (21) all_56_15 = e1
% 141.52/20.91 (22) all_57_12 = e1
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (8) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (23) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 141.52/20.91 | | e2)
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (2), (7), (16), (19), (22), (23) are inconsistent by sub-proof
% 141.52/20.91 | | #445.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (24) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.91 | | e2)
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (24) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (25) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (25) implies:
% 141.52/20.91 | | | (26) all_57_14 = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (1), (3), (4), (5), (6), (9), (10), (11), (12), (13), (14),
% 141.52/20.91 | | | (15), (16), (17), (18), (20), (21), (22), (26) are inconsistent
% 141.52/20.91 | | | by sub-proof #398.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (27) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | ALPHA: (27) implies:
% 141.52/20.91 | | | (28) op(e0, e0) = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (2), (3), (12), (13), (14), (16), (20), (28) are inconsistent
% 141.52/20.91 | | | by sub-proof #643.
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #331 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (e2 = e1)
% 141.52/20.91 (2) ~ (all_52_9 = e2)
% 141.52/20.91 (3) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 141.52/20.91 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (5) all_57_4 = e1
% 141.52/20.91 (6) op(e2, e1) = all_52_9
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (3) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (7) all_57_4 = e2 & op(e3, e1) = e2
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (7) implies:
% 141.52/20.91 | | (8) all_57_4 = e2
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #1088.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (9) all_57_5 = e2 & op(e2, e1) = e2
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (9) implies:
% 141.52/20.91 | | (10) op(e2, e1) = e2
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (2), (4), (6), (10) are inconsistent by sub-proof #890.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #332 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (2) op(e1, e3) = all_52_2
% 141.52/20.91 (3) op(e1, e3) = e1
% 141.52/20.91 (4) ~ (all_52_2 = e1)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | GROUND_INST: instantiating (1) with all_52_2, e1, e3, e1, simplifying with
% 141.52/20.91 | (2), (3) gives:
% 141.52/20.91 | (5) all_52_2 = e1
% 141.52/20.91 |
% 141.52/20.91 | REDUCE: (4), (5) imply:
% 141.52/20.91 | (6) $false
% 141.52/20.91 |
% 141.52/20.91 | CLOSE: (6) is inconsistent.
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #333 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) ~ (all_4_2 = e0)
% 141.52/20.91 (2) ~ (e2 = e1)
% 141.52/20.91 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.91 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.91 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.91 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.91 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.91 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.91 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.91 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/20.91 (5) op(e1, e1) = all_4_2
% 141.52/20.91 (6) ~ (all_4_2 = e3)
% 141.52/20.91 (7) ~ (all_4_2 = e2)
% 141.52/20.91 (8) all_54_10 = all_4_2
% 141.52/20.91 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.91 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.91 (10) ~ (e3 = e1)
% 141.52/20.91 (11) all_56_15 = e1
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (4) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (12) all_54_10 = e3
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (6), (8), (12) are inconsistent by sub-proof #1112.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (13) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/20.91 | |
% 141.52/20.91 | | BETA: splitting (13) gives:
% 141.52/20.91 | |
% 141.52/20.91 | | Case 1:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (14) all_54_10 = e2
% 141.52/20.91 | | |
% 141.52/20.91 | | | REF_CLOSE: (7), (8), (14) are inconsistent by sub-proof #1111.
% 141.52/20.91 | | |
% 141.52/20.91 | | Case 2:
% 141.52/20.91 | | |
% 141.52/20.91 | | | (15) all_54_10 = e1 | all_54_10 = e0
% 141.52/20.91 | | |
% 141.52/20.91 | | | BETA: splitting (3) gives:
% 141.52/20.91 | | |
% 141.52/20.91 | | | Case 1:
% 141.52/20.91 | | | |
% 141.52/20.91 | | | | (16) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.52/20.91 | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/20.91 | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/20.91 | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 141.52/20.91 | | | |
% 141.52/20.91 | | | | REF_CLOSE: (2), (10), (11), (16) are inconsistent by sub-proof #334.
% 141.52/20.91 | | | |
% 141.52/20.91 | | | Case 2:
% 141.52/20.91 | | | |
% 141.52/20.91 | | | | (17) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.52/20.91 | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.52/20.91 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 141.52/20.91 | | | | e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/20.91 | | | |
% 141.52/20.91 | | | | REF_CLOSE: (1), (5), (8), (9), (15), (17) are inconsistent by sub-proof
% 141.52/20.91 | | | | #456.
% 141.52/20.91 | | | |
% 141.52/20.91 | | | End of split
% 141.52/20.91 | | |
% 141.52/20.91 | | End of split
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #334 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.91 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.91 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.91 $i(all_56_12))
% 141.52/20.91 (2) all_56_15 = e1
% 141.52/20.91 (3) ~ (e3 = e1)
% 141.52/20.91 (4) ~ (e2 = e1)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | BETA: splitting (1) gives:
% 141.52/20.91 |
% 141.52/20.91 | Case 1:
% 141.52/20.91 | |
% 141.52/20.91 | | (5) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.91 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.91 | |
% 141.52/20.91 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #335.
% 141.52/20.91 | |
% 141.52/20.91 | Case 2:
% 141.52/20.91 | |
% 141.52/20.91 | | (6) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 141.52/20.91 | | e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/20.91 | |
% 141.52/20.91 | | ALPHA: (6) implies:
% 141.52/20.91 | | (7) all_56_15 = e2
% 141.52/20.91 | |
% 141.52/20.91 | | COMBINE_EQS: (2), (7) imply:
% 141.52/20.91 | | (8) e2 = e1
% 141.52/20.91 | |
% 141.52/20.91 | | REDUCE: (4), (8) imply:
% 141.52/20.91 | | (9) $false
% 141.52/20.91 | |
% 141.52/20.91 | | CLOSE: (9) is inconsistent.
% 141.52/20.91 | |
% 141.52/20.91 | End of split
% 141.52/20.91 |
% 141.52/20.91 End of proof
% 141.52/20.91
% 141.52/20.91 Sub-proof #335 shows that the following formulas are inconsistent:
% 141.52/20.91 ----------------------------------------------------------------
% 141.52/20.91 (1) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.91 op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.91 (2) all_56_15 = e1
% 141.52/20.91 (3) ~ (e3 = e1)
% 141.52/20.91
% 141.52/20.91 Begin of proof
% 141.52/20.91 |
% 141.52/20.91 | ALPHA: (1) implies:
% 141.52/20.91 | (4) all_56_15 = e3
% 141.52/20.91 |
% 141.52/20.91 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.91 | (5) e3 = e1
% 141.52/20.91 |
% 141.52/20.92 | REDUCE: (3), (5) imply:
% 141.52/20.92 | (6) $false
% 141.52/20.92 |
% 141.52/20.92 | CLOSE: (6) is inconsistent.
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #336 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/20.92 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/20.92 (2) ~ (e2 = e1)
% 141.52/20.92 (3) all_57_5 = e1
% 141.52/20.92 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.52/20.92 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.92 (5) ~ (e3 = e0)
% 141.52/20.92 (6) op(e1, e1) = e1
% 141.52/20.92 (7) ~ (e1 = e0)
% 141.52/20.92 (8) ~ (e2 = e0)
% 141.52/20.92 (9) ~ (e3 = e2)
% 141.52/20.92 (10) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.52/20.92 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.52/20.92 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.92 (12) ~ (e3 = e1)
% 141.52/20.92 (13) op(e2, e1) = all_52_9
% 141.52/20.92 (14) ~ (all_52_9 = e0)
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | BETA: splitting (10) gives:
% 141.52/20.92 |
% 141.52/20.92 | Case 1:
% 141.52/20.92 | |
% 141.52/20.92 | | (15) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 141.52/20.92 | | e2)
% 141.52/20.92 | |
% 141.52/20.92 | | BETA: splitting (15) gives:
% 141.52/20.92 | |
% 141.52/20.92 | | Case 1:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (16) all_57_4 = e2 & op(e3, e1) = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (16) implies:
% 141.52/20.92 | | | (17) all_57_4 = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | BETA: splitting (1) gives:
% 141.52/20.92 | | |
% 141.52/20.92 | | | Case 1:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 141.52/20.92 | | | | = e3)
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | REF_CLOSE: (3), (9), (12), (17), (18) are inconsistent by sub-proof
% 141.52/20.92 | | | | #820.
% 141.52/20.92 | | | |
% 141.52/20.92 | | | Case 2:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | (19) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 141.52/20.92 | | | | = e3)
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | BETA: splitting (19) gives:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | Case 1:
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | (20) all_57_8 = e3 & op(e1, e1) = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | ALPHA: (20) implies:
% 141.52/20.92 | | | | | (21) op(e1, e1) = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | REF_CLOSE: (6), (11), (12), (21) are inconsistent by sub-proof #1096.
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | Case 2:
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | (22) all_57_14 = e3 & op(e0, e1) = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | ALPHA: (22) implies:
% 141.52/20.92 | | | | | (23) all_57_14 = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | BETA: splitting (4) gives:
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | Case 1:
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | (24) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2,
% 141.52/20.92 | | | | | | e1) = e0)
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | REF_CLOSE: (8), (11), (13), (14), (17), (24) are inconsistent by
% 141.52/20.92 | | | | | | sub-proof #914.
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | Case 2:
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | (25) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 141.52/20.92 | | | | | | e1) = e0)
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | REF_CLOSE: (5), (6), (7), (11), (23), (25) are inconsistent by
% 141.52/20.92 | | | | | | sub-proof #625.
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | End of split
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | End of split
% 141.52/20.92 | | | |
% 141.52/20.92 | | | End of split
% 141.52/20.92 | | |
% 141.52/20.92 | | Case 2:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (26) all_57_5 = e2 & op(e2, e1) = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | REF_CLOSE: (2), (3), (26) are inconsistent by sub-proof #1012.
% 141.52/20.92 | | |
% 141.52/20.92 | | End of split
% 141.52/20.92 | |
% 141.52/20.92 | Case 2:
% 141.52/20.92 | |
% 141.52/20.92 | | (27) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 141.52/20.92 | | e2)
% 141.52/20.92 | |
% 141.52/20.92 | | BETA: splitting (27) gives:
% 141.52/20.92 | |
% 141.52/20.92 | | Case 1:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (28) all_57_8 = e2 & op(e1, e1) = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (28) implies:
% 141.52/20.92 | | | (29) op(e1, e1) = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | REF_CLOSE: (2), (6), (11), (29) are inconsistent by sub-proof #1085.
% 141.52/20.92 | | |
% 141.52/20.92 | | Case 2:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (30) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (30) implies:
% 141.52/20.92 | | | (31) all_57_14 = e2
% 141.52/20.92 | | |
% 141.52/20.92 | | | BETA: splitting (1) gives:
% 141.52/20.92 | | |
% 141.52/20.92 | | | Case 1:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | (32) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 141.52/20.92 | | | | = e3)
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | BETA: splitting (32) gives:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | Case 1:
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | (33) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | ALPHA: (33) implies:
% 141.52/20.92 | | | | | (34) all_57_4 = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | BETA: splitting (4) gives:
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | Case 1:
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | (35) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2,
% 141.52/20.92 | | | | | | e1) = e0)
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | BETA: splitting (35) gives:
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | Case 1:
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | | (36) all_57_4 = e0 & op(e3, e1) = e0
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | | REF_CLOSE: (5), (34), (36) are inconsistent by sub-proof #337.
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | Case 2:
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | | (37) all_57_5 = e0 & op(e2, e1) = e0
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | | ALPHA: (37) implies:
% 141.52/20.92 | | | | | | | (38) op(e2, e1) = e0
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | | REF_CLOSE: (11), (13), (14), (38) are inconsistent by sub-proof
% 141.52/20.92 | | | | | | | #1091.
% 141.52/20.92 | | | | | | |
% 141.52/20.92 | | | | | | End of split
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | Case 2:
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | (39) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0,
% 141.52/20.92 | | | | | | e1) = e0)
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | | REF_CLOSE: (6), (7), (8), (11), (31), (39) are inconsistent by
% 141.52/20.92 | | | | | | sub-proof #919.
% 141.52/20.92 | | | | | |
% 141.52/20.92 | | | | | End of split
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | Case 2:
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | (40) all_57_5 = e3 & op(e2, e1) = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | ALPHA: (40) implies:
% 141.52/20.92 | | | | | (41) all_57_5 = e3
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | | REF_CLOSE: (3), (12), (41) are inconsistent by sub-proof #1035.
% 141.52/20.92 | | | | |
% 141.52/20.92 | | | | End of split
% 141.52/20.92 | | | |
% 141.52/20.92 | | | Case 2:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | (42) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 141.52/20.92 | | | | = e3)
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | REF_CLOSE: (6), (9), (11), (12), (31), (42) are inconsistent by
% 141.52/20.92 | | | | sub-proof #1010.
% 141.52/20.92 | | | |
% 141.52/20.92 | | | End of split
% 141.52/20.92 | | |
% 141.52/20.92 | | End of split
% 141.52/20.92 | |
% 141.52/20.92 | End of split
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #337 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) all_57_4 = e0 & op(e3, e1) = e0
% 141.52/20.92 (2) all_57_4 = e3
% 141.52/20.92 (3) ~ (e3 = e0)
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | ALPHA: (1) implies:
% 141.52/20.92 | (4) all_57_4 = e0
% 141.52/20.92 |
% 141.52/20.92 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.92 | (5) e3 = e0
% 141.52/20.92 |
% 141.52/20.92 | REDUCE: (3), (5) imply:
% 141.52/20.92 | (6) $false
% 141.52/20.92 |
% 141.52/20.92 | CLOSE: (6) is inconsistent.
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #338 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) ~ (all_52_4 = all_52_7)
% 141.52/20.92 (2) ~ (all_52_3 = all_52_7)
% 141.52/20.92 (3) ~ (all_52_14 = e1)
% 141.52/20.92 (4) ~ (all_52_7 = e1)
% 141.52/20.92 (5) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.92 (6) op(e1, e2) = all_52_6
% 141.52/20.92 (7) ~ (e2 = e1)
% 141.52/20.92 (8) all_54_13 = all_52_7
% 141.52/20.92 (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.92 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.92 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.92 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.92 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.92 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.92 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.92 (10) op(e0, e3) = all_52_3
% 141.52/20.92 (11) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.92 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.92 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.92 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.92 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.92 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.92 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.92 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.92 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.92 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.92 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.92 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.92 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.92 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.92 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.92 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.92 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.92 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.92 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.92 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.92 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.92 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.92 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.92 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.92 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.92 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.92 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.92 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.92 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.92 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.92 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.92 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.92 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.92 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.92 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.92 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.92 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.92 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.92 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.92 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.92 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.92 (12) ~ (all_52_4 = all_52_6)
% 141.52/20.92 (13) op(e3, e3) = e2
% 141.52/20.92 (14) op(e1, e1) = all_4_2
% 141.52/20.92 (15) all_54_9 = all_52_6
% 141.52/20.92 (16) ~ (all_52_6 = all_52_7)
% 141.52/20.92 (17) op(e0, e0) = e1
% 141.52/20.92 (18) ~ (all_52_3 = all_52_11)
% 141.52/20.92 (19) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.52/20.92 (20) op(e3, e2) = all_52_4
% 141.52/20.92 (21) op(e0, e1) = all_52_11
% 141.52/20.92 (22) ~ (all_4_2 = e2)
% 141.52/20.92 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.92 (24) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.52/20.92 (25) ~ (e3 = e1)
% 141.52/20.92 (26) op(e0, e2) = all_52_7
% 141.52/20.92 (27) all_56_15 = e1
% 141.52/20.92 (28) ~ (all_52_6 = e0)
% 141.52/20.92 (29) op(e1, e0) = all_52_14
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | ALPHA: (5) implies:
% 141.52/20.92 | (30) op(e0, e3) = e0
% 141.52/20.92 |
% 141.52/20.92 | GROUND_INST: instantiating (23) with all_52_3, e0, e3, e0, simplifying with
% 141.52/20.92 | (10), (30) gives:
% 141.52/20.92 | (31) all_52_3 = e0
% 141.52/20.92 |
% 141.52/20.92 | REDUCE: (2), (31) imply:
% 141.52/20.92 | (32) ~ (all_52_7 = e0)
% 141.52/20.92 |
% 141.52/20.92 | SIMP: (32) implies:
% 141.52/20.92 | (33) ~ (all_52_7 = e0)
% 141.52/20.92 |
% 141.52/20.92 | REDUCE: (18), (31) imply:
% 141.52/20.92 | (34) ~ (all_52_11 = e0)
% 141.52/20.92 |
% 141.52/20.92 | SIMP: (34) implies:
% 141.52/20.92 | (35) ~ (all_52_11 = e0)
% 141.52/20.92 |
% 141.52/20.92 | BETA: splitting (11) gives:
% 141.52/20.92 |
% 141.52/20.92 | Case 1:
% 141.52/20.92 | |
% 141.52/20.92 | | (36) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 141.52/20.92 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.92 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.92 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.92 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.52/20.92 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.52/20.92 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.52/20.92 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.92 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.92 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.52/20.92 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.52/20.92 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 141.52/20.92 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.52/20.92 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.52/20.92 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.52/20.92 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.52/20.92 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.52/20.92 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.92 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.52/20.92 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.52/20.92 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.52/20.92 | | $i(all_56_12))))
% 141.52/20.92 | |
% 141.52/20.92 | | BETA: splitting (36) gives:
% 141.52/20.92 | |
% 141.52/20.92 | | Case 1:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (37) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 141.52/20.92 | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.92 | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.92 | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.92 | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.52/20.92 | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.52/20.92 | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.52/20.92 | | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.92 | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.92 | | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.52/20.92 | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (37) implies:
% 141.52/20.92 | | | (38) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.92 | | | e3) = all_56_10 & $i(all_56_10))
% 141.52/20.92 | | |
% 141.52/20.92 | | | REF_CLOSE: (17), (23), (25), (30), (38) are inconsistent by sub-proof
% 141.52/20.92 | | | #346.
% 141.52/20.92 | | |
% 141.52/20.92 | | Case 2:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (39) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 141.52/20.92 | | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.52/20.92 | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 141.52/20.92 | | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.92 | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.52/20.92 | | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.52/20.92 | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.52/20.92 | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.52/20.92 | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.52/20.92 | | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 141.52/20.92 | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (39) implies:
% 141.52/20.92 | | | (40) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 141.52/20.92 | | | e2) = all_56_12 & $i(all_56_12))
% 141.52/20.92 | | | (41) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.52/20.92 | | | e2) = all_56_7 & $i(all_56_7))
% 141.52/20.92 | | | (42) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.92 | | | e0) = all_56_15 & $i(all_56_15))
% 141.52/20.92 | | | (43) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3,
% 141.52/20.92 | | | e3) = all_56_9 & $i(all_56_9))
% 141.52/20.92 | | |
% 141.52/20.92 | | | BETA: splitting (40) gives:
% 141.52/20.92 | | |
% 141.52/20.92 | | | Case 1:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | (44) all_56_15 = e2 & op(e0, e0) = e2
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | ALPHA: (44) implies:
% 141.52/20.92 | | | | (45) all_56_15 = e2
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | REF_CLOSE: (23), (26), (33), (42), (45) are inconsistent by sub-proof
% 141.52/20.92 | | | | #976.
% 141.52/20.92 | | | |
% 141.52/20.92 | | | Case 2:
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | (46) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | ALPHA: (46) implies:
% 141.52/20.92 | | | | (47) ~ (all_56_12 = e0)
% 141.52/20.92 | | | | (48) op(e0, e2) = all_56_12
% 141.52/20.92 | | | |
% 141.52/20.92 | | | | REF_CLOSE: (1), (4), (6), (8), (12), (13), (14), (15), (16), (19), (20),
% 141.52/20.92 | | | | (22), (23), (24), (26), (28), (41), (43), (47), (48) are
% 141.52/20.92 | | | | inconsistent by sub-proof #344.
% 141.52/20.92 | | | |
% 141.52/20.92 | | | End of split
% 141.52/20.92 | | |
% 141.52/20.92 | | End of split
% 141.52/20.92 | |
% 141.52/20.92 | Case 2:
% 141.52/20.92 | |
% 141.52/20.92 | | (49) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.52/20.92 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/20.92 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.52/20.92 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.92 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.52/20.92 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.52/20.92 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.52/20.92 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.52/20.92 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.92 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.52/20.92 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.52/20.92 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | (
% 141.52/20.92 | | ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.52/20.92 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/20.92 | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 141.52/20.92 | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.92 | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/20.92 | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.92 | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 141.52/20.92 | | e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.52/20.92 | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.52/20.92 | | $i(all_56_8))))
% 141.52/20.92 | |
% 141.52/20.92 | | REF_CLOSE: (3), (7), (9), (21), (23), (27), (29), (30), (35), (49) are
% 141.52/20.92 | | inconsistent by sub-proof #340.
% 141.52/20.92 | |
% 141.52/20.92 | End of split
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #339 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 141.52/20.92 (2) op(e3, e3) = e2
% 141.52/20.92 (3) ~ (all_52_1 = e0)
% 141.52/20.92 (4) op(e2, e3) = all_52_1
% 141.52/20.92 (5) ~ (e2 = e0)
% 141.52/20.92 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | BETA: splitting (1) gives:
% 141.52/20.92 |
% 141.52/20.92 | Case 1:
% 141.52/20.92 | |
% 141.52/20.92 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.92 | |
% 141.52/20.92 | | ALPHA: (7) implies:
% 141.52/20.92 | | (8) op(e3, e3) = e0
% 141.52/20.92 | |
% 141.52/20.92 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #880.
% 141.52/20.92 | |
% 141.52/20.92 | Case 2:
% 141.52/20.92 | |
% 141.52/20.92 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 141.52/20.92 | |
% 141.52/20.92 | | REF_CLOSE: (3), (4), (6), (9) are inconsistent by sub-proof #1028.
% 141.52/20.92 | |
% 141.52/20.92 | End of split
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #340 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) ~ (all_52_14 = e1)
% 141.52/20.92 (2) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.92 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.92 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.92 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.92 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.92 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.92 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.92 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.52/20.92 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.52/20.92 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.52/20.92 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.52/20.92 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.92 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/20.92 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.52/20.92 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.92 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/20.92 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.92 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.92 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.52/20.92 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.92 (3) ~ (e2 = e1)
% 141.52/20.92 (4) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.92 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.92 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.92 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.92 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.92 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.92 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.92 (5) ~ (all_52_11 = e0)
% 141.52/20.92 (6) op(e0, e1) = all_52_11
% 141.52/20.92 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.92 (8) all_56_15 = e1
% 141.52/20.92 (9) op(e0, e3) = e0
% 141.52/20.92 (10) op(e1, e0) = all_52_14
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | BETA: splitting (2) gives:
% 141.52/20.92 |
% 141.52/20.92 | Case 1:
% 141.52/20.92 | |
% 141.52/20.92 | | (11) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.52/20.92 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/20.92 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.52/20.92 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.92 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.52/20.92 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.52/20.92 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.52/20.92 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.52/20.92 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.92 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 141.52/20.92 | | e1) = all_56_14 & $i(all_56_14)))
% 141.52/20.92 | |
% 141.52/20.92 | | ALPHA: (11) implies:
% 141.52/20.92 | | (12) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.92 | | e0) = all_56_15 & $i(all_56_15))
% 141.52/20.92 | |
% 141.52/20.92 | | REF_CLOSE: (5), (6), (7), (8), (12) are inconsistent by sub-proof #432.
% 141.52/20.92 | |
% 141.52/20.92 | Case 2:
% 141.52/20.92 | |
% 141.52/20.92 | | (13) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.52/20.92 | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.52/20.92 | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.52/20.92 | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.92 | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.52/20.92 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.52/20.92 | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.52/20.92 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.52/20.92 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.52/20.92 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.52/20.92 | | e0) = all_56_8 & $i(all_56_8)))
% 141.52/20.92 | |
% 141.52/20.92 | | ALPHA: (13) implies:
% 141.52/20.92 | | (14) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.52/20.92 | | e1) = all_56_13 & $i(all_56_13))
% 141.52/20.92 | |
% 141.52/20.92 | | BETA: splitting (14) gives:
% 141.52/20.92 | |
% 141.52/20.92 | | Case 1:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (15) all_56_8 = e1 & op(e1, e0) = e1
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (15) implies:
% 141.52/20.92 | | | (16) op(e1, e0) = e1
% 141.52/20.92 | | |
% 141.52/20.92 | | | REF_CLOSE: (1), (7), (10), (16) are inconsistent by sub-proof #459.
% 141.52/20.92 | | |
% 141.52/20.92 | | Case 2:
% 141.52/20.92 | | |
% 141.52/20.92 | | | (17) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.52/20.92 | | |
% 141.52/20.92 | | | ALPHA: (17) implies:
% 141.52/20.92 | | | (18) ~ (all_56_13 = e0)
% 141.52/20.92 | | |
% 141.52/20.92 | | | REF_CLOSE: (3), (4), (7), (8), (9), (18) are inconsistent by sub-proof
% 141.52/20.92 | | | #420.
% 141.52/20.92 | | |
% 141.52/20.92 | | End of split
% 141.52/20.92 | |
% 141.52/20.92 | End of split
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #341 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.92 (2) op(e1, e2) = all_52_6
% 141.52/20.92 (3) op(e1, e2) = e1
% 141.52/20.92 (4) ~ (all_52_6 = e1)
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | GROUND_INST: instantiating (1) with all_52_6, e1, e2, e1, simplifying with
% 141.52/20.92 | (2), (3) gives:
% 141.52/20.92 | (5) all_52_6 = e1
% 141.52/20.92 |
% 141.52/20.92 | REDUCE: (4), (5) imply:
% 141.52/20.92 | (6) $false
% 141.52/20.92 |
% 141.52/20.92 | CLOSE: (6) is inconsistent.
% 141.52/20.92 |
% 141.52/20.92 End of proof
% 141.52/20.92
% 141.52/20.92 Sub-proof #342 shows that the following formulas are inconsistent:
% 141.52/20.92 ----------------------------------------------------------------
% 141.52/20.92 (1) op(e2, e0) = e3
% 141.52/20.92 (2) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) = all_16_1
% 141.52/20.92 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0) =
% 141.52/20.92 all_16_1 & $i(all_16_1))
% 141.52/20.92 (3) op(e3, e2) = e1
% 141.52/20.92 (4) op(e2, e0) = all_18_1
% 141.52/20.92 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.92 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.92
% 141.52/20.92 Begin of proof
% 141.52/20.92 |
% 141.52/20.92 | BETA: splitting (2) gives:
% 141.52/20.92 |
% 141.52/20.92 | Case 1:
% 141.52/20.92 | |
% 141.52/20.92 | | (6) ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 141.52/20.92 | | all_16_1 & $i(all_16_0) & $i(all_16_1)
% 141.52/20.92 | |
% 141.52/20.92 | | ALPHA: (6) implies:
% 141.52/20.92 | | (7) ~ (all_16_0 = e1)
% 141.52/20.92 | | (8) op(e2, e0) = all_16_1
% 141.52/20.92 | | (9) op(all_16_1, e2) = all_16_0
% 141.52/20.92 | |
% 141.52/20.92 | | GROUND_INST: instantiating (5) with e3, all_18_1, e0, e2, simplifying with
% 141.52/20.92 | | (1), (4) gives:
% 141.52/20.92 | | (10) all_18_1 = e3
% 141.52/20.92 | |
% 141.52/20.93 | | GROUND_INST: instantiating (5) with all_16_1, all_18_1, e0, e2, simplifying
% 141.52/20.93 | | with (4), (8) gives:
% 141.52/20.93 | | (11) all_18_1 = all_16_1
% 141.52/20.93 | |
% 141.52/20.93 | | COMBINE_EQS: (10), (11) imply:
% 141.52/20.93 | | (12) all_16_1 = e3
% 141.52/20.93 | |
% 141.52/20.93 | | SIMP: (12) implies:
% 141.52/20.93 | | (13) all_16_1 = e3
% 141.52/20.93 | |
% 141.52/20.93 | | REDUCE: (9), (13) imply:
% 141.52/20.93 | | (14) op(e3, e2) = all_16_0
% 141.52/20.93 | |
% 141.52/20.93 | | GROUND_INST: instantiating (5) with e1, all_16_0, e2, e3, simplifying with
% 141.52/20.93 | | (3), (14) gives:
% 141.52/20.93 | | (15) all_16_0 = e1
% 141.52/20.93 | |
% 141.52/20.93 | | REDUCE: (7), (15) imply:
% 141.52/20.93 | | (16) $false
% 141.52/20.93 | |
% 141.52/20.93 | | CLOSE: (16) is inconsistent.
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (17) ~ (all_16_1 = e3) & op(e2, e0) = all_16_1 & $i(all_16_1)
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (17) implies:
% 141.52/20.93 | | (18) ~ (all_16_1 = e3)
% 141.52/20.93 | | (19) op(e2, e0) = all_16_1
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (1), (4), (5), (18), (19) are inconsistent by sub-proof #343.
% 141.52/20.93 | |
% 141.52/20.93 | End of split
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #343 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) op(e2, e0) = e3
% 141.52/20.93 (2) ~ (all_16_1 = e3)
% 141.52/20.93 (3) op(e2, e0) = all_18_1
% 141.52/20.93 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (5) op(e2, e0) = all_16_1
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | GROUND_INST: instantiating (4) with all_16_1, all_18_1, e0, e2, simplifying
% 141.52/20.93 | with (3), (5) gives:
% 141.52/20.93 | (6) all_18_1 = all_16_1
% 141.52/20.93 |
% 141.52/20.93 | GROUND_INST: instantiating (4) with e3, all_18_1, e0, e2, simplifying with
% 141.52/20.93 | (1), (3) gives:
% 141.52/20.93 | (7) all_18_1 = e3
% 141.52/20.93 |
% 141.52/20.93 | COMBINE_EQS: (6), (7) imply:
% 141.52/20.93 | (8) all_16_1 = e3
% 141.52/20.93 |
% 141.52/20.93 | SIMP: (8) implies:
% 141.52/20.93 | (9) all_16_1 = e3
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (2), (9) imply:
% 141.52/20.93 | (10) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (10) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #344 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) ~ (all_52_4 = all_52_7)
% 141.52/20.93 (2) ~ (all_52_7 = e1)
% 141.52/20.93 (3) op(e1, e2) = all_52_6
% 141.52/20.93 (4) all_54_13 = all_52_7
% 141.52/20.93 (5) ~ (all_52_4 = all_52_6)
% 141.52/20.93 (6) op(e3, e3) = e2
% 141.52/20.93 (7) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 141.52/20.93 all_56_7 & $i(all_56_7))
% 141.52/20.93 (8) op(e1, e1) = all_4_2
% 141.52/20.93 (9) all_54_9 = all_52_6
% 141.52/20.93 (10) ~ (all_52_6 = all_52_7)
% 141.52/20.93 (11) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.52/20.93 (12) op(e3, e2) = all_52_4
% 141.52/20.93 (13) ~ (all_4_2 = e2)
% 141.52/20.93 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (15) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.52/20.93 (16) op(e0, e2) = all_52_7
% 141.52/20.93 (17) op(e0, e2) = all_56_12
% 141.52/20.93 (18) ~ (all_52_6 = e0)
% 141.52/20.93 (19) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.52/20.93 all_56_9 & $i(all_56_9))
% 141.52/20.93 (20) ~ (all_56_12 = e0)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | BETA: splitting (19) gives:
% 141.52/20.93 |
% 141.52/20.93 | Case 1:
% 141.52/20.93 | |
% 141.52/20.93 | | (21) all_56_0 = e3 & op(e3, e2) = e3
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (21) implies:
% 141.52/20.93 | | (22) op(e3, e2) = e3
% 141.52/20.93 | |
% 141.52/20.93 | | BETA: splitting (7) gives:
% 141.52/20.93 | |
% 141.52/20.93 | | Case 1:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (23) all_56_13 = e2 & op(e1, e1) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | ALPHA: (23) implies:
% 141.52/20.93 | | | (24) op(e1, e1) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (8), (13), (14), (24) are inconsistent by sub-proof #1124.
% 141.52/20.93 | | |
% 141.52/20.93 | | Case 2:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (25) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)
% 141.52/20.93 | | |
% 141.52/20.93 | | | ALPHA: (25) implies:
% 141.52/20.93 | | | (26) ~ (all_56_7 = e1)
% 141.52/20.93 | | | (27) op(e1, e2) = all_56_7
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (1), (2), (3), (4), (5), (9), (10), (11), (12), (14), (15),
% 141.52/20.93 | | | (16), (17), (18), (20), (22), (26), (27) are inconsistent by
% 141.52/20.93 | | | sub-proof #361.
% 141.52/20.93 | | |
% 141.52/20.93 | | End of split
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (28) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (28) implies:
% 141.52/20.93 | | (29) ~ (all_56_9 = e2)
% 141.52/20.93 | | (30) op(e3, e3) = all_56_9
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (6), (14), (29), (30) are inconsistent by sub-proof #391.
% 141.52/20.93 | |
% 141.52/20.93 | End of split
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #345 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_56_9 = e2
% 141.52/20.93 (2) ~ (all_52_4 = e3)
% 141.52/20.93 (3) op(e3, e2) = all_52_4
% 141.52/20.93 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (5) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.52/20.93 all_56_9 & $i(all_56_9))
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | BETA: splitting (5) gives:
% 141.52/20.93 |
% 141.52/20.93 | Case 1:
% 141.52/20.93 | |
% 141.52/20.93 | | (6) all_56_0 = e3 & op(e3, e2) = e3
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (6) implies:
% 141.52/20.93 | | (7) op(e3, e2) = e3
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1107.
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (8) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (8) implies:
% 141.52/20.93 | | (9) ~ (all_56_9 = e2)
% 141.52/20.93 | |
% 141.52/20.93 | | REDUCE: (1), (9) imply:
% 141.52/20.93 | | (10) $false
% 141.52/20.93 | |
% 141.52/20.93 | | CLOSE: (10) is inconsistent.
% 141.52/20.93 | |
% 141.52/20.93 | End of split
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #346 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 141.52/20.93 all_56_10 & $i(all_56_10))
% 141.52/20.93 (2) op(e0, e0) = e1
% 141.52/20.93 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (4) ~ (e3 = e1)
% 141.52/20.93 (5) op(e0, e3) = e0
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | BETA: splitting (1) gives:
% 141.52/20.93 |
% 141.52/20.93 | Case 1:
% 141.52/20.93 | |
% 141.52/20.93 | | (6) all_56_15 = e3 & op(e0, e0) = e3
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (6) implies:
% 141.52/20.93 | | (7) op(e0, e0) = e3
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #732.
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (8) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.93 | |
% 141.52/20.93 | | ALPHA: (8) implies:
% 141.52/20.93 | | (9) ~ (all_56_10 = e0)
% 141.52/20.93 | | (10) op(e0, e3) = all_56_10
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #954.
% 141.52/20.93 | |
% 141.52/20.93 | End of split
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #347 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_57_14 = e1 & op(e0, e1) = e1
% 141.52/20.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (3) op(e0, e1) = all_52_11
% 141.52/20.93 (4) ~ (all_52_11 = e1)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | ALPHA: (1) implies:
% 141.52/20.93 | (5) op(e0, e1) = e1
% 141.52/20.93 |
% 141.52/20.93 | GROUND_INST: instantiating (2) with all_52_11, e1, e1, e0, simplifying with
% 141.52/20.93 | (3), (5) gives:
% 141.52/20.93 | (6) all_52_11 = e1
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (4), (6) imply:
% 141.52/20.93 | (7) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (7) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #348 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_57_5 = e1 & op(e2, e1) = e1
% 141.52/20.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (3) op(e2, e1) = all_52_9
% 141.52/20.93 (4) ~ (all_52_9 = e1)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | ALPHA: (1) implies:
% 141.52/20.93 | (5) op(e2, e1) = e1
% 141.52/20.93 |
% 141.52/20.93 | GROUND_INST: instantiating (2) with all_52_9, e1, e1, e2, simplifying with
% 141.52/20.93 | (3), (5) gives:
% 141.52/20.93 | (6) all_52_9 = e1
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (4), (6) imply:
% 141.52/20.93 | (7) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (7) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #349 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_57_4 = e1 & op(e3, e1) = e1
% 141.52/20.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (3) op(e3, e1) = all_52_8
% 141.52/20.93 (4) ~ (all_52_8 = e1)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | ALPHA: (1) implies:
% 141.52/20.93 | (5) op(e3, e1) = e1
% 141.52/20.93 |
% 141.52/20.93 | GROUND_INST: instantiating (2) with all_52_8, e1, e1, e3, simplifying with
% 141.52/20.93 | (3), (5) gives:
% 141.52/20.93 | (6) all_52_8 = e1
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (4), (6) imply:
% 141.52/20.93 | (7) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (7) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #350 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_57_12 = e1 & op(e0, e3) = e1
% 141.52/20.93 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (3) op(e0, e3) = all_52_3
% 141.52/20.93 (4) ~ (all_52_3 = e1)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | ALPHA: (1) implies:
% 141.52/20.93 | (5) op(e0, e3) = e1
% 141.52/20.93 |
% 141.52/20.93 | GROUND_INST: instantiating (2) with all_52_3, e1, e3, e0, simplifying with
% 141.52/20.93 | (3), (5) gives:
% 141.52/20.93 | (6) all_52_3 = e1
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (4), (6) imply:
% 141.52/20.93 | (7) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (7) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #351 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_57_10 = e3 & op(e2, e0) = e3
% 141.52/20.93 (2) all_57_10 = e0
% 141.52/20.93 (3) ~ (e3 = e0)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | ALPHA: (1) implies:
% 141.52/20.93 | (4) all_57_10 = e3
% 141.52/20.93 |
% 141.52/20.93 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.93 | (5) e3 = e0
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (3), (5) imply:
% 141.52/20.93 | (6) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (6) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #352 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.52/20.93 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.52/20.93 (2) ~ (e2 = e1)
% 141.52/20.93 (3) ~ (all_56_9 = e2)
% 141.52/20.93 (4) ~ (e2 = e0)
% 141.52/20.93 (5) ~ (e3 = e2)
% 141.52/20.93 (6) all_57_9 = e3
% 141.52/20.93 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (8) all_57_4 = e1
% 141.52/20.93 (9) all_57_1 = e0
% 141.52/20.93 (10) op(e3, e3) = all_56_9
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | BETA: splitting (1) gives:
% 141.52/20.93 |
% 141.52/20.93 | Case 1:
% 141.52/20.93 | |
% 141.52/20.93 | | (11) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 141.52/20.93 | | e2)
% 141.52/20.93 | |
% 141.52/20.93 | | BETA: splitting (11) gives:
% 141.52/20.93 | |
% 141.52/20.93 | | Case 1:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (12) all_57_0 = e2 & op(e3, e3) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | ALPHA: (12) implies:
% 141.52/20.93 | | | (13) op(e3, e3) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (3), (7), (10), (13) are inconsistent by sub-proof #391.
% 141.52/20.93 | | |
% 141.52/20.93 | | Case 2:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (14) all_57_1 = e2 & op(e3, e2) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (4), (9), (14) are inconsistent by sub-proof #353.
% 141.52/20.93 | | |
% 141.52/20.93 | | End of split
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (15) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 141.52/20.93 | | e2)
% 141.52/20.93 | |
% 141.52/20.93 | | BETA: splitting (15) gives:
% 141.52/20.93 | |
% 141.52/20.93 | | Case 1:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (16) all_57_4 = e2 & op(e3, e1) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (2), (8), (16) are inconsistent by sub-proof #1109.
% 141.52/20.93 | | |
% 141.52/20.93 | | Case 2:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (17) all_57_9 = e2 & op(e3, e0) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | ALPHA: (17) implies:
% 141.52/20.93 | | | (18) all_57_9 = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #581.
% 141.52/20.93 | | |
% 141.52/20.93 | | End of split
% 141.52/20.93 | |
% 141.52/20.93 | End of split
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #353 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) all_57_1 = e2 & op(e3, e2) = e2
% 141.52/20.93 (2) all_57_1 = e0
% 141.52/20.93 (3) ~ (e2 = e0)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | ALPHA: (1) implies:
% 141.52/20.93 | (4) all_57_1 = e2
% 141.52/20.93 |
% 141.52/20.93 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.93 | (5) e2 = e0
% 141.52/20.93 |
% 141.52/20.93 | SIMP: (5) implies:
% 141.52/20.93 | (6) e2 = e0
% 141.52/20.93 |
% 141.52/20.93 | REDUCE: (3), (6) imply:
% 141.52/20.93 | (7) $false
% 141.52/20.93 |
% 141.52/20.93 | CLOSE: (7) is inconsistent.
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #354 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.93 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.52/20.93 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.93 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.93 (3) op(e1, e2) = all_52_6
% 141.52/20.93 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.93 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/20.93 (5) ~ (e2 = e1)
% 141.52/20.93 (6) ~ (all_52_4 = e1)
% 141.52/20.93 (7) ~ (all_52_7 = e0)
% 141.52/20.93 (8) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.93 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.93 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.93 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.93 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.93 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.93 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.93 (9) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/20.93 (10) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.93 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.93 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.93 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.93 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.93 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.93 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.93 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.93 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.93 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.93 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.93 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.93 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.93 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.93 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.93 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.93 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.93 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.93 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.93 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.93 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.93 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.93 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.93 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.93 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.93 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.93 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.93 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.93 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.93 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.93 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.93 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.93 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.93 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.93 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.93 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.93 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.93 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.93 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.93 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.93 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.93 (11) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.52/20.93 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.93 (12) ~ (all_52_8 = all_4_2)
% 141.52/20.93 (13) all_57_15 = e1
% 141.52/20.93 (14) ~ (all_52_1 = e1)
% 141.52/20.93 (15) ~ (e3 = e0)
% 141.52/20.93 (16) op(e1, e1) = all_4_2
% 141.52/20.93 (17) op(e3, e1) = all_52_8
% 141.52/20.93 (18) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.93 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.93 e2)
% 141.52/20.93 (19) op(e0, e0) = e1
% 141.52/20.93 (20) op(e2, e3) = all_52_1
% 141.52/20.93 (21) ~ (all_52_6 = all_52_14)
% 141.52/20.93 (22) ~ (all_4_2 = e3)
% 141.52/20.93 (23) ~ (e1 = e0)
% 141.52/20.93 (24) op(e3, e2) = all_52_4
% 141.52/20.93 (25) ~ (e2 = e0)
% 141.52/20.93 (26) ~ (e3 = e2)
% 141.52/20.93 (27) op(e0, e1) = all_52_11
% 141.52/20.93 (28) ~ (all_52_9 = all_4_2)
% 141.52/20.93 (29) ~ (all_4_2 = e2)
% 141.52/20.93 (30) all_54_10 = all_4_2
% 141.52/20.93 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (32) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.93 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.93 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.93 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.93 (33) ~ (all_52_11 = all_4_2)
% 141.52/20.93 (34) ~ (e3 = e1)
% 141.52/20.93 (35) op(e0, e2) = all_52_7
% 141.52/20.93 (36) op(e0, e0) = all_56_15
% 141.52/20.93 (37) op(e2, e2) = e0
% 141.52/20.93 (38) all_56_15 = e1
% 141.52/20.93 (39) op(e2, e1) = all_52_9
% 141.52/20.93 (40) ~ (all_52_13 = e1)
% 141.52/20.93 (41) op(e2, e0) = all_52_13
% 141.52/20.93 (42) op(e1, e0) = all_52_14
% 141.52/20.93 (43) ~ (all_52_9 = e0)
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | BETA: splitting (4) gives:
% 141.52/20.93 |
% 141.52/20.93 | Case 1:
% 141.52/20.93 | |
% 141.52/20.93 | | (44) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 141.52/20.93 | | e1)
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (14), (20), (23), (31), (37), (44) are inconsistent by sub-proof
% 141.52/20.93 | | #845.
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (45) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 141.52/20.93 | | e1)
% 141.52/20.93 | |
% 141.52/20.93 | | BETA: splitting (45) gives:
% 141.52/20.93 | |
% 141.52/20.93 | | Case 1:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (46) all_57_5 = e1 & op(e2, e1) = e1
% 141.52/20.93 | | |
% 141.52/20.93 | | | ALPHA: (46) implies:
% 141.52/20.93 | | | (47) op(e2, e1) = e1
% 141.52/20.93 | | |
% 141.52/20.93 | | | BETA: splitting (1) gives:
% 141.52/20.93 | | |
% 141.52/20.93 | | | Case 1:
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | (48) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 141.52/20.93 | | | | = e1)
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | REF_CLOSE: (6), (23), (24), (31), (37), (48) are inconsistent by
% 141.52/20.93 | | | | sub-proof #843.
% 141.52/20.93 | | | |
% 141.52/20.93 | | | Case 2:
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | (49) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 141.52/20.93 | | | | = e1)
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | BETA: splitting (49) gives:
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | Case 1:
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | (50) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | ALPHA: (50) implies:
% 141.52/20.93 | | | | | (51) op(e1, e2) = e1
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | GROUND_INST: instantiating (31) with all_52_6, e1, e2, e1, simplifying
% 141.52/20.93 | | | | | with (3), (51) gives:
% 141.52/20.93 | | | | | (52) all_52_6 = e1
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | GROUND_INST: instantiating (31) with all_52_9, e1, e1, e2, simplifying
% 141.52/20.93 | | | | | with (39), (47) gives:
% 141.52/20.93 | | | | | (53) all_52_9 = e1
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | REDUCE: (21), (52) imply:
% 141.52/20.93 | | | | | (54) ~ (all_52_14 = e1)
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | SIMP: (54) implies:
% 141.52/20.93 | | | | | (55) ~ (all_52_14 = e1)
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | REDUCE: (28), (53) imply:
% 141.52/20.93 | | | | | (56) ~ (all_4_2 = e1)
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | SIMP: (56) implies:
% 141.52/20.93 | | | | | (57) ~ (all_4_2 = e1)
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | BETA: splitting (9) gives:
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | Case 1:
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | | (58) all_54_10 = e3
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | | REF_CLOSE: (22), (30), (58) are inconsistent by sub-proof #1112.
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | Case 2:
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | | (59) ~ (all_54_10 = e3)
% 141.52/20.93 | | | | | | (60) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | | BETA: splitting (60) gives:
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | | Case 1:
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | | (61) all_54_10 = e2
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | | REF_CLOSE: (29), (30), (61) are inconsistent by sub-proof #1111.
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | Case 2:
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | | (62) ~ (all_54_10 = e2)
% 141.52/20.93 | | | | | | | (63) all_54_10 = e1 | all_54_10 = e0
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | | BETA: splitting (63) gives:
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | | Case 1:
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | (64) all_54_10 = e1
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | REF_CLOSE: (30), (57), (64) are inconsistent by sub-proof #378.
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | Case 2:
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | (65) all_54_10 = e0
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | COMBINE_EQS: (30), (65) imply:
% 141.52/20.93 | | | | | | | | (66) all_4_2 = e0
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | SIMP: (66) implies:
% 141.52/20.93 | | | | | | | | (67) all_4_2 = e0
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | REDUCE: (12), (67) imply:
% 141.52/20.93 | | | | | | | | (68) ~ (all_52_8 = e0)
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | REDUCE: (33), (67) imply:
% 141.52/20.93 | | | | | | | | (69) ~ (all_52_11 = e0)
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | REDUCE: (57), (67) imply:
% 141.52/20.93 | | | | | | | | (70) ~ (e1 = e0)
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | | REF_CLOSE: (5), (7), (8), (10), (11), (16), (17), (19), (22),
% 141.52/20.93 | | | | | | | | (23), (27), (29), (31), (32), (34), (35), (36), (38),
% 141.52/20.93 | | | | | | | | (39), (42), (43), (51), (55), (68), (69) are
% 141.52/20.93 | | | | | | | | inconsistent by sub-proof #419.
% 141.52/20.93 | | | | | | | |
% 141.52/20.93 | | | | | | | End of split
% 141.52/20.93 | | | | | | |
% 141.52/20.93 | | | | | | End of split
% 141.52/20.93 | | | | | |
% 141.52/20.93 | | | | | End of split
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | Case 2:
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | (71) all_57_13 = e1 & op(e0, e2) = e1
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | ALPHA: (71) implies:
% 141.52/20.93 | | | | | (72) all_57_13 = e1
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | | REF_CLOSE: (2), (5), (7), (13), (15), (18), (19), (23), (25), (26),
% 141.52/20.93 | | | | | (31), (32), (34), (35), (72) are inconsistent by sub-proof
% 141.52/20.93 | | | | | #355.
% 141.52/20.93 | | | | |
% 141.52/20.93 | | | | End of split
% 141.52/20.93 | | | |
% 141.52/20.93 | | | End of split
% 141.52/20.93 | | |
% 141.52/20.93 | | Case 2:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (73) all_57_10 = e1 & op(e2, e0) = e1
% 141.52/20.93 | | |
% 141.52/20.93 | | | REF_CLOSE: (31), (40), (41), (73) are inconsistent by sub-proof #460.
% 141.52/20.93 | | |
% 141.52/20.93 | | End of split
% 141.52/20.93 | |
% 141.52/20.93 | End of split
% 141.52/20.93 |
% 141.52/20.93 End of proof
% 141.52/20.93
% 141.52/20.93 Sub-proof #355 shows that the following formulas are inconsistent:
% 141.52/20.93 ----------------------------------------------------------------
% 141.52/20.93 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.93 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.93 (2) ~ (e2 = e1)
% 141.52/20.93 (3) ~ (all_52_7 = e0)
% 141.52/20.93 (4) all_57_15 = e1
% 141.52/20.93 (5) ~ (e3 = e0)
% 141.52/20.93 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.52/20.93 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.93 (7) op(e0, e0) = e1
% 141.52/20.93 (8) ~ (e1 = e0)
% 141.52/20.93 (9) all_57_13 = e1
% 141.52/20.93 (10) ~ (e2 = e0)
% 141.52/20.93 (11) ~ (e3 = e2)
% 141.52/20.93 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.93 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.93 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.93 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.93 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.93 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.93 (14) ~ (e3 = e1)
% 141.52/20.93 (15) op(e0, e2) = all_52_7
% 141.52/20.93
% 141.52/20.93 Begin of proof
% 141.52/20.93 |
% 141.52/20.93 | BETA: splitting (6) gives:
% 141.52/20.93 |
% 141.52/20.93 | Case 1:
% 141.52/20.93 | |
% 141.52/20.93 | | (16) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 141.52/20.93 | | e2)
% 141.52/20.93 | |
% 141.52/20.93 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 141.52/20.93 | | (14), (15), (16) are inconsistent by sub-proof #357.
% 141.52/20.93 | |
% 141.52/20.93 | Case 2:
% 141.52/20.93 | |
% 141.52/20.93 | | (17) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.93 | | e2)
% 141.52/20.93 | |
% 141.52/20.93 | | BETA: splitting (17) gives:
% 141.52/20.93 | |
% 141.52/20.93 | | Case 1:
% 141.52/20.93 | | |
% 141.52/20.93 | | | (18) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | ALPHA: (18) implies:
% 141.52/20.93 | | | (19) all_57_14 = e2
% 141.52/20.93 | | |
% 141.52/20.93 | | | BETA: splitting (13) gives:
% 141.52/20.93 | | |
% 141.52/20.93 | | | Case 1:
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | (20) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.93 | | | |
% 141.52/20.93 | | | | REF_CLOSE: (4), (8), (20) are inconsistent by sub-proof #358.
% 141.52/20.93 | | | |
% 141.52/20.93 | | | Case 2:
% 141.52/20.93 | | | |
% 141.52/20.94 | | | | (21) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 141.52/20.94 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 141.52/20.94 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.94 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | ALPHA: (21) implies:
% 141.52/20.94 | | | | (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.94 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | BETA: splitting (22) gives:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | Case 1:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (23) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | ALPHA: (23) implies:
% 141.52/20.94 | | | | | (24) all_57_12 = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 141.52/20.94 | | | | | (12), (13), (14), (15), (24) are inconsistent by sub-proof
% 141.52/20.94 | | | | | #356.
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | Case 2:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (25) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 141.52/20.94 | | | | | e1) = e0)
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | REF_CLOSE: (3), (10), (12), (15), (19), (25) are inconsistent by
% 141.52/20.94 | | | | | sub-proof #653.
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | End of split
% 141.52/20.94 | | | |
% 141.52/20.94 | | | End of split
% 141.52/20.94 | | |
% 141.52/20.94 | | Case 2:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (26) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | ALPHA: (26) implies:
% 141.52/20.94 | | | (27) op(e0, e0) = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (2), (7), (12), (27) are inconsistent by sub-proof #1070.
% 141.52/20.94 | | |
% 141.52/20.94 | | End of split
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #356 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.94 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.94 (2) ~ (e2 = e1)
% 141.52/20.94 (3) ~ (all_52_7 = e0)
% 141.52/20.94 (4) all_57_15 = e1
% 141.52/20.94 (5) ~ (e3 = e0)
% 141.52/20.94 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.52/20.94 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.94 (7) op(e0, e0) = e1
% 141.52/20.94 (8) ~ (e1 = e0)
% 141.52/20.94 (9) all_57_13 = e1
% 141.52/20.94 (10) ~ (e2 = e0)
% 141.52/20.94 (11) ~ (e3 = e2)
% 141.52/20.94 (12) all_57_12 = e0
% 141.52/20.94 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.94 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.94 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.94 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.94 (15) ~ (e3 = e1)
% 141.52/20.94 (16) op(e0, e2) = all_52_7
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (6) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (17) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 141.52/20.94 | | e2)
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (13), (14),
% 141.52/20.94 | | (15), (16), (17) are inconsistent by sub-proof #357.
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (18) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.94 | | e2)
% 141.52/20.94 | |
% 141.52/20.94 | | BETA: splitting (18) gives:
% 141.52/20.94 | |
% 141.52/20.94 | | Case 1:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (19) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | ALPHA: (19) implies:
% 141.52/20.94 | | | (20) all_57_14 = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (1), (5), (7), (9), (11), (12), (13), (15), (20) are
% 141.52/20.94 | | | inconsistent by sub-proof #412.
% 141.52/20.94 | | |
% 141.52/20.94 | | Case 2:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (21) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | ALPHA: (21) implies:
% 141.52/20.94 | | | (22) op(e0, e0) = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (2), (7), (13), (22) are inconsistent by sub-proof #1070.
% 141.52/20.94 | | |
% 141.52/20.94 | | End of split
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #357 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.94 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.94 (2) ~ (e2 = e1)
% 141.52/20.94 (3) ~ (all_52_7 = e0)
% 141.52/20.94 (4) all_57_15 = e1
% 141.52/20.94 (5) ~ (e3 = e0)
% 141.52/20.94 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.94 (7) op(e0, e0) = e1
% 141.52/20.94 (8) ~ (e1 = e0)
% 141.52/20.94 (9) all_57_13 = e1
% 141.52/20.94 (10) ~ (e2 = e0)
% 141.52/20.94 (11) ~ (e3 = e2)
% 141.52/20.94 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.94 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.94 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.94 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.94 (14) ~ (e3 = e1)
% 141.52/20.94 (15) op(e0, e2) = all_52_7
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (6) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (16) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/20.94 | |
% 141.52/20.94 | | ALPHA: (16) implies:
% 141.52/20.94 | | (17) all_57_12 = e2
% 141.52/20.94 | |
% 141.52/20.94 | | BETA: splitting (13) gives:
% 141.52/20.94 | |
% 141.52/20.94 | | Case 1:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (18) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (4), (8), (18) are inconsistent by sub-proof #358.
% 141.52/20.94 | | |
% 141.52/20.94 | | Case 2:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (19) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0)
% 141.52/20.94 | | | = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0
% 141.52/20.94 | | | & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.52/20.94 | | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.52/20.94 | | |
% 141.52/20.94 | | | ALPHA: (19) implies:
% 141.52/20.94 | | | (20) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2)
% 141.52/20.94 | | | = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.94 | | |
% 141.52/20.94 | | | BETA: splitting (20) gives:
% 141.52/20.94 | | |
% 141.52/20.94 | | | Case 1:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | (21) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | REF_CLOSE: (10), (17), (21) are inconsistent by sub-proof #958.
% 141.52/20.94 | | | |
% 141.52/20.94 | | | Case 2:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | (22) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 141.52/20.94 | | | | e1) = e0)
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | BETA: splitting (22) gives:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | Case 1:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (23) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | ALPHA: (23) implies:
% 141.52/20.94 | | | | | (24) op(e0, e2) = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | REF_CLOSE: (3), (12), (15), (24) are inconsistent by sub-proof #977.
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | Case 2:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (25) all_57_14 = e0 & op(e0, e1) = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | ALPHA: (25) implies:
% 141.52/20.94 | | | | | (26) all_57_14 = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | BETA: splitting (1) gives:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | Case 1:
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | (27) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 141.52/20.94 | | | | | | op(e0, e2) = e3)
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | BETA: splitting (27) gives:
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | Case 1:
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | (28) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | REF_CLOSE: (11), (17), (28) are inconsistent by sub-proof #780.
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | Case 2:
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | (29) all_57_13 = e3 & op(e0, e2) = e3
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | REF_CLOSE: (9), (14), (29) are inconsistent by sub-proof #414.
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | End of split
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | Case 2:
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | (30) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 &
% 141.52/20.94 | | | | | | op(e0, e0) = e3)
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | BETA: splitting (30) gives:
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | Case 1:
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | (31) all_57_14 = e3 & op(e0, e1) = e3
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | REF_CLOSE: (5), (26), (31) are inconsistent by sub-proof #777.
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | Case 2:
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | (32) all_57_15 = e3 & op(e0, e0) = e3
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | ALPHA: (32) implies:
% 141.52/20.94 | | | | | | | (33) op(e0, e0) = e3
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | | REF_CLOSE: (7), (12), (14), (33) are inconsistent by sub-proof
% 141.52/20.94 | | | | | | | #732.
% 141.52/20.94 | | | | | | |
% 141.52/20.94 | | | | | | End of split
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | End of split
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | End of split
% 141.52/20.94 | | | |
% 141.52/20.94 | | | End of split
% 141.52/20.94 | | |
% 141.52/20.94 | | End of split
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (34) all_57_13 = e2 & op(e0, e2) = e2
% 141.52/20.94 | |
% 141.52/20.94 | | ALPHA: (34) implies:
% 141.52/20.94 | | (35) all_57_13 = e2
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (2), (9), (35) are inconsistent by sub-proof #1057.
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #358 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.94 (2) all_57_15 = e1
% 141.52/20.94 (3) ~ (e1 = e0)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | ALPHA: (1) implies:
% 141.52/20.94 | (4) all_57_15 = e0
% 141.52/20.94 |
% 141.52/20.94 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.94 | (5) e1 = e0
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (3), (5) imply:
% 141.52/20.94 | (6) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (6) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #359 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) op(e2, e1) = e3
% 141.52/20.94 (2) ( ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) = all_20_1
% 141.52/20.94 & $i(all_20_0) & $i(all_20_1)) | ( ~ (all_20_1 = e0) & op(e2, e1) =
% 141.52/20.94 all_20_1 & $i(all_20_1))
% 141.52/20.94 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (4) ~ (all_38_1 = e3)
% 141.52/20.94 (5) op(e2, e1) = all_38_1
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (2) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (6) ~ (all_20_0 = e3) & op(all_20_1, e2) = all_20_0 & op(e2, e1) =
% 141.52/20.94 | | all_20_1 & $i(all_20_0) & $i(all_20_1)
% 141.52/20.94 | |
% 141.52/20.94 | | ALPHA: (6) implies:
% 141.52/20.94 | | (7) op(e2, e1) = all_20_1
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (1), (3), (4), (5), (7) are inconsistent by sub-proof #360.
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (8) ~ (all_20_1 = e0) & op(e2, e1) = all_20_1 & $i(all_20_1)
% 141.52/20.94 | |
% 141.52/20.94 | | ALPHA: (8) implies:
% 141.52/20.94 | | (9) op(e2, e1) = all_20_1
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (1), (3), (4), (5), (9) are inconsistent by sub-proof #360.
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #360 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) op(e2, e1) = e3
% 141.52/20.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (3) ~ (all_38_1 = e3)
% 141.52/20.94 (4) op(e2, e1) = all_38_1
% 141.52/20.94 (5) op(e2, e1) = all_20_1
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (2) with all_20_1, all_38_1, e1, e2, simplifying
% 141.52/20.94 | with (4), (5) gives:
% 141.52/20.94 | (6) all_38_1 = all_20_1
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (2) with e3, all_38_1, e1, e2, simplifying with
% 141.52/20.94 | (1), (4) gives:
% 141.52/20.94 | (7) all_38_1 = e3
% 141.52/20.94 |
% 141.52/20.94 | COMBINE_EQS: (6), (7) imply:
% 141.52/20.94 | (8) all_20_1 = e3
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (3), (7) imply:
% 141.52/20.94 | (9) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (9) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #361 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) ~ (all_52_4 = all_52_7)
% 141.52/20.94 (2) ~ (all_52_7 = e1)
% 141.52/20.94 (3) op(e1, e2) = all_52_6
% 141.52/20.94 (4) all_54_13 = all_52_7
% 141.52/20.94 (5) ~ (all_52_4 = all_52_6)
% 141.52/20.94 (6) all_54_9 = all_52_6
% 141.52/20.94 (7) ~ (all_52_6 = all_52_7)
% 141.52/20.94 (8) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.52/20.94 (9) op(e3, e2) = all_52_4
% 141.52/20.94 (10) ~ (all_56_7 = e1)
% 141.52/20.94 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (12) all_54_13 = e3 | all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.52/20.94 (13) op(e3, e2) = e3
% 141.52/20.94 (14) op(e0, e2) = all_52_7
% 141.52/20.94 (15) op(e0, e2) = all_56_12
% 141.52/20.94 (16) ~ (all_52_6 = e0)
% 141.52/20.94 (17) op(e1, e2) = all_56_7
% 141.52/20.94 (18) ~ (all_56_12 = e0)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (11) with all_52_7, all_56_12, e2, e0, simplifying
% 141.52/20.94 | with (14), (15) gives:
% 141.52/20.94 | (19) all_56_12 = all_52_7
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (11) with all_52_6, all_56_7, e2, e1, simplifying
% 141.52/20.94 | with (3), (17) gives:
% 141.52/20.94 | (20) all_56_7 = all_52_6
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (11) with all_52_4, e3, e2, e3, simplifying with
% 141.52/20.94 | (9), (13) gives:
% 141.52/20.94 | (21) all_52_4 = e3
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (10), (20) imply:
% 141.52/20.94 | (22) ~ (all_52_6 = e1)
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (18), (19) imply:
% 141.52/20.94 | (23) ~ (all_52_7 = e0)
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (5), (21) imply:
% 141.52/20.94 | (24) ~ (all_52_6 = e3)
% 141.52/20.94 |
% 141.52/20.94 | SIMP: (24) implies:
% 141.52/20.94 | (25) ~ (all_52_6 = e3)
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (1), (21) imply:
% 141.52/20.94 | (26) ~ (all_52_7 = e3)
% 141.52/20.94 |
% 141.52/20.94 | SIMP: (26) implies:
% 141.52/20.94 | (27) ~ (all_52_7 = e3)
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (12) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (28) all_54_13 = e3
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (4), (27), (28) are inconsistent by sub-proof #364.
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (29) all_54_13 = e2 | all_54_13 = e1 | all_54_13 = e0
% 141.52/20.94 | |
% 141.52/20.94 | | BETA: splitting (29) gives:
% 141.52/20.94 | |
% 141.52/20.94 | | Case 1:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (30) all_54_13 = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | COMBINE_EQS: (4), (30) imply:
% 141.52/20.94 | | | (31) all_52_7 = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | SIMP: (31) implies:
% 141.52/20.94 | | | (32) all_52_7 = e2
% 141.52/20.94 | | |
% 141.52/20.94 | | | REDUCE: (7), (32) imply:
% 141.52/20.94 | | | (33) ~ (all_52_6 = e2)
% 141.52/20.94 | | |
% 141.52/20.94 | | | BETA: splitting (8) gives:
% 141.52/20.94 | | |
% 141.52/20.94 | | | Case 1:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | (34) all_54_9 = e3
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | COMBINE_EQS: (6), (34) imply:
% 141.52/20.94 | | | | (35) all_52_6 = e3
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | SIMP: (35) implies:
% 141.52/20.94 | | | | (36) all_52_6 = e3
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | REDUCE: (25), (36) imply:
% 141.52/20.94 | | | | (37) $false
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | CLOSE: (37) is inconsistent.
% 141.52/20.94 | | | |
% 141.52/20.94 | | | Case 2:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | (38) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | BETA: splitting (38) gives:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | Case 1:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (39) all_54_9 = e2
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | COMBINE_EQS: (6), (39) imply:
% 141.52/20.94 | | | | | (40) all_52_6 = e2
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | SIMP: (40) implies:
% 141.52/20.94 | | | | | (41) all_52_6 = e2
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | REDUCE: (33), (41) imply:
% 141.52/20.94 | | | | | (42) $false
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | CLOSE: (42) is inconsistent.
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | Case 2:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (43) all_54_9 = e1 | all_54_9 = e0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | REF_CLOSE: (6), (16), (22), (43) are inconsistent by sub-proof #960.
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | End of split
% 141.52/20.94 | | | |
% 141.52/20.94 | | | End of split
% 141.52/20.94 | | |
% 141.52/20.94 | | Case 2:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (44) all_54_13 = e1 | all_54_13 = e0
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (2), (4), (23), (44) are inconsistent by sub-proof #362.
% 141.52/20.94 | | |
% 141.52/20.94 | | End of split
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #362 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) all_54_13 = e1 | all_54_13 = e0
% 141.52/20.94 (2) all_54_13 = all_52_7
% 141.52/20.94 (3) ~ (all_52_7 = e1)
% 141.52/20.94 (4) ~ (all_52_7 = e0)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (1) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (5) all_54_13 = e1
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #363.
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (6) all_54_13 = e0
% 141.52/20.94 | |
% 141.52/20.94 | | COMBINE_EQS: (2), (6) imply:
% 141.52/20.94 | | (7) all_52_7 = e0
% 141.52/20.94 | |
% 141.52/20.94 | | SIMP: (7) implies:
% 141.52/20.94 | | (8) all_52_7 = e0
% 141.52/20.94 | |
% 141.52/20.94 | | REDUCE: (4), (8) imply:
% 141.52/20.94 | | (9) $false
% 141.52/20.94 | |
% 141.52/20.94 | | CLOSE: (9) is inconsistent.
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #363 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) all_54_13 = all_52_7
% 141.52/20.94 (2) all_54_13 = e1
% 141.52/20.94 (3) ~ (all_52_7 = e1)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.94 | (4) all_52_7 = e1
% 141.52/20.94 |
% 141.52/20.94 | SIMP: (4) implies:
% 141.52/20.94 | (5) all_52_7 = e1
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (3), (5) imply:
% 141.52/20.94 | (6) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (6) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #364 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) all_54_13 = all_52_7
% 141.52/20.94 (2) all_54_13 = e3
% 141.52/20.94 (3) ~ (all_52_7 = e3)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.94 | (4) all_52_7 = e3
% 141.52/20.94 |
% 141.52/20.94 | SIMP: (4) implies:
% 141.52/20.94 | (5) all_52_7 = e3
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (3), (5) imply:
% 141.52/20.94 | (6) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (6) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #365 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (2) op(e3, e3) = all_14_2
% 141.52/20.94 (3) op(e3, e3) = e1
% 141.52/20.94 (4) ~ (all_14_2 = e1)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (1) with all_14_2, e1, e3, e3, simplifying with
% 141.52/20.94 | (2), (3) gives:
% 141.52/20.94 | (5) all_14_2 = e1
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (4), (5) imply:
% 141.52/20.94 | (6) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (6) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #366 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) all_57_13 = e1 & op(e0, e2) = e1
% 141.52/20.94 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (3) op(e0, e2) = all_52_7
% 141.52/20.94 (4) ~ (all_52_7 = e1)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | ALPHA: (1) implies:
% 141.52/20.94 | (5) op(e0, e2) = e1
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (2) with all_52_7, e1, e2, e0, simplifying with
% 141.52/20.94 | (3), (5) gives:
% 141.52/20.94 | (6) all_52_7 = e1
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (4), (6) imply:
% 141.52/20.94 | (7) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (7) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #367 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) ~ (e3 = e0)
% 141.52/20.94 (2) op(e0, e0) = e1
% 141.52/20.94 (3) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 141.52/20.94 (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/20.94 (4) all_57_11 = e2
% 141.52/20.94 (5) all_57_9 = e2
% 141.52/20.94 (6) ~ (e2 = e0)
% 141.52/20.94 (7) ~ (e3 = e2)
% 141.52/20.94 (8) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.94 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.94 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (10) ~ (e3 = e1)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (3) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (11) all_57_9 = e0 & op(e3, e0) = e0
% 141.52/20.94 | |
% 141.52/20.94 | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #368.
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (12) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 141.52/20.94 | | e0)
% 141.52/20.94 | |
% 141.52/20.94 | | BETA: splitting (12) gives:
% 141.52/20.94 | |
% 141.52/20.94 | | Case 1:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (13) all_57_10 = e0 & op(e2, e0) = e0
% 141.52/20.94 | | |
% 141.52/20.94 | | | ALPHA: (13) implies:
% 141.52/20.94 | | | (14) all_57_10 = e0
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (14) are inconsistent
% 141.52/20.94 | | | by sub-proof #392.
% 141.52/20.94 | | |
% 141.52/20.94 | | Case 2:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (15) all_57_11 = e0 & op(e1, e0) = e0
% 141.52/20.94 | | |
% 141.52/20.94 | | | REF_CLOSE: (4), (6), (15) are inconsistent by sub-proof #992.
% 141.52/20.94 | | |
% 141.52/20.94 | | End of split
% 141.52/20.94 | |
% 141.52/20.94 | End of split
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #368 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) all_57_9 = e0 & op(e3, e0) = e0
% 141.52/20.94 (2) all_57_9 = e2
% 141.52/20.94 (3) ~ (e2 = e0)
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | ALPHA: (1) implies:
% 141.52/20.94 | (4) all_57_9 = e0
% 141.52/20.94 |
% 141.52/20.94 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.94 | (5) e2 = e0
% 141.52/20.94 |
% 141.52/20.94 | REDUCE: (3), (5) imply:
% 141.52/20.94 | (6) $false
% 141.52/20.94 |
% 141.52/20.94 | CLOSE: (6) is inconsistent.
% 141.52/20.94 |
% 141.52/20.94 End of proof
% 141.52/20.94
% 141.52/20.94 Sub-proof #369 shows that the following formulas are inconsistent:
% 141.52/20.94 ----------------------------------------------------------------
% 141.52/20.94 (1) ~ (all_30_2 = e1) | ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 &
% 141.52/20.94 op(e0, e1) = all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 =
% 141.52/20.94 e2) & op(e0, e1) = all_30_1 & $i(all_30_1))
% 141.52/20.94 (2) op(e0, e1) = e3
% 141.52/20.94 (3) op(e3, e1) = e2
% 141.52/20.94 (4) op(e3, e1) = all_52_8
% 141.52/20.94 (5) ~ (all_34_2 = e1) | ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 &
% 141.52/20.94 op(e3, e1) = all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 =
% 141.52/20.94 e0) & op(e3, e1) = all_34_1 & $i(all_34_1))
% 141.52/20.94 (6) op(e2, e3) = all_52_1
% 141.52/20.94 (7) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0, e1) = all_10_1
% 141.52/20.94 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e3) & op(e0, e1) =
% 141.52/20.94 all_10_1 & $i(all_10_1))
% 141.52/20.94 (8) op(e2, e3) = e0
% 141.52/20.94 (9) ( ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 & op(e3, e1) = all_22_1
% 141.52/20.94 & $i(all_22_0) & $i(all_22_1)) | ( ~ (all_22_1 = e2) & op(e3, e1) =
% 141.52/20.94 all_22_1 & $i(all_22_1))
% 141.52/20.94 (10) op(e0, e1) = all_52_11
% 141.52/20.94 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.94 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.94 (12) all_30_2 = e1
% 141.52/20.94 (13) all_34_2 = e1
% 141.52/20.94
% 141.52/20.94 Begin of proof
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (11) with all_52_11, e3, e1, e0, simplifying with
% 141.52/20.94 | (2), (10) gives:
% 141.52/20.94 | (14) all_52_11 = e3
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (11) with all_52_1, e0, e3, e2, simplifying with
% 141.52/20.94 | (6), (8) gives:
% 141.52/20.94 | (15) all_52_1 = e0
% 141.52/20.94 |
% 141.52/20.94 | GROUND_INST: instantiating (11) with all_52_8, e2, e1, e3, simplifying with
% 141.52/20.94 | (3), (4) gives:
% 141.52/20.94 | (16) all_52_8 = e2
% 141.52/20.94 |
% 141.52/20.94 | BETA: splitting (1) gives:
% 141.52/20.94 |
% 141.52/20.94 | Case 1:
% 141.52/20.94 | |
% 141.52/20.94 | | (17) ~ (all_30_2 = e1)
% 141.52/20.94 | |
% 141.52/20.94 | | REDUCE: (12), (17) imply:
% 141.52/20.94 | | (18) $false
% 141.52/20.94 | |
% 141.52/20.94 | | CLOSE: (18) is inconsistent.
% 141.52/20.94 | |
% 141.52/20.94 | Case 2:
% 141.52/20.94 | |
% 141.52/20.94 | | (19) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 141.52/20.94 | | all_30_1 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e2) &
% 141.52/20.94 | | op(e0, e1) = all_30_1 & $i(all_30_1))
% 141.52/20.94 | |
% 141.52/20.94 | | BETA: splitting (5) gives:
% 141.52/20.94 | |
% 141.52/20.94 | | Case 1:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (20) ~ (all_34_2 = e1)
% 141.52/20.94 | | |
% 141.52/20.94 | | | REDUCE: (13), (20) imply:
% 141.52/20.94 | | | (21) $false
% 141.52/20.94 | | |
% 141.52/20.94 | | | CLOSE: (21) is inconsistent.
% 141.52/20.94 | | |
% 141.52/20.94 | | Case 2:
% 141.52/20.94 | | |
% 141.52/20.94 | | | (22) ( ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 141.52/20.94 | | | all_34_1 & $i(all_34_0) & $i(all_34_1)) | ( ~ (all_34_1 = e0) &
% 141.52/20.94 | | | op(e3, e1) = all_34_1 & $i(all_34_1))
% 141.52/20.94 | | |
% 141.52/20.94 | | | BETA: splitting (22) gives:
% 141.52/20.94 | | |
% 141.52/20.94 | | | Case 1:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | (23) ~ (all_34_0 = e2) & op(all_34_1, e3) = all_34_0 & op(e3, e1) =
% 141.52/20.94 | | | | all_34_1 & $i(all_34_0) & $i(all_34_1)
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | ALPHA: (23) implies:
% 141.52/20.94 | | | | (24) op(e3, e1) = all_34_1
% 141.52/20.94 | | | | (25) op(all_34_1, e3) = all_34_0
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | BETA: splitting (9) gives:
% 141.52/20.94 | | | |
% 141.52/20.94 | | | | Case 1:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | (26) ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 & op(e3, e1)
% 141.52/20.94 | | | | | = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | ALPHA: (26) implies:
% 141.52/20.94 | | | | | (27) ~ (all_22_0 = e0)
% 141.52/20.94 | | | | | (28) op(e3, e1) = all_22_1
% 141.52/20.94 | | | | | (29) op(all_22_1, e3) = all_22_0
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | BETA: splitting (7) gives:
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | | Case 1:
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | GROUND_INST: instantiating (11) with e2, all_34_1, e1, e3,
% 141.52/20.94 | | | | | | simplifying with (3), (24) gives:
% 141.52/20.94 | | | | | | (30) all_34_1 = e2
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | GROUND_INST: instantiating (11) with all_22_1, all_34_1, e1, e3,
% 141.52/20.94 | | | | | | simplifying with (24), (28) gives:
% 141.52/20.94 | | | | | | (31) all_34_1 = all_22_1
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | COMBINE_EQS: (30), (31) imply:
% 141.52/20.94 | | | | | | (32) all_22_1 = e2
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | SIMP: (32) implies:
% 141.52/20.94 | | | | | | (33) all_22_1 = e2
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | REDUCE: (25), (30) imply:
% 141.52/20.94 | | | | | | (34) op(e2, e3) = all_34_0
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | REDUCE: (29), (33) imply:
% 141.52/20.94 | | | | | | (35) op(e2, e3) = all_22_0
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | GROUND_INST: instantiating (11) with e0, all_34_0, e3, e2,
% 141.52/20.94 | | | | | | simplifying with (8), (34) gives:
% 141.52/20.94 | | | | | | (36) all_34_0 = e0
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | GROUND_INST: instantiating (11) with all_22_0, all_34_0, e3, e2,
% 141.52/20.94 | | | | | | simplifying with (34), (35) gives:
% 141.52/20.94 | | | | | | (37) all_34_0 = all_22_0
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | COMBINE_EQS: (36), (37) imply:
% 141.52/20.94 | | | | | | (38) all_22_0 = e0
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | REDUCE: (27), (38) imply:
% 141.52/20.94 | | | | | | (39) $false
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | CLOSE: (39) is inconsistent.
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | Case 2:
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | (40) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 & $i(all_10_1)
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | | REF_CLOSE: (2), (11), (19), (40) are inconsistent by sub-proof #371.
% 141.52/20.94 | | | | | |
% 141.52/20.94 | | | | | End of split
% 141.52/20.94 | | | | |
% 141.52/20.94 | | | | Case 2:
% 141.52/20.94 | | | | |
% 141.52/20.95 | | | | | (41) ~ (all_22_1 = e2) & op(e3, e1) = all_22_1 & $i(all_22_1)
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | ALPHA: (41) implies:
% 141.52/20.95 | | | | | (42) ~ (all_22_1 = e2)
% 141.52/20.95 | | | | | (43) op(e3, e1) = all_22_1
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | REF_CLOSE: (3), (11), (24), (42), (43) are inconsistent by sub-proof
% 141.52/20.95 | | | | | #370.
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | End of split
% 141.52/20.95 | | | |
% 141.52/20.95 | | | Case 2:
% 141.52/20.95 | | | |
% 141.52/20.95 | | | | (44) ~ (all_34_1 = e0) & op(e3, e1) = all_34_1 & $i(all_34_1)
% 141.52/20.95 | | | |
% 141.52/20.95 | | | | ALPHA: (44) implies:
% 141.52/20.95 | | | | (45) op(e3, e1) = all_34_1
% 141.52/20.95 | | | |
% 141.52/20.95 | | | | BETA: splitting (9) gives:
% 141.52/20.95 | | | |
% 141.52/20.95 | | | | Case 1:
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | (46) ~ (all_22_0 = e0) & op(all_22_1, e3) = all_22_0 & op(e3, e1)
% 141.52/20.95 | | | | | = all_22_1 & $i(all_22_0) & $i(all_22_1)
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | ALPHA: (46) implies:
% 141.52/20.95 | | | | | (47) ~ (all_22_0 = e0)
% 141.52/20.95 | | | | | (48) op(e3, e1) = all_22_1
% 141.52/20.95 | | | | | (49) op(all_22_1, e3) = all_22_0
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | GROUND_INST: instantiating (11) with e2, all_34_1, e1, e3, simplifying
% 141.52/20.95 | | | | | with (3), (45) gives:
% 141.52/20.95 | | | | | (50) all_34_1 = e2
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | GROUND_INST: instantiating (11) with all_22_1, all_34_1, e1, e3,
% 141.52/20.95 | | | | | simplifying with (45), (48) gives:
% 141.52/20.95 | | | | | (51) all_34_1 = all_22_1
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | COMBINE_EQS: (50), (51) imply:
% 141.52/20.95 | | | | | (52) all_22_1 = e2
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | SIMP: (52) implies:
% 141.52/20.95 | | | | | (53) all_22_1 = e2
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | REDUCE: (49), (53) imply:
% 141.52/20.95 | | | | | (54) op(e2, e3) = all_22_0
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | GROUND_INST: instantiating (11) with e0, all_22_0, e3, e2, simplifying
% 141.52/20.95 | | | | | with (8), (54) gives:
% 141.52/20.95 | | | | | (55) all_22_0 = e0
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | REDUCE: (47), (55) imply:
% 141.52/20.95 | | | | | (56) $false
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | CLOSE: (56) is inconsistent.
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | Case 2:
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | (57) ~ (all_22_1 = e2) & op(e3, e1) = all_22_1 & $i(all_22_1)
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | ALPHA: (57) implies:
% 141.52/20.95 | | | | | (58) ~ (all_22_1 = e2)
% 141.52/20.95 | | | | | (59) op(e3, e1) = all_22_1
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | | REF_CLOSE: (3), (11), (45), (58), (59) are inconsistent by sub-proof
% 141.52/20.95 | | | | | #370.
% 141.52/20.95 | | | | |
% 141.52/20.95 | | | | End of split
% 141.52/20.95 | | | |
% 141.52/20.95 | | | End of split
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #370 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) op(e3, e1) = all_34_1
% 141.52/20.95 (2) op(e3, e1) = e2
% 141.52/20.95 (3) op(e3, e1) = all_22_1
% 141.52/20.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (5) ~ (all_22_1 = e2)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | GROUND_INST: instantiating (4) with e2, all_34_1, e1, e3, simplifying with
% 141.52/20.95 | (1), (2) gives:
% 141.52/20.95 | (6) all_34_1 = e2
% 141.52/20.95 |
% 141.52/20.95 | GROUND_INST: instantiating (4) with all_22_1, all_34_1, e1, e3, simplifying
% 141.52/20.95 | with (1), (3) gives:
% 141.52/20.95 | (7) all_34_1 = all_22_1
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (6), (7) imply:
% 141.52/20.95 | (8) all_22_1 = e2
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (8) implies:
% 141.52/20.95 | (9) all_22_1 = e2
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (5), (9) imply:
% 141.52/20.95 | (10) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (10) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #371 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 & $i(all_10_1)
% 141.52/20.95 (2) ( ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 & op(e0, e1) = all_30_1
% 141.52/20.95 & $i(all_30_0) & $i(all_30_1)) | ( ~ (all_30_1 = e2) & op(e0, e1) =
% 141.52/20.95 all_30_1 & $i(all_30_1))
% 141.52/20.95 (3) op(e0, e1) = e3
% 141.52/20.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | ALPHA: (1) implies:
% 141.52/20.95 | (5) ~ (all_10_1 = e3)
% 141.52/20.95 | (6) op(e0, e1) = all_10_1
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (2) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (7) ~ (all_30_0 = e3) & op(all_30_1, e0) = all_30_0 & op(e0, e1) =
% 141.52/20.95 | | all_30_1 & $i(all_30_0) & $i(all_30_1)
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (7) implies:
% 141.52/20.95 | | (8) op(e0, e1) = all_30_1
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (3), (4), (5), (6), (8) are inconsistent by sub-proof #372.
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (9) ~ (all_30_1 = e2) & op(e0, e1) = all_30_1 & $i(all_30_1)
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (9) implies:
% 141.52/20.95 | | (10) op(e0, e1) = all_30_1
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (3), (4), (5), (6), (10) are inconsistent by sub-proof #372.
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #372 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) op(e0, e1) = e3
% 141.52/20.95 (2) op(e0, e1) = all_10_1
% 141.52/20.95 (3) op(e0, e1) = all_30_1
% 141.52/20.95 (4) ~ (all_10_1 = e3)
% 141.52/20.95 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | GROUND_INST: instantiating (5) with e3, all_30_1, e1, e0, simplifying with
% 141.52/20.95 | (1), (3) gives:
% 141.52/20.95 | (6) all_30_1 = e3
% 141.52/20.95 |
% 141.52/20.95 | GROUND_INST: instantiating (5) with all_10_1, all_30_1, e1, e0, simplifying
% 141.52/20.95 | with (2), (3) gives:
% 141.52/20.95 | (7) all_30_1 = all_10_1
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (6), (7) imply:
% 141.52/20.95 | (8) all_10_1 = e3
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (4), (8) imply:
% 141.52/20.95 | (9) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (9) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #373 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_57_6 = e3
% 141.52/20.95 (2) all_57_7 = e1
% 141.52/20.95 (3) ~ (e3 = e0)
% 141.52/20.95 (4) op(e1, e1) = all_4_2
% 141.52/20.95 (5) ~ (all_4_2 = e3)
% 141.52/20.95 (6) all_57_11 = e2
% 141.52/20.95 (7) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.95 (8) ~ (e3 = e2)
% 141.52/20.95 (9) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/20.95 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/20.95 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (11) ~ (e3 = e1)
% 141.52/20.95 (12) all_57_9 = e0
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | ALPHA: (7) implies:
% 141.52/20.95 | (13) all_57_9 = e3
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (12), (13) imply:
% 141.52/20.95 | (14) e3 = e0
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (14) implies:
% 141.52/20.95 | (15) e3 = e0
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (1), (15) imply:
% 141.52/20.95 | (16) all_57_6 = e0
% 141.52/20.95 |
% 141.52/20.95 | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (16) are
% 141.52/20.95 | inconsistent by sub-proof #454.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #374 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_57_6 = e3
% 141.52/20.95 (2) all_57_4 = e3
% 141.52/20.95 (3) all_57_7 = e1
% 141.52/20.95 (4) all_57_13 = e0
% 141.52/20.95 (5) ~ (e3 = e0)
% 141.52/20.95 (6) op(e1, e1) = all_4_2
% 141.52/20.95 (7) ~ (all_4_2 = e3)
% 141.52/20.95 (8) all_57_11 = e2
% 141.52/20.95 (9) op(e2, e2) = e2
% 141.52/20.95 (10) ~ (e3 = e2)
% 141.52/20.95 (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/20.95 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/20.95 (12) op(e3, e3) = e1
% 141.52/20.95 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (14) ~ (e3 = e1)
% 141.52/20.95 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.95 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.95 (16) all_57_1 = e2
% 141.52/20.95 (17) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.95 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.95 (18) all_57_9 = e0
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (17) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (19) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.52/20.95 | | e3)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (19) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (20) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (20) implies:
% 141.52/20.95 | | | (21) all_57_1 = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | COMBINE_EQS: (16), (21) imply:
% 141.52/20.95 | | | (22) e3 = e2
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (1), (3), (6), (7), (8), (10), (11), (13), (14), (22) are
% 141.52/20.95 | | | inconsistent by sub-proof #376.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (23) all_57_3 = e3 & op(e2, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (23) implies:
% 141.52/20.95 | | | (24) op(e2, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (9), (10), (13), (24) are inconsistent by sub-proof #728.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (25) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.52/20.95 | | e3)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (25) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (26) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (26) implies:
% 141.52/20.95 | | | (27) all_57_7 = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | COMBINE_EQS: (3), (27) imply:
% 141.52/20.95 | | | (28) e3 = e1
% 141.52/20.95 | | |
% 141.52/20.95 | | | SIMP: (28) implies:
% 141.52/20.95 | | | (29) e3 = e1
% 141.52/20.95 | | |
% 141.52/20.95 | | | COMBINE_EQS: (2), (29) imply:
% 141.52/20.95 | | | (30) all_57_4 = e1
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (5), (10), (12), (13), (14), (15), (16), (18), (30) are
% 141.52/20.95 | | | inconsistent by sub-proof #375.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (31) all_57_13 = e3 & op(e0, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (31) implies:
% 141.52/20.95 | | | (32) all_57_13 = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | COMBINE_EQS: (4), (32) imply:
% 141.52/20.95 | | | (33) e3 = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | COMBINE_EQS: (1), (33) imply:
% 141.52/20.95 | | | (34) all_57_6 = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (3), (5), (6), (7), (8), (10), (11), (13), (14), (34) are
% 141.52/20.95 | | | inconsistent by sub-proof #454.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #375 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) ~ (e3 = e0)
% 141.52/20.95 (2) ~ (e3 = e2)
% 141.52/20.95 (3) op(e3, e3) = e1
% 141.52/20.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (5) all_57_4 = e1
% 141.52/20.95 (6) ~ (e3 = e1)
% 141.52/20.95 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.95 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.95 (8) all_57_1 = e2
% 141.52/20.95 (9) all_57_9 = e0
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (7) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 141.52/20.95 | | e3)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (10) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (11) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (11) implies:
% 141.52/20.95 | | | (12) op(e3, e3) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | GROUND_INST: instantiating (4) with e1, e3, e3, e3, simplifying with (3),
% 141.52/20.95 | | | (12) gives:
% 141.52/20.95 | | | (13) e3 = e1
% 141.52/20.95 | | |
% 141.52/20.95 | | | REDUCE: (6), (13) imply:
% 141.52/20.95 | | | (14) $false
% 141.52/20.95 | | |
% 141.52/20.95 | | | CLOSE: (14) is inconsistent.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (15) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (2), (8), (15) are inconsistent by sub-proof #842.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (16) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 141.52/20.95 | | e3)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (16) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (17) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (17) implies:
% 141.52/20.95 | | | (18) all_57_4 = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (5), (6), (18) are inconsistent by sub-proof #631.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (19) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (19) implies:
% 141.52/20.95 | | | (20) all_57_9 = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | COMBINE_EQS: (9), (20) imply:
% 141.52/20.95 | | | (21) e3 = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | REDUCE: (1), (21) imply:
% 141.52/20.95 | | | (22) $false
% 141.52/20.95 | | |
% 141.52/20.95 | | | CLOSE: (22) is inconsistent.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #376 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_57_6 = e3
% 141.52/20.95 (2) all_57_7 = e1
% 141.52/20.95 (3) op(e1, e1) = all_4_2
% 141.52/20.95 (4) e3 = e2
% 141.52/20.95 (5) ~ (all_4_2 = e3)
% 141.52/20.95 (6) all_57_11 = e2
% 141.52/20.95 (7) ~ (e3 = e2)
% 141.52/20.95 (8) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/20.95 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/20.95 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (10) ~ (e3 = e1)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (4) implies:
% 141.52/20.95 | (11) e3 = e2
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (1), (11) imply:
% 141.52/20.95 | (12) all_57_6 = e2
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (8) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (13) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 141.52/20.95 | | e3)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (13) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (14) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (7), (12), (14) are inconsistent by sub-proof #916.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (15) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (2), (10), (15) are inconsistent by sub-proof #586.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (16) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 141.52/20.95 | | e3)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (16) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (17) all_57_8 = e3 & op(e1, e1) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (17) implies:
% 141.52/20.95 | | | (18) op(e1, e1) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (3), (5), (9), (18) are inconsistent by sub-proof #1127.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (19) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #386.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #377 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) ~ (e2 = e0)
% 141.52/20.95 (2) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.52/20.95 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (4) ~ (all_52_13 = e2)
% 141.52/20.95 (5) op(e2, e0) = all_52_13
% 141.52/20.95 (6) all_57_9 = e0
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (2) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (7) all_57_9 = e2 & op(e3, e0) = e2
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (7) implies:
% 141.52/20.95 | | (8) all_57_9 = e2
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #1018.
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (9) all_57_10 = e2 & op(e2, e0) = e2
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (9) implies:
% 141.52/20.95 | | (10) op(e2, e0) = e2
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1030.
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #378 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_54_10 = all_4_2
% 141.52/20.95 (2) all_54_10 = e1
% 141.52/20.95 (3) ~ (all_4_2 = e1)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.95 | (4) all_4_2 = e1
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (4) implies:
% 141.52/20.95 | (5) all_4_2 = e1
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (3), (5) imply:
% 141.52/20.95 | (6) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (6) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #379 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) ~ (e2 = e1)
% 141.52/20.95 (2) ~ (all_52_4 = e1)
% 141.52/20.95 (3) op(e2, e2) = e2
% 141.52/20.95 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 141.52/20.95 (5) op(e3, e2) = all_52_4
% 141.52/20.95 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (4) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (7) all_57_1 = e1 & op(e3, e2) = e1
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (2), (5), (6), (7) are inconsistent by sub-proof #844.
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (8) implies:
% 141.52/20.95 | | (9) op(e2, e2) = e1
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (1), (3), (6), (9) are inconsistent by sub-proof #749.
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #380 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) op(e0, e1) = all_30_1
% 141.52/20.95 (2) op(e0, e1) = e2
% 141.52/20.95 (3) ( ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0, e1) = all_10_1
% 141.52/20.95 & $i(all_10_0) & $i(all_10_1)) | ( ~ (all_10_1 = e3) & op(e0, e1) =
% 141.52/20.95 all_10_1 & $i(all_10_1))
% 141.52/20.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (5) ~ (all_30_1 = e2)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (3) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (6) ~ (all_10_0 = e2) & op(all_10_1, e0) = all_10_0 & op(e0, e1) =
% 141.52/20.95 | | all_10_1 & $i(all_10_0) & $i(all_10_1)
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (6) implies:
% 141.52/20.95 | | (7) op(e0, e1) = all_10_1
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (1), (2), (4), (5), (7) are inconsistent by sub-proof #381.
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (8) ~ (all_10_1 = e3) & op(e0, e1) = all_10_1 & $i(all_10_1)
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (8) implies:
% 141.52/20.95 | | (9) op(e0, e1) = all_10_1
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (1), (2), (4), (5), (9) are inconsistent by sub-proof #381.
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #381 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) op(e0, e1) = all_10_1
% 141.52/20.95 (2) op(e0, e1) = all_30_1
% 141.52/20.95 (3) op(e0, e1) = e2
% 141.52/20.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (5) ~ (all_30_1 = e2)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | GROUND_INST: instantiating (4) with e2, all_30_1, e1, e0, simplifying with
% 141.52/20.95 | (2), (3) gives:
% 141.52/20.95 | (6) all_30_1 = e2
% 141.52/20.95 |
% 141.52/20.95 | GROUND_INST: instantiating (4) with all_10_1, all_30_1, e1, e0, simplifying
% 141.52/20.95 | with (1), (2) gives:
% 141.52/20.95 | (7) all_30_1 = all_10_1
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (6), (7) imply:
% 141.52/20.95 | (8) all_10_1 = e2
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (5), (6) imply:
% 141.52/20.95 | (9) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (9) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #382 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_54_7 = all_30_0
% 141.52/20.95 (2) all_54_7 = e1
% 141.52/20.95 (3) ~ (all_30_0 = e1)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.95 | (4) all_30_0 = e1
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (4) implies:
% 141.52/20.95 | (5) all_30_0 = e1
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (3), (5) imply:
% 141.52/20.95 | (6) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (6) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #383 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_54_7 = all_30_0
% 141.52/20.95 (2) all_54_7 = e2
% 141.52/20.95 (3) ~ (all_30_0 = e2)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.95 | (4) all_30_0 = e2
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (4) implies:
% 141.52/20.95 | (5) all_30_0 = e2
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (3), (5) imply:
% 141.52/20.95 | (6) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (6) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #384 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_54_7 = all_30_0
% 141.52/20.95 (2) all_54_7 = e3
% 141.52/20.95 (3) ~ (all_30_0 = e3)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.95 | (4) all_30_0 = e3
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (4) implies:
% 141.52/20.95 | (5) all_30_0 = e3
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (3), (5) imply:
% 141.52/20.95 | (6) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (6) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #385 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) op(e0, e0) = e1
% 141.52/20.95 (2) all_57_11 = e2
% 141.52/20.95 (3) ~ (e3 = e2)
% 141.52/20.95 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (5) ~ (e3 = e1)
% 141.52/20.95 (6) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (6) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #386.
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 141.52/20.95 | |
% 141.52/20.95 | | ALPHA: (8) implies:
% 141.52/20.95 | | (9) op(e0, e0) = e3
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #732.
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #386 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/20.95 (2) all_57_11 = e2
% 141.52/20.95 (3) ~ (e3 = e2)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | ALPHA: (1) implies:
% 141.52/20.95 | (4) all_57_11 = e3
% 141.52/20.95 |
% 141.52/20.95 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.95 | (5) e3 = e2
% 141.52/20.95 |
% 141.52/20.95 | REDUCE: (3), (5) imply:
% 141.52/20.95 | (6) $false
% 141.52/20.95 |
% 141.52/20.95 | CLOSE: (6) is inconsistent.
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #387 shows that the following formulas are inconsistent:
% 141.52/20.95 ----------------------------------------------------------------
% 141.52/20.95 (1) all_54_7 = all_52_13
% 141.52/20.95 (2) ~ (all_52_9 = all_52_13)
% 141.52/20.95 (3) all_54_7 = e1 | all_54_7 = e0
% 141.52/20.95 (4) ~ (all_52_1 = e0)
% 141.52/20.95 (5) ~ (e3 = e0)
% 141.52/20.95 (6) op(e2, e3) = all_52_1
% 141.52/20.95 (7) op(e2, e2) = e2
% 141.52/20.95 (8) all_57_10 = e3
% 141.52/20.95 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.95 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.95 (10) ~ (e2 = e0)
% 141.52/20.95 (11) op(e2, e1) = all_52_9
% 141.52/20.95 (12) ~ (all_52_13 = e1)
% 141.52/20.95 (13) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.95 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.52/20.95
% 141.52/20.95 Begin of proof
% 141.52/20.95 |
% 141.52/20.95 | SIMP: (10) implies:
% 141.52/20.95 | (14) ~ (e2 = e0)
% 141.52/20.95 |
% 141.52/20.95 | BETA: splitting (13) gives:
% 141.52/20.95 |
% 141.52/20.95 | Case 1:
% 141.52/20.95 | |
% 141.52/20.95 | | (15) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 141.52/20.95 | | e0)
% 141.52/20.95 | |
% 141.52/20.95 | | REF_CLOSE: (4), (6), (7), (9), (14), (15) are inconsistent by sub-proof
% 141.52/20.95 | | #394.
% 141.52/20.95 | |
% 141.52/20.95 | Case 2:
% 141.52/20.95 | |
% 141.52/20.95 | | (16) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.52/20.95 | | e0)
% 141.52/20.95 | |
% 141.52/20.95 | | BETA: splitting (16) gives:
% 141.52/20.95 | |
% 141.52/20.95 | | Case 1:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (17) all_57_5 = e0 & op(e2, e1) = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (17) implies:
% 141.52/20.95 | | | (18) op(e2, e1) = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (1), (2), (3), (9), (11), (12), (18) are inconsistent by
% 141.52/20.95 | | | sub-proof #675.
% 141.52/20.95 | | |
% 141.52/20.95 | | Case 2:
% 141.52/20.95 | | |
% 141.52/20.95 | | | (19) all_57_10 = e0 & op(e2, e0) = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | ALPHA: (19) implies:
% 141.52/20.95 | | | (20) all_57_10 = e0
% 141.52/20.95 | | |
% 141.52/20.95 | | | REF_CLOSE: (5), (8), (20) are inconsistent by sub-proof #935.
% 141.52/20.95 | | |
% 141.52/20.95 | | End of split
% 141.52/20.95 | |
% 141.52/20.95 | End of split
% 141.52/20.95 |
% 141.52/20.95 End of proof
% 141.52/20.95
% 141.52/20.95 Sub-proof #388 shows that the following formulas are inconsistent:
% 141.52/20.96 ----------------------------------------------------------------
% 141.52/20.96 (1) ~ (all_52_1 = e2)
% 141.52/20.96 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/20.96 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/20.96 (3) ~ (all_52_14 = e1)
% 141.52/20.96 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.96 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/20.96 (5) ~ (e2 = e1)
% 141.52/20.96 (6) all_54_7 = all_52_13
% 141.52/20.96 (7) all_54_3 = all_52_12
% 141.52/20.96 (8) ~ (all_52_9 = all_52_13)
% 141.52/20.96 (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.96 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.96 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.96 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.96 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.96 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.96 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.96 (10) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/20.96 (11) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.96 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.96 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.96 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.96 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.96 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.96 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.96 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.96 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.96 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.96 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.96 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.96 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.96 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.96 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.96 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.96 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.96 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.96 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.96 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.96 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.96 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.96 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.96 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.96 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.96 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.96 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.96 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.96 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.96 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.96 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.96 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.96 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.96 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.96 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.96 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.96 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.96 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.96 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.96 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.96 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.96 (12) all_54_7 = e1 | all_54_7 = e0
% 141.52/20.96 (13) all_57_14 = e2
% 141.52/20.96 (14) all_48_2 = all_4_2
% 141.52/20.96 (15) op(e3, e3) = e2
% 141.52/20.96 (16) ~ (all_52_1 = e0)
% 141.52/20.96 (17) op(e1, e1) = all_4_2
% 141.52/20.96 (18) op(e3, e1) = all_52_8
% 141.52/20.96 (19) op(e1, e0) = e2
% 141.52/20.96 (20) op(e0, e1) = e2
% 141.52/20.96 (21) op(e0, e0) = e1
% 141.52/20.96 (22) op(e2, e3) = all_52_1
% 141.52/20.96 (23) ~ (all_52_12 = e0)
% 141.52/20.96 (24) ~ (all_52_12 = e1)
% 141.52/20.96 (25) ~ (all_4_2 = e3)
% 141.52/20.96 (26) all_57_11 = e2
% 141.52/20.96 (27) ~ (all_52_8 = all_52_12)
% 141.52/20.96 (28) op(e2, e2) = e2
% 141.52/20.96 (29) op(e3, e2) = all_52_4
% 141.52/20.96 (30) ~ (e2 = e0)
% 141.52/20.96 (31) op(e3, e0) = all_52_12
% 141.52/20.96 (32) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.52/20.96 (33) ~ (all_52_9 = all_4_2)
% 141.52/20.96 (34) all_57_9 = e3
% 141.52/20.96 (35) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.96 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.96 (36) ~ (all_4_2 = e2)
% 141.52/20.96 (37) all_54_10 = all_4_2
% 141.52/20.96 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.96 (39) ~ (all_52_13 = e2)
% 141.52/20.96 (40) ~ (all_52_12 = e2)
% 141.52/20.96 (41) ~ (all_48_2 = e0) | ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 &
% 141.52/20.96 op(e1, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 141.52/20.96 e2) & op(e1, e0) = all_48_1 & $i(all_48_1))
% 141.52/20.96 (42) all_56_15 = e1
% 141.52/20.96 (43) op(e2, e1) = all_52_9
% 141.52/20.96 (44) op(e3, e3) = all_14_2
% 141.52/20.96 (45) ~ (all_52_13 = e1)
% 141.52/20.96 (46) ~ (all_52_4 = all_52_12)
% 141.52/20.96 (47) op(e2, e0) = all_52_13
% 141.52/20.96 (48) op(e3, e0) = e3
% 141.52/20.96 (49) ~ (all_14_2 = e0)
% 141.52/20.96 (50) op(e1, e0) = all_52_14
% 141.52/20.96 (51) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.96 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 141.52/20.96
% 141.52/20.96 Begin of proof
% 141.52/20.96 |
% 141.52/20.96 | BETA: splitting (32) gives:
% 141.52/20.96 |
% 141.52/20.96 | Case 1:
% 141.52/20.96 | |
% 141.52/20.96 | | (52) all_54_3 = e3
% 141.52/20.96 | |
% 141.52/20.96 | | COMBINE_EQS: (7), (52) imply:
% 141.52/20.96 | | (53) all_52_12 = e3
% 141.52/20.96 | |
% 141.52/20.96 | | SIMP: (53) implies:
% 141.52/20.96 | | (54) all_52_12 = e3
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (46), (54) imply:
% 141.52/20.96 | | (55) ~ (all_52_4 = e3)
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (27), (54) imply:
% 141.52/20.96 | | (56) ~ (all_52_8 = e3)
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (40), (54) imply:
% 141.52/20.96 | | (57) ~ (e3 = e2)
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (24), (54) imply:
% 141.52/20.96 | | (58) ~ (e3 = e1)
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (23), (54) imply:
% 141.52/20.96 | | (59) ~ (e3 = e0)
% 141.52/20.96 | |
% 141.52/20.96 | | BETA: splitting (11) gives:
% 141.52/20.96 | |
% 141.52/20.96 | | Case 1:
% 141.52/20.96 | | |
% 141.52/20.96 | | | (60) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 141.52/20.96 | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11
% 141.52/20.96 | | | & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.96 | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13)))
% 141.52/20.96 | | | & ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.52/20.96 | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3
% 141.52/20.96 | | | & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.52/20.96 | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) =
% 141.52/20.96 | | | e3) | ( ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 141.52/20.96 | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 141.52/20.96 | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10))))
% 141.52/20.96 | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 141.52/20.96 | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.52/20.96 | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) =
% 141.52/20.96 | | | e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.96 | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.96 | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.96 | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) &
% 141.52/20.96 | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2
% 141.52/20.96 | | | & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 141.52/20.96 | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) =
% 141.52/20.96 | | | e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.52/20.96 | | | $i(all_56_12))))
% 141.52/20.96 | | |
% 141.52/20.96 | | | BETA: splitting (60) gives:
% 141.52/20.96 | | |
% 141.52/20.96 | | | Case 1:
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | (61) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 141.52/20.96 | | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11
% 141.52/20.96 | | | | & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.96 | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13)))
% 141.52/20.96 | | | | & ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.52/20.96 | | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3
% 141.52/20.96 | | | | & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 141.52/20.96 | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) =
% 141.52/20.96 | | | | e3) | ( ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 141.52/20.96 | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~
% 141.52/20.96 | | | | (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | ALPHA: (61) implies:
% 141.52/20.96 | | | | (62) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 141.52/20.96 | | | | op(e1, e3) = all_56_6 & $i(all_56_6))
% 141.52/20.96 | | | | (63) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) &
% 141.52/20.96 | | | | op(e2, e3) = all_56_3 & $i(all_56_3))
% 141.52/20.96 | | | | (64) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) &
% 141.52/20.96 | | | | op(e1, e1) = all_56_13 & $i(all_56_13))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | BETA: splitting (63) gives:
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | Case 1:
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | (65) all_56_11 = e3 & op(e2, e2) = e3
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | ALPHA: (65) implies:
% 141.52/20.96 | | | | | (66) op(e2, e2) = e3
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | REF_CLOSE: (28), (38), (57), (66) are inconsistent by sub-proof #728.
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | Case 2:
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | (67) ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | ALPHA: (67) implies:
% 141.52/20.96 | | | | | (68) op(e2, e3) = all_56_3
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | BETA: splitting (51) gives:
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | | Case 1:
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | | (69) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2,
% 141.52/20.96 | | | | | | e2) = e0)
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | | REF_CLOSE: (16), (22), (28), (30), (38), (69) are inconsistent by
% 141.52/20.96 | | | | | | sub-proof #394.
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | Case 2:
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | | (70) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2,
% 141.52/20.96 | | | | | | e0) = e0)
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | | BETA: splitting (70) gives:
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | | Case 1:
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | (71) all_57_5 = e0 & op(e2, e1) = e0
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | ALPHA: (71) implies:
% 141.52/20.96 | | | | | | | (72) op(e2, e1) = e0
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | REF_CLOSE: (6), (8), (12), (38), (43), (45), (72) are inconsistent
% 141.52/20.96 | | | | | | | by sub-proof #675.
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | Case 2:
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | (73) all_57_10 = e0 & op(e2, e0) = e0
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | ALPHA: (73) implies:
% 141.52/20.96 | | | | | | | (74) all_57_10 = e0
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | BETA: splitting (2) gives:
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | | (75) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 141.52/20.96 | | | | | | | | op(e2, e1) = e3)
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | | BETA: splitting (75) gives:
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | (76) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | ALPHA: (76) implies:
% 141.52/20.96 | | | | | | | | | (77) op(e3, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | REF_CLOSE: (18), (38), (56), (77) are inconsistent by
% 141.52/20.96 | | | | | | | | | sub-proof #1106.
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | (78) all_57_5 = e3 & op(e2, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | ALPHA: (78) implies:
% 141.52/20.96 | | | | | | | | | (79) op(e2, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | BETA: splitting (4) gives:
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | (80) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 141.52/20.96 | | | | | | | | | | op(e2, e2) = e1)
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | BETA: splitting (80) gives:
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | (81) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | ALPHA: (81) implies:
% 141.52/20.96 | | | | | | | | | | | (82) op(e2, e3) = e1
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | BETA: splitting (62) gives:
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | (83) all_56_13 = e3 & op(e1, e1) = e3
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | ALPHA: (83) implies:
% 141.52/20.96 | | | | | | | | | | | | (84) op(e1, e1) = e3
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | REF_CLOSE: (17), (25), (38), (84) are inconsistent by
% 141.52/20.96 | | | | | | | | | | | | sub-proof #1127.
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | (85) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 141.52/20.96 | | | | | | | | | | | | $i(all_56_6)
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | ALPHA: (85) implies:
% 141.52/20.96 | | | | | | | | | | | | (86) ~ (all_56_6 = e1)
% 141.52/20.96 | | | | | | | | | | | | (87) op(e1, e3) = all_56_6
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | BETA: splitting (64) gives:
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | (88) all_56_6 = e1 & op(e1, e3) = e1
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | ALPHA: (88) implies:
% 141.52/20.96 | | | | | | | | | | | | | (89) op(e1, e3) = e1
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | REF_CLOSE: (38), (86), (87), (89) are inconsistent by
% 141.52/20.96 | | | | | | | | | | | | | sub-proof #435.
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | (90) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 141.52/20.96 | | | | | | | | | | | | | $i(all_56_13)
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | ALPHA: (90) implies:
% 141.52/20.96 | | | | | | | | | | | | | (91) op(e1, e1) = all_56_13
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_4_2, all_56_13, e1,
% 141.52/20.96 | | | | | | | | | | | | | e1, simplifying with (17), (91) gives:
% 141.52/20.96 | | | | | | | | | | | | | (92) all_56_13 = all_4_2
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_52_9, e3, e1, e2,
% 141.52/20.96 | | | | | | | | | | | | | simplifying with (43), (79) gives:
% 141.52/20.96 | | | | | | | | | | | | | (93) all_52_9 = e3
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | GROUND_INST: instantiating (38) with all_52_1, all_56_3, e3,
% 141.52/20.96 | | | | | | | | | | | | | e2, simplifying with (22), (68) gives:
% 141.52/20.96 | | | | | | | | | | | | | (94) all_56_3 = all_52_1
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | GROUND_INST: instantiating (38) with e1, all_56_3, e3, e2,
% 141.52/20.96 | | | | | | | | | | | | | simplifying with (68), (82) gives:
% 141.52/20.96 | | | | | | | | | | | | | (95) all_56_3 = e1
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | COMBINE_EQS: (94), (95) imply:
% 141.52/20.96 | | | | | | | | | | | | | (96) all_52_1 = e1
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | SIMP: (96) implies:
% 141.52/20.96 | | | | | | | | | | | | | (97) all_52_1 = e1
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | REDUCE: (1), (97) imply:
% 141.52/20.96 | | | | | | | | | | | | | (98) ~ (e2 = e1)
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | REDUCE: (33), (93) imply:
% 141.52/20.96 | | | | | | | | | | | | | (99) ~ (all_4_2 = e3)
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | BETA: splitting (41) gives:
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | | (100) ~ (all_48_2 = e0)
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | | REDUCE: (14), (100) imply:
% 141.52/20.96 | | | | | | | | | | | | | | (101) ~ (all_4_2 = e0)
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | | REF_CLOSE: (5), (9), (10), (17), (25), (36), (37), (38),
% 141.52/20.96 | | | | | | | | | | | | | | (42), (44), (49), (101) are inconsistent by
% 141.52/20.96 | | | | | | | | | | | | | | sub-proof #455.
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | | (102) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0
% 141.52/20.96 | | | | | | | | | | | | | | & op(e1, e0) = all_48_1 & $i(all_48_0) &
% 141.52/20.96 | | | | | | | | | | | | | | $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0)
% 141.52/20.96 | | | | | | | | | | | | | | = all_48_1 & $i(all_48_1))
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | | REF_CLOSE: (19), (38), (79), (102) are inconsistent by
% 141.52/20.96 | | | | | | | | | | | | | | sub-proof #648.
% 141.52/20.96 | | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | | End of split
% 141.52/20.96 | | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | | End of split
% 141.52/20.96 | | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | End of split
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | (103) all_57_3 = e1 & op(e2, e2) = e1
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | ALPHA: (103) implies:
% 141.52/20.96 | | | | | | | | | | | (104) op(e2, e2) = e1
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | | REF_CLOSE: (5), (28), (38), (104) are inconsistent by
% 141.52/20.96 | | | | | | | | | | | sub-proof #749.
% 141.52/20.96 | | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | End of split
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | (105) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1
% 141.52/20.96 | | | | | | | | | | & op(e2, e0) = e1)
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | | REF_CLOSE: (2), (13), (17), (18), (25), (38), (45), (47),
% 141.52/20.96 | | | | | | | | | | (56), (57), (58), (105) are inconsistent by
% 141.52/20.96 | | | | | | | | | | sub-proof #444.
% 141.52/20.96 | | | | | | | | | |
% 141.52/20.96 | | | | | | | | | End of split
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | End of split
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | | (106) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 141.52/20.96 | | | | | | | | op(e0, e1) = e3)
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | | BETA: splitting (106) gives:
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | | Case 1:
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | (107) all_57_8 = e3 & op(e1, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | ALPHA: (107) implies:
% 141.52/20.96 | | | | | | | | | (108) op(e1, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | REF_CLOSE: (17), (25), (38), (108) are inconsistent by
% 141.52/20.96 | | | | | | | | | sub-proof #1127.
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | Case 2:
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | (109) all_57_14 = e3 & op(e0, e1) = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | ALPHA: (109) implies:
% 141.52/20.96 | | | | | | | | | (110) all_57_14 = e3
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | COMBINE_EQS: (13), (110) imply:
% 141.52/20.96 | | | | | | | | | (111) e3 = e2
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | COMBINE_EQS: (34), (111) imply:
% 141.52/20.96 | | | | | | | | | (112) all_57_9 = e2
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | | REF_CLOSE: (21), (26), (35), (38), (57), (58), (59), (74),
% 141.52/20.96 | | | | | | | | | (112) are inconsistent by sub-proof #392.
% 141.52/20.96 | | | | | | | | |
% 141.52/20.96 | | | | | | | | End of split
% 141.52/20.96 | | | | | | | |
% 141.52/20.96 | | | | | | | End of split
% 141.52/20.96 | | | | | | |
% 141.52/20.96 | | | | | | End of split
% 141.52/20.96 | | | | | |
% 141.52/20.96 | | | | | End of split
% 141.52/20.96 | | | | |
% 141.52/20.96 | | | | End of split
% 141.52/20.96 | | | |
% 141.52/20.96 | | | Case 2:
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | (113) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 141.52/20.96 | | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.52/20.96 | | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) =
% 141.52/20.96 | | | | e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.96 | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.96 | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.96 | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) &
% 141.52/20.96 | | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2
% 141.52/20.96 | | | | & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 141.52/20.96 | | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) =
% 141.52/20.96 | | | | e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.52/20.96 | | | | $i(all_56_12)))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | ALPHA: (113) implies:
% 141.52/20.96 | | | | (114) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) &
% 141.52/20.96 | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | REF_CLOSE: (15), (29), (38), (55), (114) are inconsistent by sub-proof
% 141.52/20.96 | | | | #390.
% 141.52/20.96 | | | |
% 141.52/20.96 | | | End of split
% 141.52/20.96 | | |
% 141.52/20.96 | | Case 2:
% 141.52/20.96 | | |
% 141.52/20.96 | | | (115) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.52/20.96 | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.52/20.96 | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) =
% 141.52/20.96 | | | e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.52/20.96 | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 141.52/20.96 | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 141.52/20.96 | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 141.52/20.96 | | | op(e2, e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 &
% 141.52/20.96 | | | op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.52/20.96 | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0)
% 141.52/20.96 | | | = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.96 | | | $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.52/20.96 | | | & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) &
% 141.52/20.96 | | | op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 &
% 141.52/20.96 | | | op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.52/20.96 | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.52/20.96 | | | = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.96 | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/20.96 | | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.96 | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) &
% 141.52/20.96 | | | op(e2, e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 141.52/20.96 | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.52/20.96 | | | all_56_8 & $i(all_56_8))))
% 141.52/20.96 | | |
% 141.52/20.96 | | | BETA: splitting (115) gives:
% 141.52/20.96 | | |
% 141.52/20.96 | | | Case 1:
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | (116) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 141.52/20.96 | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 141.52/20.96 | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) =
% 141.52/20.96 | | | | e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 141.52/20.96 | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 141.52/20.96 | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 141.52/20.96 | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 141.52/20.96 | | | | op(e2, e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 &
% 141.52/20.96 | | | | op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.52/20.96 | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0)
% 141.52/20.96 | | | | = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.96 | | | | $i(all_56_14)))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | ALPHA: (116) implies:
% 141.52/20.96 | | | | (117) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) &
% 141.52/20.96 | | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | REF_CLOSE: (20), (30), (38), (42), (117) are inconsistent by sub-proof
% 141.52/20.96 | | | | #389.
% 141.52/20.96 | | | |
% 141.52/20.96 | | | Case 2:
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | (118) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 141.52/20.96 | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 141.52/20.96 | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) =
% 141.52/20.96 | | | | e2) | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 141.52/20.96 | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 141.52/20.96 | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13)))
% 141.52/20.96 | | | | & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) &
% 141.52/20.96 | | | | op(e3, e0) = all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 &
% 141.52/20.96 | | | | op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 141.52/20.96 | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) =
% 141.52/20.96 | | | | e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.52/20.96 | | | | $i(all_56_8)))
% 141.52/20.96 | | | |
% 141.52/20.96 | | | | REF_CLOSE: (3), (9), (38), (39), (44), (47), (49), (50), (118) are
% 141.52/20.96 | | | | inconsistent by sub-proof #431.
% 141.52/20.96 | | | |
% 141.52/20.96 | | | End of split
% 141.52/20.96 | | |
% 141.52/20.96 | | End of split
% 141.52/20.96 | |
% 141.52/20.96 | Case 2:
% 141.52/20.96 | |
% 141.52/20.96 | | (119) ~ (all_54_3 = e3)
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (7), (119) imply:
% 141.52/20.96 | | (120) ~ (all_52_12 = e3)
% 141.52/20.96 | |
% 141.52/20.96 | | REF_CLOSE: (31), (38), (48), (120) are inconsistent by sub-proof #1105.
% 141.52/20.96 | |
% 141.52/20.96 | End of split
% 141.52/20.96 |
% 141.52/20.96 End of proof
% 141.52/20.96
% 141.52/20.96 Sub-proof #389 shows that the following formulas are inconsistent:
% 141.52/20.96 ----------------------------------------------------------------
% 141.52/20.96 (1) op(e0, e1) = e2
% 141.52/20.96 (2) ~ (e2 = e0)
% 141.52/20.96 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.96 (4) all_56_15 = e1
% 141.52/20.96 (5) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.52/20.96 all_56_15 & $i(all_56_15))
% 141.52/20.96
% 141.52/20.96 Begin of proof
% 141.52/20.96 |
% 141.52/20.96 | BETA: splitting (5) gives:
% 141.52/20.96 |
% 141.52/20.96 | Case 1:
% 141.52/20.96 | |
% 141.52/20.96 | | (6) all_56_14 = e0 & op(e0, e1) = e0
% 141.52/20.96 | |
% 141.52/20.96 | | ALPHA: (6) implies:
% 141.52/20.96 | | (7) op(e0, e1) = e0
% 141.52/20.96 | |
% 141.52/20.96 | | GROUND_INST: instantiating (3) with e2, e0, e1, e0, simplifying with (1),
% 141.52/20.96 | | (7) gives:
% 141.52/20.96 | | (8) e2 = e0
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (2), (8) imply:
% 141.52/20.96 | | (9) $false
% 141.52/20.96 | |
% 141.52/20.96 | | CLOSE: (9) is inconsistent.
% 141.52/20.96 | |
% 141.52/20.96 | Case 2:
% 141.52/20.96 | |
% 141.52/20.96 | | (10) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.52/20.96 | |
% 141.52/20.96 | | ALPHA: (10) implies:
% 141.52/20.96 | | (11) ~ (all_56_15 = e1)
% 141.52/20.96 | |
% 141.52/20.96 | | REDUCE: (4), (11) imply:
% 141.52/20.96 | | (12) $false
% 141.52/20.96 | |
% 141.52/20.96 | | CLOSE: (12) is inconsistent.
% 141.52/20.96 | |
% 141.52/20.96 | End of split
% 141.52/20.96 |
% 141.52/20.96 End of proof
% 141.52/20.96
% 141.52/20.96 Sub-proof #390 shows that the following formulas are inconsistent:
% 141.52/20.96 ----------------------------------------------------------------
% 141.52/20.96 (1) op(e3, e3) = e2
% 141.52/20.96 (2) ~ (all_52_4 = e3)
% 141.52/20.96 (3) op(e3, e2) = all_52_4
% 141.52/20.96 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.96 (5) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 141.52/20.96 all_56_9 & $i(all_56_9))
% 141.52/20.96
% 141.52/20.96 Begin of proof
% 141.52/20.96 |
% 141.52/20.96 | BETA: splitting (5) gives:
% 141.52/20.96 |
% 141.52/20.96 | Case 1:
% 141.52/20.96 | |
% 141.52/20.96 | | (6) all_56_0 = e3 & op(e3, e2) = e3
% 141.52/20.96 | |
% 141.52/20.96 | | ALPHA: (6) implies:
% 141.52/20.96 | | (7) op(e3, e2) = e3
% 141.52/20.96 | |
% 141.52/20.96 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1107.
% 141.52/20.96 | |
% 141.52/20.96 | Case 2:
% 141.52/20.96 | |
% 141.52/20.96 | | (8) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 141.52/20.96 | |
% 141.52/20.96 | | ALPHA: (8) implies:
% 141.52/20.96 | | (9) ~ (all_56_9 = e2)
% 141.52/20.96 | | (10) op(e3, e3) = all_56_9
% 141.52/20.96 | |
% 141.52/20.96 | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #391.
% 141.52/20.96 | |
% 141.52/20.96 | End of split
% 141.52/20.96 |
% 141.52/20.96 End of proof
% 141.52/20.96
% 141.52/20.96 Sub-proof #391 shows that the following formulas are inconsistent:
% 141.52/20.96 ----------------------------------------------------------------
% 141.52/20.96 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.96 (2) op(e3, e3) = all_56_9
% 141.52/20.96 (3) op(e3, e3) = e2
% 141.52/20.96 (4) ~ (all_56_9 = e2)
% 141.52/20.96
% 141.52/20.96 Begin of proof
% 141.52/20.96 |
% 141.52/20.96 | GROUND_INST: instantiating (1) with e2, all_56_9, e3, e3, simplifying with
% 141.52/20.96 | (2), (3) gives:
% 141.52/20.96 | (5) all_56_9 = e2
% 141.52/20.96 |
% 141.52/20.96 | REDUCE: (4), (5) imply:
% 141.52/20.96 | (6) $false
% 141.52/20.96 |
% 141.52/20.96 | CLOSE: (6) is inconsistent.
% 141.52/20.96 |
% 141.52/20.96 End of proof
% 141.52/20.96
% 141.52/20.96 Sub-proof #392 shows that the following formulas are inconsistent:
% 141.52/20.96 ----------------------------------------------------------------
% 141.52/20.96 (1) ~ (e3 = e0)
% 141.52/20.96 (2) op(e0, e0) = e1
% 141.52/20.96 (3) all_57_11 = e2
% 141.52/20.96 (4) all_57_9 = e2
% 141.52/20.96 (5) ~ (e3 = e2)
% 141.52/20.96 (6) all_57_10 = e0
% 141.52/20.96 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/20.96 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.96 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.96 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.96 (9) ~ (e3 = e1)
% 141.52/20.96
% 141.52/20.96 Begin of proof
% 141.52/20.96 |
% 141.52/20.96 | BETA: splitting (7) gives:
% 141.52/20.96 |
% 141.52/20.96 | Case 1:
% 141.52/20.96 | |
% 141.52/20.96 | | (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 141.52/20.96 | | e3)
% 141.52/20.96 | |
% 141.52/20.96 | | BETA: splitting (10) gives:
% 141.52/20.96 | |
% 141.52/20.96 | | Case 1:
% 141.52/20.96 | | |
% 141.52/20.96 | | | (11) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.96 | | |
% 141.52/20.96 | | | ALPHA: (11) implies:
% 141.52/20.96 | | | (12) all_57_9 = e3
% 141.52/20.96 | | |
% 141.52/20.96 | | | REF_CLOSE: (4), (5), (12) are inconsistent by sub-proof #581.
% 141.52/20.96 | | |
% 141.52/20.96 | | Case 2:
% 141.52/20.96 | | |
% 141.52/20.96 | | | (13) all_57_10 = e3 & op(e2, e0) = e3
% 141.52/20.96 | | |
% 141.52/20.96 | | | ALPHA: (13) implies:
% 141.52/20.96 | | | (14) all_57_10 = e3
% 141.52/20.96 | | |
% 141.52/20.96 | | | REF_CLOSE: (1), (6), (14) are inconsistent by sub-proof #935.
% 141.52/20.96 | | |
% 141.52/20.96 | | End of split
% 141.52/20.96 | |
% 141.52/20.96 | Case 2:
% 141.52/20.96 | |
% 141.52/20.96 | | (15) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.52/20.96 | | e3)
% 141.52/20.96 | |
% 141.52/20.96 | | REF_CLOSE: (2), (3), (5), (8), (9), (15) are inconsistent by sub-proof #393.
% 141.52/20.96 | |
% 141.52/20.96 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #393 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) op(e0, e0) = e1
% 141.52/20.97 (2) all_57_11 = e2
% 141.52/20.97 (3) ~ (e3 = e2)
% 141.52/20.97 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (5) ~ (e3 = e1)
% 141.52/20.97 (6) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (6) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (7) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (7) implies:
% 141.52/20.97 | | (8) all_57_11 = e3
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #1055.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (9) all_57_15 = e3 & op(e0, e0) = e3
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (9) implies:
% 141.52/20.97 | | (10) op(e0, e0) = e3
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #732.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #394 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) ~ (all_52_1 = e0)
% 141.52/20.97 (2) op(e2, e3) = all_52_1
% 141.52/20.97 (3) op(e2, e2) = e2
% 141.52/20.97 (4) ~ (e2 = e0)
% 141.52/20.97 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (6) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (6) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (7) all_57_2 = e0 & op(e2, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (1), (2), (5), (7) are inconsistent by sub-proof #1028.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (8) implies:
% 141.52/20.97 | | (9) op(e2, e2) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1076.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #395 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) all_54_7 = all_10_0
% 141.52/20.97 (2) all_54_7 = e1
% 141.52/20.97 (3) ~ (all_10_0 = e1)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.97 | (4) all_10_0 = e1
% 141.52/20.97 |
% 141.52/20.97 | SIMP: (4) implies:
% 141.52/20.97 | (5) all_10_0 = e1
% 141.52/20.97 |
% 141.52/20.97 | REDUCE: (3), (5) imply:
% 141.52/20.97 | (6) $false
% 141.52/20.97 |
% 141.52/20.97 | CLOSE: (6) is inconsistent.
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #396 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) all_54_7 = all_10_0
% 141.52/20.97 (2) all_54_7 = e2
% 141.52/20.97 (3) ~ (all_10_0 = e2)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.97 | (4) all_10_0 = e2
% 141.52/20.97 |
% 141.52/20.97 | SIMP: (4) implies:
% 141.52/20.97 | (5) all_10_0 = e2
% 141.52/20.97 |
% 141.52/20.97 | REDUCE: (3), (5) imply:
% 141.52/20.97 | (6) $false
% 141.52/20.97 |
% 141.52/20.97 | CLOSE: (6) is inconsistent.
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #397 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) all_54_7 = all_10_0
% 141.52/20.97 (2) all_54_7 = e3
% 141.52/20.97 (3) ~ (all_10_0 = e3)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.97 | (4) all_10_0 = e3
% 141.52/20.97 |
% 141.52/20.97 | SIMP: (4) implies:
% 141.52/20.97 | (5) all_10_0 = e3
% 141.52/20.97 |
% 141.52/20.97 | REDUCE: (3), (5) imply:
% 141.52/20.97 | (6) $false
% 141.52/20.97 |
% 141.52/20.97 | CLOSE: (6) is inconsistent.
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #398 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.97 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.97 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.97 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.97 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.97 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.97 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.97 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.97 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.97 (3) all_57_14 = e2
% 141.52/20.97 (4) all_57_15 = e1
% 141.52/20.97 (5) ~ (e3 = e0)
% 141.52/20.97 (6) op(e1, e1) = all_4_2
% 141.52/20.97 (7) op(e0, e0) = e1
% 141.52/20.97 (8) ~ (all_4_2 = e3)
% 141.52/20.97 (9) ~ (e1 = e0)
% 141.52/20.97 (10) op(e2, e2) = e2
% 141.52/20.97 (11) ~ (e2 = e0)
% 141.52/20.97 (12) ~ (e3 = e2)
% 141.52/20.97 (13) ~ (all_4_2 = e2)
% 141.52/20.97 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (15) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.97 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.97 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.97 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.97 (16) ~ (e3 = e1)
% 141.52/20.97 (17) op(e0, e0) = all_56_15
% 141.52/20.97 (18) all_56_15 = e1
% 141.52/20.97 (19) all_57_12 = e1
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (1) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (20) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.52/20.97 | | e3)
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (20) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (21) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (21) implies:
% 141.52/20.97 | | | (22) all_57_12 = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (16), (19), (22) are inconsistent by sub-proof #834.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (23) all_57_13 = e3 & op(e0, e2) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (23) implies:
% 141.52/20.97 | | | (24) all_57_13 = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | BETA: splitting (15) gives:
% 141.52/20.97 | | |
% 141.52/20.97 | | | Case 1:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | (25) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (13), (14), (17),
% 141.52/20.97 | | | | (18), (25) are inconsistent by sub-proof #401.
% 141.52/20.97 | | | |
% 141.52/20.97 | | | Case 2:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | (26) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 141.52/20.97 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 141.52/20.97 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.97 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | ALPHA: (26) implies:
% 141.52/20.97 | | | | (27) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.97 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | REF_CLOSE: (3), (5), (9), (11), (19), (24), (27) are inconsistent by
% 141.52/20.97 | | | | sub-proof #400.
% 141.52/20.97 | | | |
% 141.52/20.97 | | | End of split
% 141.52/20.97 | | |
% 141.52/20.97 | | End of split
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (28) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.52/20.97 | | e3)
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (3), (7), (12), (14), (16), (28) are inconsistent by sub-proof
% 141.52/20.97 | | #399.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #399 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) all_57_14 = e2
% 141.52/20.97 (2) op(e0, e0) = e1
% 141.52/20.97 (3) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.97 (4) ~ (e3 = e2)
% 141.52/20.97 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (6) ~ (e3 = e1)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (3) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (7) all_57_14 = e3 & op(e0, e1) = e3
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (7) implies:
% 141.52/20.97 | | (8) all_57_14 = e3
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #1011.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (9) all_57_15 = e3 & op(e0, e0) = e3
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (9) implies:
% 141.52/20.97 | | (10) op(e0, e0) = e3
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #732.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #400 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) all_57_14 = e2
% 141.52/20.97 (2) ~ (e3 = e0)
% 141.52/20.97 (3) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.52/20.97 (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.97 (4) ~ (e1 = e0)
% 141.52/20.97 (5) ~ (e2 = e0)
% 141.52/20.97 (6) all_57_13 = e3
% 141.52/20.97 (7) all_57_12 = e1
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (3) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (8) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (4), (7), (8) are inconsistent by sub-proof #837.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (9) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 141.52/20.97 | | e0)
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (9) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (10) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (2), (6), (10) are inconsistent by sub-proof #1016.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (11) all_57_14 = e0 & op(e0, e1) = e0
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #920.
% 141.52/20.97 | | |
% 141.52/20.97 | | End of split
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #401 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.97 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.97 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.97 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.97 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.97 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.97 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.97 (2) all_57_15 = e1
% 141.52/20.97 (3) ~ (e3 = e0)
% 141.52/20.97 (4) op(e1, e1) = all_4_2
% 141.52/20.97 (5) ~ (all_4_2 = e3)
% 141.52/20.97 (6) ~ (e1 = e0)
% 141.52/20.97 (7) op(e2, e2) = e2
% 141.52/20.97 (8) ~ (e2 = e0)
% 141.52/20.97 (9) ~ (all_4_2 = e2)
% 141.52/20.97 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (11) op(e0, e0) = all_56_15
% 141.52/20.97 (12) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.97 (13) all_56_15 = e1
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | ALPHA: (12) implies:
% 141.52/20.97 | (14) all_57_15 = e0
% 141.52/20.97 | (15) op(e0, e0) = e0
% 141.52/20.97 |
% 141.52/20.97 | COMBINE_EQS: (2), (14) imply:
% 141.52/20.97 | (16) e1 = e0
% 141.52/20.97 |
% 141.52/20.97 | COMBINE_EQS: (13), (16) imply:
% 141.52/20.97 | (17) all_56_15 = e0
% 141.52/20.97 |
% 141.52/20.97 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (15), (17) are
% 141.52/20.97 | inconsistent by sub-proof #743.
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #402 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) ~ (e2 = e1)
% 141.52/20.97 (2) op(e3, e3) = e2
% 141.52/20.97 (3) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.52/20.97 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/20.97 (4) ~ (e3 = e0)
% 141.52/20.97 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.97 (6) ~ (e1 = e0)
% 141.52/20.97 (7) ~ (e2 = e0)
% 141.52/20.97 (8) all_57_6 = e2
% 141.52/20.97 (9) ~ (e3 = e2)
% 141.52/20.97 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (11) ~ (e3 = e1)
% 141.52/20.97 (12) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (12) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (13) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (13) implies:
% 141.52/20.97 | | (14) op(e3, e3) = e1
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (1), (2), (10), (14) are inconsistent by sub-proof #818.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (15) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (15) implies:
% 141.52/20.97 | | (16) all_57_2 = e1
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (3) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (17) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 141.52/20.97 | | | e0)
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (2), (6), (7), (10), (16), (17) are inconsistent by sub-proof
% 141.52/20.97 | | | #405.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (18) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 141.52/20.97 | | | e0)
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (11), (16), (18) are
% 141.52/20.97 | | | inconsistent by sub-proof #403.
% 141.52/20.97 | | |
% 141.52/20.97 | | End of split
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #403 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/20.97 (2) op(e3, e3) = e2
% 141.52/20.97 (3) ~ (e3 = e0)
% 141.52/20.97 (4) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.97 (5) ~ (e2 = e0)
% 141.52/20.97 (6) all_57_6 = e2
% 141.52/20.97 (7) ~ (e3 = e2)
% 141.52/20.97 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (9) ~ (e3 = e1)
% 141.52/20.97 (10) all_57_2 = e1
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (1) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (11) all_57_6 = e0 & op(e1, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (5), (6), (11) are inconsistent by sub-proof #994.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (12) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (12) implies:
% 141.52/20.97 | | (13) all_57_12 = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (13) are inconsistent by
% 141.52/20.97 | | sub-proof #404.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #404 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) op(e3, e3) = e2
% 141.52/20.97 (2) ~ (e3 = e0)
% 141.52/20.97 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.52/20.97 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.52/20.97 (4) all_57_6 = e2
% 141.52/20.97 (5) ~ (e3 = e2)
% 141.52/20.97 (6) all_57_12 = e0
% 141.52/20.97 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (8) ~ (e3 = e1)
% 141.52/20.97 (9) all_57_2 = e1
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (3) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 141.52/20.97 | | e3)
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (10) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (11) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (11) implies:
% 141.52/20.97 | | | (12) op(e3, e3) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (1), (5), (7), (12) are inconsistent by sub-proof #450.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (13) all_57_2 = e3 & op(e2, e3) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (13) implies:
% 141.52/20.97 | | | (14) all_57_2 = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (8), (9), (14) are inconsistent by sub-proof #701.
% 141.52/20.97 | | |
% 141.52/20.97 | | End of split
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (15) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 141.52/20.97 | | e3)
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (15) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (16) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (16) implies:
% 141.52/20.97 | | | (17) all_57_6 = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (4), (5), (17) are inconsistent by sub-proof #1004.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (18) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (18) implies:
% 141.52/20.97 | | | (19) all_57_12 = e3
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (2), (6), (19) are inconsistent by sub-proof #828.
% 141.52/20.97 | | |
% 141.52/20.97 | | End of split
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #405 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 141.52/20.97 (2) op(e3, e3) = e2
% 141.52/20.97 (3) ~ (e1 = e0)
% 141.52/20.97 (4) ~ (e2 = e0)
% 141.52/20.97 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (6) all_57_2 = e1
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (1) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (7) implies:
% 141.52/20.97 | | (8) op(e3, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #880.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #449.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #406 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) ~ (e2 = e1)
% 141.52/20.97 (2) ~ (all_52_9 = e2)
% 141.52/20.97 (3) op(e3, e3) = e2
% 141.52/20.97 (4) ~ (e3 = e0)
% 141.52/20.97 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.52/20.97 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.52/20.97 (6) ~ (e1 = e0)
% 141.52/20.97 (7) ~ (e2 = e0)
% 141.52/20.97 (8) ~ (e3 = e2)
% 141.52/20.97 (9) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 141.52/20.97 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (11) ~ (e3 = e1)
% 141.52/20.97 (12) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.97 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.97 (13) op(e2, e1) = all_52_9
% 141.52/20.97 (14) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.97 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (9) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (15) all_57_4 = e2 & op(e3, e1) = e2
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (15) implies:
% 141.52/20.97 | | (16) all_57_4 = e2
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (14), (16)
% 141.52/20.97 | | are inconsistent by sub-proof #407.
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (17) all_57_5 = e2 & op(e2, e1) = e2
% 141.52/20.97 | |
% 141.52/20.97 | | ALPHA: (17) implies:
% 141.52/20.97 | | (18) op(e2, e1) = e2
% 141.52/20.97 | |
% 141.52/20.97 | | REF_CLOSE: (2), (10), (13), (18) are inconsistent by sub-proof #890.
% 141.52/20.97 | |
% 141.52/20.97 | End of split
% 141.52/20.97 |
% 141.52/20.97 End of proof
% 141.52/20.97
% 141.52/20.97 Sub-proof #407 shows that the following formulas are inconsistent:
% 141.52/20.97 ----------------------------------------------------------------
% 141.52/20.97 (1) all_57_4 = e2
% 141.52/20.97 (2) ~ (e2 = e1)
% 141.52/20.97 (3) op(e3, e3) = e2
% 141.52/20.97 (4) ~ (e3 = e0)
% 141.52/20.97 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.52/20.97 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.52/20.97 (6) ~ (e1 = e0)
% 141.52/20.97 (7) ~ (e2 = e0)
% 141.52/20.97 (8) ~ (e3 = e2)
% 141.52/20.97 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.97 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.97 (10) ~ (e3 = e1)
% 141.52/20.97 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.97 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.97 (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 141.52/20.97 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.97
% 141.52/20.97 Begin of proof
% 141.52/20.97 |
% 141.52/20.97 | BETA: splitting (5) gives:
% 141.52/20.97 |
% 141.52/20.97 | Case 1:
% 141.52/20.97 | |
% 141.52/20.97 | | (13) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 141.52/20.97 | | e1)
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (13) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (14) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (14) implies:
% 141.52/20.97 | | | (15) op(e3, e3) = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (2), (3), (9), (15) are inconsistent by sub-proof #818.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (16) all_57_1 = e1 & op(e3, e2) = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (16) implies:
% 141.52/20.97 | | | (17) all_57_1 = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | BETA: splitting (12) gives:
% 141.52/20.97 | | |
% 141.52/20.97 | | | Case 1:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | (18) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 141.52/20.97 | | | | = e0)
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | BETA: splitting (18) gives:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | Case 1:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | (19) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | ALPHA: (19) implies:
% 141.52/20.97 | | | | | (20) op(e3, e3) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | REF_CLOSE: (3), (7), (9), (20) are inconsistent by sub-proof #880.
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | Case 2:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | (21) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | REF_CLOSE: (6), (17), (21) are inconsistent by sub-proof #416.
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | End of split
% 141.52/20.97 | | | |
% 141.52/20.97 | | | Case 2:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | (22) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 141.52/20.97 | | | | = e0)
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | BETA: splitting (22) gives:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | Case 1:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | (23) all_57_4 = e0 & op(e3, e1) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | REF_CLOSE: (1), (7), (23) are inconsistent by sub-proof #1013.
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | Case 2:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | (24) all_57_9 = e0 & op(e3, e0) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | ALPHA: (24) implies:
% 141.52/20.97 | | | | | (25) all_57_9 = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | BETA: splitting (11) gives:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | Case 1:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 141.52/20.97 | | | | | | e2) = e3)
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | BETA: splitting (26) gives:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | Case 1:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (27) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | ALPHA: (27) implies:
% 141.52/20.97 | | | | | | | (28) op(e3, e3) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (3), (8), (9), (28) are inconsistent by sub-proof #450.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | Case 2:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (29) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (10), (17), (29) are inconsistent by sub-proof #724.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | End of split
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | Case 2:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | (30) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 141.52/20.97 | | | | | | e0) = e3)
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | BETA: splitting (30) gives:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | Case 1:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (31) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | ALPHA: (31) implies:
% 141.52/20.97 | | | | | | | (32) all_57_4 = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (1), (8), (32) are inconsistent by sub-proof #821.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | Case 2:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (33) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | ALPHA: (33) implies:
% 141.52/20.97 | | | | | | | (34) all_57_9 = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (4), (25), (34) are inconsistent by sub-proof #863.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | End of split
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | End of split
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | End of split
% 141.52/20.97 | | | |
% 141.52/20.97 | | | End of split
% 141.52/20.97 | | |
% 141.52/20.97 | | End of split
% 141.52/20.97 | |
% 141.52/20.97 | Case 2:
% 141.52/20.97 | |
% 141.52/20.97 | | (35) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 141.52/20.97 | | e1)
% 141.52/20.97 | |
% 141.52/20.97 | | BETA: splitting (35) gives:
% 141.52/20.97 | |
% 141.52/20.97 | | Case 1:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (36) all_57_4 = e1 & op(e3, e1) = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | REF_CLOSE: (1), (2), (36) are inconsistent by sub-proof #891.
% 141.52/20.97 | | |
% 141.52/20.97 | | Case 2:
% 141.52/20.97 | | |
% 141.52/20.97 | | | (37) all_57_9 = e1 & op(e3, e0) = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | ALPHA: (37) implies:
% 141.52/20.97 | | | (38) all_57_9 = e1
% 141.52/20.97 | | |
% 141.52/20.97 | | | BETA: splitting (12) gives:
% 141.52/20.97 | | |
% 141.52/20.97 | | | Case 1:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | (39) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2)
% 141.52/20.97 | | | | = e0)
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | BETA: splitting (39) gives:
% 141.52/20.97 | | | |
% 141.52/20.97 | | | | Case 1:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | (40) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | ALPHA: (40) implies:
% 141.52/20.97 | | | | | (41) op(e3, e3) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | REF_CLOSE: (3), (7), (9), (41) are inconsistent by sub-proof #880.
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | Case 2:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | (42) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | ALPHA: (42) implies:
% 141.52/20.97 | | | | | (43) all_57_1 = e0
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | BETA: splitting (11) gives:
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | | Case 1:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | (44) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 141.52/20.97 | | | | | | e2) = e3)
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | BETA: splitting (44) gives:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | Case 1:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (45) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | ALPHA: (45) implies:
% 141.52/20.97 | | | | | | | (46) op(e3, e3) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (3), (8), (9), (46) are inconsistent by sub-proof #450.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | Case 2:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (47) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (4), (43), (47) are inconsistent by sub-proof #408.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | End of split
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | Case 2:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | (48) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 141.52/20.97 | | | | | | e0) = e3)
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | BETA: splitting (48) gives:
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | | Case 1:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (49) all_57_4 = e3 & op(e3, e1) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | ALPHA: (49) implies:
% 141.52/20.97 | | | | | | | (50) all_57_4 = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (1), (8), (50) are inconsistent by sub-proof #821.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | Case 2:
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | (51) all_57_9 = e3 & op(e3, e0) = e3
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | | REF_CLOSE: (10), (38), (51) are inconsistent by sub-proof #487.
% 141.52/20.97 | | | | | | |
% 141.52/20.97 | | | | | | End of split
% 141.52/20.97 | | | | | |
% 141.52/20.97 | | | | | End of split
% 141.52/20.97 | | | | |
% 141.52/20.97 | | | | End of split
% 141.52/20.97 | | | |
% 141.52/20.98 | | | Case 2:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (52) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0)
% 141.52/20.98 | | | | = e0)
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | BETA: splitting (52) gives:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | Case 1:
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | (53) all_57_4 = e0 & op(e3, e1) = e0
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | REF_CLOSE: (1), (7), (53) are inconsistent by sub-proof #1013.
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | Case 2:
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | (54) all_57_9 = e0 & op(e3, e0) = e0
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | REF_CLOSE: (6), (38), (54) are inconsistent by sub-proof #813.
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | End of split
% 141.52/20.98 | | | |
% 141.52/20.98 | | | End of split
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #408 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/20.98 (2) all_57_1 = e0
% 141.52/20.98 (3) ~ (e3 = e0)
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | ALPHA: (1) implies:
% 141.52/20.98 | (4) all_57_1 = e3
% 141.52/20.98 |
% 141.52/20.98 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.98 | (5) e3 = e0
% 141.52/20.98 |
% 141.52/20.98 | SIMP: (5) implies:
% 141.52/20.98 | (6) e3 = e0
% 141.52/20.98 |
% 141.52/20.98 | REDUCE: (3), (6) imply:
% 141.52/20.98 | (7) $false
% 141.52/20.98 |
% 141.52/20.98 | CLOSE: (7) is inconsistent.
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #409 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) ~ (all_52_1 = e2)
% 141.52/20.98 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/20.98 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/20.98 (3) ~ (all_52_14 = e1)
% 141.52/20.98 (4) ~ (all_52_12 = e3)
% 141.52/20.98 (5) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.98 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/20.98 (6) ~ (all_52_8 = e3)
% 141.52/20.98 (7) ~ (e2 = e1)
% 141.52/20.98 (8) op(e3, e3) = e3
% 141.52/20.98 (9) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.98 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.98 (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 141.52/20.98 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.98 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.52/20.98 all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.98 (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.52/20.98 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0)
% 141.52/20.98 & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/20.98 (11) op(e1, e1) = e0
% 141.52/20.98 (12) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.52/20.98 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/20.98 (13) ~ (e3 = e0)
% 141.52/20.98 (14) op(e1, e1) = all_4_2
% 141.52/20.98 (15) ~ (all_52_4 = e3)
% 141.52/20.98 (16) all_57_11 = e0 & op(e1, e0) = e0
% 141.52/20.98 (17) op(e3, e1) = all_52_8
% 141.52/20.98 (18) ~ (all_52_7 = e2)
% 141.52/20.98 (19) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/20.98 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/20.98 e2)
% 141.52/20.98 (20) op(e2, e3) = all_52_1
% 141.52/20.98 (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.52/20.98 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.52/20.98 (22) ~ (all_4_2 = e3)
% 141.52/20.98 (23) ~ (e1 = e0)
% 141.52/20.98 (24) op(e2, e2) = e2
% 141.52/20.98 (25) op(e3, e2) = all_52_4
% 141.52/20.98 (26) ~ (e2 = e0)
% 141.52/20.98 (27) ~ (e3 = e2)
% 141.52/20.98 (28) all_57_0 = e3
% 141.52/20.98 (29) op(e3, e0) = all_52_12
% 141.52/20.98 (30) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/20.98 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/20.98 (31) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/20.98 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/20.98 (32) ~ (all_4_2 = e2)
% 141.52/20.98 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (34) ~ (e3 = e1)
% 141.52/20.98 (35) op(e0, e2) = all_52_7
% 141.52/20.98 (36) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/20.98 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/20.98 (37) op(e0, e0) = all_56_15
% 141.52/20.98 (38) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/20.98 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/20.98 (39) ~ (all_52_13 = e1)
% 141.52/20.98 (40) op(e2, e0) = all_52_13
% 141.52/20.98 (41) op(e1, e0) = all_52_14
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | ALPHA: (16) implies:
% 141.52/20.98 | (42) all_57_11 = e0
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (30) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (43) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 141.52/20.98 | | e3)
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (43) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (44) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (10), (12), (13), (14),
% 141.52/20.98 | | | (15), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 141.52/20.98 | | | (26), (27), (29), (33), (34), (35), (36), (37), (38), (39),
% 141.52/20.98 | | | (40), (44) are inconsistent by sub-proof #443.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (45) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (3), (7), (9), (11), (14), (23), (26), (27), (31), (32), (33),
% 141.52/20.98 | | | (34), (41), (42), (45) are inconsistent by sub-proof #410.
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (46) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 141.52/20.98 | | e3)
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (46) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (47) all_57_8 = e3 & op(e1, e1) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (47) implies:
% 141.52/20.98 | | | (48) op(e1, e1) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (14), (22), (33), (48) are inconsistent by sub-proof #1127.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (49) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (49) implies:
% 141.52/20.98 | | | (50) all_57_11 = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | COMBINE_EQS: (42), (50) imply:
% 141.52/20.98 | | | (51) e3 = e0
% 141.52/20.98 | | |
% 141.52/20.98 | | | SIMP: (51) implies:
% 141.52/20.98 | | | (52) e3 = e0
% 141.52/20.98 | | |
% 141.52/20.98 | | | COMBINE_EQS: (28), (52) imply:
% 141.52/20.98 | | | (53) all_57_0 = e0
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (4), (6), (13), (15), (17), (25), (29), (33), (36), (53) are
% 141.52/20.98 | | | inconsistent by sub-proof #1103.
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #410 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) ~ (all_52_14 = e1)
% 141.52/20.98 (2) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/20.98 (3) all_57_11 = e0
% 141.52/20.98 (4) ~ (e2 = e1)
% 141.52/20.98 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/20.98 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/20.98 (6) op(e1, e1) = e0
% 141.52/20.98 (7) op(e1, e1) = all_4_2
% 141.52/20.98 (8) ~ (e1 = e0)
% 141.52/20.98 (9) ~ (e2 = e0)
% 141.52/20.98 (10) ~ (e3 = e2)
% 141.52/20.98 (11) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/20.98 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/20.98 (12) ~ (all_4_2 = e2)
% 141.52/20.98 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (14) ~ (e3 = e1)
% 141.52/20.98 (15) op(e1, e0) = all_52_14
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | ALPHA: (2) implies:
% 141.52/20.98 | (16) all_57_7 = e3
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (5) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (17) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.52/20.98 | | e1)
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (17) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (18) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (18) implies:
% 141.52/20.98 | | | (19) all_57_6 = e1
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (3), (4), (7), (9), (10), (11), (12), (13), (16), (19) are
% 141.52/20.98 | | | inconsistent by sub-proof #411.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (20) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (14), (16), (20) are inconsistent by sub-proof #1058.
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (21) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.52/20.98 | | e1)
% 141.52/20.98 | |
% 141.52/20.98 | | REF_CLOSE: (1), (6), (8), (13), (15), (21) are inconsistent by sub-proof
% 141.52/20.98 | | #452.
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #411 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) all_57_11 = e0
% 141.52/20.98 (2) ~ (e2 = e1)
% 141.52/20.98 (3) op(e1, e1) = all_4_2
% 141.52/20.98 (4) ~ (e2 = e0)
% 141.52/20.98 (5) ~ (e3 = e2)
% 141.52/20.98 (6) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/20.98 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/20.98 (7) ~ (all_4_2 = e2)
% 141.52/20.98 (8) all_57_6 = e1
% 141.52/20.98 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (10) all_57_7 = e3
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (6) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (11) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 141.52/20.98 | | e2)
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (11) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (12) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (12) implies:
% 141.52/20.98 | | | (13) all_57_6 = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #700.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (14) all_57_7 = e2 & op(e1, e2) = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (5), (10), (14) are inconsistent by sub-proof #1084.
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (15) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 141.52/20.98 | | e2)
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (15) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (16) all_57_8 = e2 & op(e1, e1) = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (16) implies:
% 141.52/20.98 | | | (17) op(e1, e1) = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (3), (7), (9), (17) are inconsistent by sub-proof #1124.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (18) all_57_11 = e2 & op(e1, e0) = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (18) implies:
% 141.52/20.98 | | | (19) all_57_11 = e2
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (1), (4), (19) are inconsistent by sub-proof #996.
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #412 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/20.98 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.98 (2) all_57_14 = e2
% 141.52/20.98 (3) ~ (e3 = e0)
% 141.52/20.98 (4) op(e0, e0) = e1
% 141.52/20.98 (5) all_57_13 = e1
% 141.52/20.98 (6) ~ (e3 = e2)
% 141.52/20.98 (7) all_57_12 = e0
% 141.52/20.98 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (9) ~ (e3 = e1)
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (1) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (10) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.52/20.98 | | e3)
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (10) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (11) all_57_12 = e3 & op(e0, e3) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | ALPHA: (11) implies:
% 141.52/20.98 | | | (12) all_57_12 = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | COMBINE_EQS: (7), (12) imply:
% 141.52/20.98 | | | (13) e3 = e0
% 141.52/20.98 | | |
% 141.52/20.98 | | | REDUCE: (3), (13) imply:
% 141.52/20.98 | | | (14) $false
% 141.52/20.98 | | |
% 141.52/20.98 | | | CLOSE: (14) is inconsistent.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (15) all_57_13 = e3 & op(e0, e2) = e3
% 141.52/20.98 | | |
% 141.52/20.98 | | | REF_CLOSE: (5), (9), (15) are inconsistent by sub-proof #414.
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (16) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.52/20.98 | | e3)
% 141.52/20.98 | |
% 141.52/20.98 | | REF_CLOSE: (2), (4), (6), (8), (9), (16) are inconsistent by sub-proof #413.
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #413 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) all_57_14 = e2
% 141.52/20.98 (2) op(e0, e0) = e1
% 141.52/20.98 (3) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/20.98 (4) ~ (e3 = e2)
% 141.52/20.98 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (6) ~ (e3 = e1)
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (3) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (7) all_57_14 = e3 & op(e0, e1) = e3
% 141.52/20.98 | |
% 141.52/20.98 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #803.
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 141.52/20.98 | |
% 141.52/20.98 | | ALPHA: (8) implies:
% 141.52/20.98 | | (9) op(e0, e0) = e3
% 141.52/20.98 | |
% 141.52/20.98 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #732.
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #414 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) all_57_13 = e3 & op(e0, e2) = e3
% 141.52/20.98 (2) all_57_13 = e1
% 141.52/20.98 (3) ~ (e3 = e1)
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | ALPHA: (1) implies:
% 141.52/20.98 | (4) all_57_13 = e3
% 141.52/20.98 |
% 141.52/20.98 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.98 | (5) e3 = e1
% 141.52/20.98 |
% 141.52/20.98 | REDUCE: (3), (5) imply:
% 141.52/20.98 | (6) $false
% 141.52/20.98 |
% 141.52/20.98 | CLOSE: (6) is inconsistent.
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #415 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) ~ (e2 = e1)
% 141.52/20.98 (2) all_57_7 = e2
% 141.52/20.98 (3) ~ (e3 = e0)
% 141.52/20.98 (4) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 141.52/20.98 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/20.98 (5) ~ (e1 = e0)
% 141.52/20.98 (6) op(e2, e2) = e2
% 141.52/20.98 (7) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 141.52/20.98 (8) ~ (e2 = e0)
% 141.52/20.98 (9) ~ (e3 = e2)
% 141.52/20.98 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (11) ~ (e3 = e1)
% 141.52/20.98 (12) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.52/20.98 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (7) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (13) all_57_1 = e1 & op(e3, e2) = e1
% 141.52/20.98 | |
% 141.52/20.98 | | ALPHA: (13) implies:
% 141.52/20.98 | | (14) all_57_1 = e1
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (4) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (15) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 141.52/20.98 | | | e0)
% 141.52/20.98 | | |
% 141.52/20.98 | | | BETA: splitting (15) gives:
% 141.52/20.98 | | |
% 141.52/20.98 | | | Case 1:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (16) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | REF_CLOSE: (5), (14), (16) are inconsistent by sub-proof #416.
% 141.52/20.98 | | | |
% 141.52/20.98 | | | Case 2:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (17) all_57_3 = e0 & op(e2, e2) = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | ALPHA: (17) implies:
% 141.52/20.98 | | | | (18) op(e2, e2) = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | REF_CLOSE: (6), (8), (10), (18) are inconsistent by sub-proof #1076.
% 141.52/20.98 | | | |
% 141.52/20.98 | | | End of split
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (19) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.52/20.98 | | | e0)
% 141.52/20.98 | | |
% 141.52/20.98 | | | BETA: splitting (19) gives:
% 141.52/20.98 | | |
% 141.52/20.98 | | | Case 1:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (20) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | ALPHA: (20) implies:
% 141.52/20.98 | | | | (21) all_57_7 = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | REF_CLOSE: (2), (8), (21) are inconsistent by sub-proof #578.
% 141.52/20.98 | | | |
% 141.52/20.98 | | | Case 2:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (22) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | ALPHA: (22) implies:
% 141.52/20.98 | | | | (23) all_57_13 = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | REF_CLOSE: (2), (3), (6), (9), (10), (11), (12), (14), (23) are
% 141.52/20.98 | | | | inconsistent by sub-proof #722.
% 141.52/20.98 | | | |
% 141.52/20.98 | | | End of split
% 141.52/20.98 | | |
% 141.52/20.98 | | End of split
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (24) all_57_3 = e1 & op(e2, e2) = e1
% 141.52/20.98 | |
% 141.52/20.98 | | ALPHA: (24) implies:
% 141.52/20.98 | | (25) op(e2, e2) = e1
% 141.52/20.98 | |
% 141.52/20.98 | | REF_CLOSE: (1), (6), (10), (25) are inconsistent by sub-proof #749.
% 141.52/20.98 | |
% 141.52/20.98 | End of split
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #416 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) all_57_1 = e0 & op(e3, e2) = e0
% 141.52/20.98 (2) all_57_1 = e1
% 141.52/20.98 (3) ~ (e1 = e0)
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | ALPHA: (1) implies:
% 141.52/20.98 | (4) all_57_1 = e0
% 141.52/20.98 |
% 141.52/20.98 | COMBINE_EQS: (2), (4) imply:
% 141.52/20.98 | (5) e1 = e0
% 141.52/20.98 |
% 141.52/20.98 | REDUCE: (3), (5) imply:
% 141.52/20.98 | (6) $false
% 141.52/20.98 |
% 141.52/20.98 | CLOSE: (6) is inconsistent.
% 141.52/20.98 |
% 141.52/20.98 End of proof
% 141.52/20.98
% 141.52/20.98 Sub-proof #417 shows that the following formulas are inconsistent:
% 141.52/20.98 ----------------------------------------------------------------
% 141.52/20.98 (1) ~ (all_52_4 = all_52_7)
% 141.52/20.98 (2) ~ (all_52_14 = e1)
% 141.52/20.98 (3) ~ (all_52_12 = e3)
% 141.52/20.98 (4) ~ (all_52_8 = e3)
% 141.52/20.98 (5) ~ (all_52_4 = all_52_8)
% 141.52/20.98 (6) all_54_7 = all_52_13
% 141.52/20.98 (7) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/20.98 (8) all_54_3 = all_52_12
% 141.52/20.98 (9) ~ (all_52_9 = all_52_13)
% 141.52/20.98 (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 141.52/20.98 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.98 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 141.52/20.98 all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.52/20.98 (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 141.52/20.98 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0)
% 141.52/20.98 & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/20.98 (11) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.98 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.98 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.98 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.98 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 141.52/20.98 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 141.52/20.98 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 141.52/20.98 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.98 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.98 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.98 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 141.52/20.98 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 141.52/20.98 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 141.52/20.98 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 141.52/20.98 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 141.52/20.98 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/20.98 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 141.52/20.98 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 141.52/20.98 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 141.52/20.98 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 141.52/20.98 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.98 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.98 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.98 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.98 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.98 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.98 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.98 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.98 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.98 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 141.52/20.98 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 141.52/20.98 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 141.52/20.98 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 141.52/20.98 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 141.52/20.98 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.98 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/20.98 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 141.52/20.98 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.98 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.98 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 141.52/20.98 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.98 (12) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.52/20.98 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.98 (13) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 141.52/20.98 (14) all_54_1 = all_52_4
% 141.52/20.98 (15) all_54_2 = all_52_8
% 141.52/20.98 (16) op(e1, e1) = all_4_2
% 141.52/20.98 (17) ~ (all_52_4 = e3)
% 141.52/20.98 (18) op(e3, e1) = all_52_8
% 141.52/20.98 (19) op(e0, e0) = e1
% 141.52/20.98 (20) ~ (all_52_12 = e1)
% 141.52/20.98 (21) ~ (all_4_2 = e3)
% 141.52/20.98 (22) all_54_1 = e3 | all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 141.52/20.98 (23) ~ (all_52_8 = all_52_12)
% 141.52/20.98 (24) all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 141.52/20.98 (25) ~ (all_52_11 = e0)
% 141.52/20.98 (26) op(e0, e1) = all_52_11
% 141.52/20.98 (27) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.52/20.98 (28) ~ (all_4_2 = e2)
% 141.52/20.98 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.98 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.98 (30) ~ (all_52_12 = all_52_13)
% 141.52/20.98 (31) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.98 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.98 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.98 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.98 (32) ~ (all_52_8 = e0)
% 141.52/20.98 (33) ~ (all_52_13 = e2)
% 141.52/20.98 (34) op(e0, e2) = all_52_7
% 141.52/20.98 (35) op(e0, e0) = all_56_15
% 141.52/20.98 (36) all_56_15 = e1
% 141.52/20.98 (37) op(e2, e1) = all_52_9
% 141.52/20.98 (38) ~ (all_52_13 = e1)
% 141.52/20.98 (39) ~ (all_52_4 = all_52_12)
% 141.52/20.98 (40) op(e1, e0) = all_52_14
% 141.52/20.98
% 141.52/20.98 Begin of proof
% 141.52/20.98 |
% 141.52/20.98 | ALPHA: (7) implies:
% 141.52/20.98 | (41) op(e1, e2) = e1
% 141.52/20.98 |
% 141.52/20.98 | BETA: splitting (24) gives:
% 141.52/20.98 |
% 141.52/20.98 | Case 1:
% 141.52/20.98 | |
% 141.52/20.98 | | (42) all_54_7 = e2
% 141.52/20.98 | |
% 141.52/20.98 | | COMBINE_EQS: (6), (42) imply:
% 141.52/20.98 | | (43) all_52_13 = e2
% 141.52/20.98 | |
% 141.52/20.98 | | REDUCE: (33), (43) imply:
% 141.52/20.98 | | (44) $false
% 141.52/20.98 | |
% 141.52/20.98 | | CLOSE: (44) is inconsistent.
% 141.52/20.98 | |
% 141.52/20.98 | Case 2:
% 141.52/20.98 | |
% 141.52/20.98 | | (45) all_54_7 = e1 | all_54_7 = e0
% 141.52/20.98 | |
% 141.52/20.98 | | BETA: splitting (45) gives:
% 141.52/20.98 | |
% 141.52/20.98 | | Case 1:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (46) all_54_7 = e1
% 141.52/20.98 | | |
% 141.52/20.98 | | | COMBINE_EQS: (6), (46) imply:
% 141.52/20.98 | | | (47) all_52_13 = e1
% 141.52/20.98 | | |
% 141.52/20.98 | | | REDUCE: (38), (47) imply:
% 141.52/20.98 | | | (48) $false
% 141.52/20.98 | | |
% 141.52/20.98 | | | CLOSE: (48) is inconsistent.
% 141.52/20.98 | | |
% 141.52/20.98 | | Case 2:
% 141.52/20.98 | | |
% 141.52/20.98 | | | (49) all_54_7 = e0
% 141.52/20.98 | | |
% 141.52/20.98 | | | COMBINE_EQS: (6), (49) imply:
% 141.52/20.98 | | | (50) all_52_13 = e0
% 141.52/20.98 | | |
% 141.52/20.98 | | | REDUCE: (9), (50) imply:
% 141.52/20.98 | | | (51) ~ (all_52_9 = e0)
% 141.52/20.98 | | |
% 141.52/20.98 | | | REDUCE: (30), (50) imply:
% 141.52/20.98 | | | (52) ~ (all_52_12 = e0)
% 141.52/20.98 | | |
% 141.52/20.98 | | | BETA: splitting (27) gives:
% 141.52/20.98 | | |
% 141.52/20.98 | | | Case 1:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (53) all_54_3 = e3
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | REF_CLOSE: (3), (8), (53) are inconsistent by sub-proof #439.
% 141.52/20.98 | | | |
% 141.52/20.98 | | | Case 2:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | (54) all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | BETA: splitting (54) gives:
% 141.52/20.98 | | | |
% 141.52/20.98 | | | | Case 1:
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | (55) all_54_3 = e2
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | COMBINE_EQS: (8), (55) imply:
% 141.52/20.98 | | | | | (56) all_52_12 = e2
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | SIMP: (56) implies:
% 141.52/20.98 | | | | | (57) all_52_12 = e2
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | REDUCE: (39), (57) imply:
% 141.52/20.98 | | | | | (58) ~ (all_52_4 = e2)
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | REDUCE: (23), (57) imply:
% 141.52/20.98 | | | | | (59) ~ (all_52_8 = e2)
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | BETA: splitting (13) gives:
% 141.52/20.98 | | | | |
% 141.52/20.98 | | | | | Case 1:
% 141.52/20.98 | | | | | |
% 141.52/20.98 | | | | | | (60) all_54_2 = e3
% 141.52/20.98 | | | | | |
% 141.52/20.98 | | | | | | REF_CLOSE: (4), (15), (60) are inconsistent by sub-proof #538.
% 141.52/20.98 | | | | | |
% 141.52/20.98 | | | | | Case 2:
% 141.52/20.98 | | | | | |
% 141.52/20.98 | | | | | | (61) ~ (all_54_2 = e3)
% 141.52/20.98 | | | | | | (62) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 141.52/20.98 | | | | | |
% 141.52/20.98 | | | | | | BETA: splitting (62) gives:
% 141.52/20.98 | | | | | |
% 141.52/20.98 | | | | | | Case 1:
% 141.52/20.98 | | | | | | |
% 141.52/20.98 | | | | | | | (63) all_54_2 = e2
% 141.52/20.98 | | | | | | |
% 141.52/20.98 | | | | | | | REF_CLOSE: (15), (59), (63) are inconsistent by sub-proof #537.
% 141.52/20.98 | | | | | | |
% 141.52/20.98 | | | | | | Case 2:
% 141.52/20.98 | | | | | | |
% 141.52/20.98 | | | | | | | (64) ~ (all_54_2 = e2)
% 141.52/20.98 | | | | | | | (65) all_54_2 = e1 | all_54_2 = e0
% 141.52/20.98 | | | | | | |
% 141.52/20.98 | | | | | | | BETA: splitting (65) gives:
% 141.52/20.98 | | | | | | |
% 141.52/20.98 | | | | | | | Case 1:
% 141.52/20.98 | | | | | | | |
% 141.52/20.98 | | | | | | | | (66) all_54_2 = e1
% 141.52/20.98 | | | | | | | |
% 141.52/20.98 | | | | | | | | COMBINE_EQS: (15), (66) imply:
% 141.52/20.98 | | | | | | | | (67) all_52_8 = e1
% 141.52/20.98 | | | | | | | |
% 141.52/20.98 | | | | | | | | SIMP: (67) implies:
% 141.52/20.99 | | | | | | | | (68) all_52_8 = e1
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | REDUCE: (5), (68) imply:
% 141.52/20.99 | | | | | | | | (69) ~ (all_52_4 = e1)
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | REDUCE: (4), (68) imply:
% 141.52/20.99 | | | | | | | | (70) ~ (e3 = e1)
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | SIMP: (70) implies:
% 141.52/20.99 | | | | | | | | (71) ~ (e3 = e1)
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | REDUCE: (59), (68) imply:
% 141.52/20.99 | | | | | | | | (72) ~ (e2 = e1)
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | SIMP: (72) implies:
% 141.52/20.99 | | | | | | | | (73) ~ (e2 = e1)
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | BETA: splitting (22) gives:
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | Case 1:
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | | (74) all_54_1 = e3
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | | REF_CLOSE: (14), (17), (74) are inconsistent by sub-proof
% 141.52/20.99 | | | | | | | | | #424.
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | Case 2:
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | | (75) all_54_1 = e2 | all_54_1 = e1 | all_54_1 = e0
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | | BETA: splitting (75) gives:
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | | Case 1:
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | (76) all_54_1 = e2
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | REF_CLOSE: (14), (58), (76) are inconsistent by sub-proof
% 141.52/20.99 | | | | | | | | | | #423.
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | Case 2:
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | (77) all_54_1 = e1 | all_54_1 = e0
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | BETA: splitting (77) gives:
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | Case 1:
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | (78) all_54_1 = e1
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | COMBINE_EQS: (14), (78) imply:
% 141.52/20.99 | | | | | | | | | | | (79) all_52_4 = e1
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | SIMP: (79) implies:
% 141.52/20.99 | | | | | | | | | | | (80) all_52_4 = e1
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | REDUCE: (69), (80) imply:
% 141.52/20.99 | | | | | | | | | | | (81) $false
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | CLOSE: (81) is inconsistent.
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | Case 2:
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | (82) all_54_1 = e0
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | COMBINE_EQS: (14), (82) imply:
% 141.52/20.99 | | | | | | | | | | | (83) all_52_4 = e0
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | SIMP: (83) implies:
% 141.52/20.99 | | | | | | | | | | | (84) all_52_4 = e0
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | REDUCE: (1), (84) imply:
% 141.52/20.99 | | | | | | | | | | | (85) ~ (all_52_7 = e0)
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | SIMP: (85) implies:
% 141.52/20.99 | | | | | | | | | | | (86) ~ (all_52_7 = e0)
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | REDUCE: (69), (84) imply:
% 141.52/20.99 | | | | | | | | | | | (87) ~ (e1 = e0)
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | SIMP: (87) implies:
% 141.52/20.99 | | | | | | | | | | | (88) ~ (e1 = e0)
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | | REF_CLOSE: (2), (10), (11), (12), (16), (18), (19), (21),
% 141.52/20.99 | | | | | | | | | | | (25), (26), (28), (29), (31), (32), (34), (35),
% 141.52/20.99 | | | | | | | | | | | (36), (37), (40), (41), (51), (71), (73), (86),
% 141.52/20.99 | | | | | | | | | | | (88) are inconsistent by sub-proof #419.
% 141.52/20.99 | | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | | End of split
% 141.52/20.99 | | | | | | | | | |
% 141.52/20.99 | | | | | | | | | End of split
% 141.52/20.99 | | | | | | | | |
% 141.52/20.99 | | | | | | | | End of split
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | Case 2:
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | (89) all_54_2 = e0
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | | REF_CLOSE: (15), (32), (89) are inconsistent by sub-proof #536.
% 141.52/20.99 | | | | | | | |
% 141.52/20.99 | | | | | | | End of split
% 141.52/20.99 | | | | | | |
% 141.52/20.99 | | | | | | End of split
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | End of split
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | Case 2:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | (90) all_54_3 = e1 | all_54_3 = e0
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | REF_CLOSE: (8), (20), (52), (90) are inconsistent by sub-proof #418.
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | End of split
% 141.52/20.99 | | | |
% 141.52/20.99 | | | End of split
% 141.52/20.99 | | |
% 141.52/20.99 | | End of split
% 141.52/20.99 | |
% 141.52/20.99 | End of split
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #418 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) all_54_3 = e1 | all_54_3 = e0
% 141.52/20.99 (2) all_54_3 = all_52_12
% 141.52/20.99 (3) ~ (all_52_12 = e1)
% 141.52/20.99 (4) ~ (all_52_12 = e0)
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | BETA: splitting (1) gives:
% 141.52/20.99 |
% 141.52/20.99 | Case 1:
% 141.52/20.99 | |
% 141.52/20.99 | | (5) all_54_3 = e1
% 141.52/20.99 | |
% 141.52/20.99 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #982.
% 141.52/20.99 | |
% 141.52/20.99 | Case 2:
% 141.52/20.99 | |
% 141.52/20.99 | | (6) all_54_3 = e0
% 141.52/20.99 | |
% 141.52/20.99 | | COMBINE_EQS: (2), (6) imply:
% 141.52/20.99 | | (7) all_52_12 = e0
% 141.52/20.99 | |
% 141.52/20.99 | | SIMP: (7) implies:
% 141.52/20.99 | | (8) all_52_12 = e0
% 141.52/20.99 | |
% 141.52/20.99 | | REDUCE: (4), (8) imply:
% 141.52/20.99 | | (9) $false
% 141.52/20.99 | |
% 141.52/20.99 | | CLOSE: (9) is inconsistent.
% 141.52/20.99 | |
% 141.52/20.99 | End of split
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #419 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) ~ (all_52_14 = e1)
% 141.52/20.99 (2) ~ (e2 = e1)
% 141.52/20.99 (3) ~ (all_52_7 = e0)
% 141.52/20.99 (4) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.99 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.99 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.99 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.99 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.99 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.99 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.99 (5) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 141.52/20.99 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.99 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.99 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.99 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 141.52/20.99 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 141.52/20.99 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 141.52/20.99 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 141.52/20.99 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 141.52/20.99 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 141.52/20.99 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.52/20.99 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.99 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.52/20.99 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 141.52/20.99 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.52/20.99 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.52/20.99 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.99 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 141.52/20.99 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 141.52/20.99 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 141.52/20.99 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/20.99 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.99 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/20.99 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/20.99 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/20.99 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/20.99 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/20.99 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.52/20.99 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.52/20.99 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.52/20.99 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.52/20.99 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/20.99 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/20.99 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.52/20.99 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.99 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/20.99 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.99 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/20.99 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.52/20.99 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/20.99 (6) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 141.52/20.99 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.99 (7) op(e1, e2) = e1
% 141.52/20.99 (8) op(e1, e1) = all_4_2
% 141.52/20.99 (9) op(e3, e1) = all_52_8
% 141.52/20.99 (10) op(e0, e0) = e1
% 141.52/20.99 (11) ~ (all_4_2 = e3)
% 141.52/20.99 (12) ~ (e1 = e0)
% 141.52/20.99 (13) ~ (all_52_11 = e0)
% 141.52/20.99 (14) op(e0, e1) = all_52_11
% 141.52/20.99 (15) ~ (all_4_2 = e2)
% 141.52/20.99 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.99 (17) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/20.99 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/20.99 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/20.99 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/20.99 (18) ~ (all_52_8 = e0)
% 141.52/20.99 (19) ~ (e3 = e1)
% 141.52/20.99 (20) op(e0, e2) = all_52_7
% 141.52/20.99 (21) op(e0, e0) = all_56_15
% 141.52/20.99 (22) all_56_15 = e1
% 141.52/20.99 (23) op(e2, e1) = all_52_9
% 141.52/20.99 (24) op(e1, e0) = all_52_14
% 141.52/20.99 (25) ~ (all_52_9 = e0)
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | BETA: splitting (5) gives:
% 141.52/20.99 |
% 141.52/20.99 | Case 1:
% 141.52/20.99 | |
% 141.52/20.99 | | (26) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3)
% 141.52/20.99 | | = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.99 | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.99 | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.99 | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.52/20.99 | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.52/20.99 | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.52/20.99 | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.99 | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.99 | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.52/20.99 | | op(e0, e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) =
% 141.52/20.99 | | all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | (
% 141.52/20.99 | | ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.52/20.99 | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 141.52/20.99 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 141.52/20.99 | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 141.52/20.99 | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 141.52/20.99 | | (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.99 | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.52/20.99 | | e2) = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 141.52/20.99 | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 141.52/20.99 | | $i(all_56_12))))
% 141.52/20.99 | |
% 141.52/20.99 | | BETA: splitting (26) gives:
% 141.52/20.99 | |
% 141.52/20.99 | | Case 1:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (27) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 141.52/20.99 | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 141.52/20.99 | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 141.52/20.99 | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.99 | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) &
% 141.52/20.99 | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 141.52/20.99 | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3
% 141.52/20.99 | | | & $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 141.52/20.99 | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 141.52/20.99 | | | ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 141.52/20.99 | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 141.52/20.99 | | |
% 141.52/20.99 | | | ALPHA: (27) implies:
% 141.52/20.99 | | | (28) (all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 141.52/20.99 | | | e3) = all_56_10 & $i(all_56_10))
% 141.52/20.99 | | |
% 141.52/20.99 | | | BETA: splitting (28) gives:
% 141.52/20.99 | | |
% 141.52/20.99 | | | Case 1:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | (29) all_56_15 = e3 & op(e0, e0) = e3
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | ALPHA: (29) implies:
% 141.52/20.99 | | | | (30) op(e0, e0) = e3
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | REF_CLOSE: (10), (16), (19), (30) are inconsistent by sub-proof #732.
% 141.52/20.99 | | | |
% 141.52/20.99 | | | Case 2:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | (31) ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | ALPHA: (31) implies:
% 141.52/20.99 | | | | (32) ~ (all_56_10 = e0)
% 141.52/20.99 | | | | (33) op(e0, e3) = all_56_10
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | BETA: splitting (17) gives:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | Case 1:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | (34) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | ALPHA: (34) implies:
% 141.52/20.99 | | | | | (35) op(e0, e0) = e0
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | REF_CLOSE: (4), (6), (8), (9), (11), (12), (13), (14), (15), (16),
% 141.52/20.99 | | | | | (18), (21), (23), (25), (35) are inconsistent by sub-proof
% 141.52/20.99 | | | | | #518.
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | Case 2:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | (36) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 141.52/20.99 | | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 141.52/20.99 | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.99 | | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | ALPHA: (36) implies:
% 141.52/20.99 | | | | | (37) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.99 | | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | BETA: splitting (37) gives:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | Case 1:
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | (38) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | ALPHA: (38) implies:
% 141.52/20.99 | | | | | | (39) op(e0, e3) = e0
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | REF_CLOSE: (16), (32), (33), (39) are inconsistent by sub-proof
% 141.52/20.99 | | | | | | #954.
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | Case 2:
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | (40) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 141.52/20.99 | | | | | | op(e0, e1) = e0)
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | REF_CLOSE: (3), (13), (14), (16), (20), (40) are inconsistent by
% 141.52/20.99 | | | | | | sub-proof #885.
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | End of split
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | End of split
% 141.52/20.99 | | | |
% 141.52/20.99 | | | End of split
% 141.52/20.99 | | |
% 141.52/20.99 | | Case 2:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (41) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3,
% 141.52/20.99 | | | e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 141.52/20.99 | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~
% 141.52/20.99 | | | (all_56_13 = e2) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/20.99 | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3,
% 141.52/20.99 | | | e2) = all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 141.52/20.99 | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 141.52/20.99 | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 141.52/20.99 | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.52/20.99 | | | ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 141.52/20.99 | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 141.52/20.99 | | |
% 141.52/20.99 | | | ALPHA: (41) implies:
% 141.52/20.99 | | | (42) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1,
% 141.52/20.99 | | | e2) = all_56_7 & $i(all_56_7))
% 141.52/20.99 | | |
% 141.52/20.99 | | | REF_CLOSE: (7), (8), (15), (16), (42) are inconsistent by sub-proof #421.
% 141.52/20.99 | | |
% 141.52/20.99 | | End of split
% 141.52/20.99 | |
% 141.52/20.99 | Case 2:
% 141.52/20.99 | |
% 141.52/20.99 | | (43) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.52/20.99 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/20.99 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.52/20.99 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.99 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.52/20.99 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.52/20.99 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.52/20.99 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.52/20.99 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.99 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.52/20.99 | | op(e0, e1) = all_56_14 & $i(all_56_14)))) | (op(e0, e0) =
% 141.52/20.99 | | all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | (
% 141.52/20.99 | | ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.52/20.99 | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/20.99 | | e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 141.52/20.99 | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/20.99 | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/20.99 | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/20.99 | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2,
% 141.52/20.99 | | e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 141.52/20.99 | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 141.52/20.99 | | $i(all_56_8))))
% 141.52/20.99 | |
% 141.52/20.99 | | BETA: splitting (43) gives:
% 141.52/20.99 | |
% 141.52/20.99 | | Case 1:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (44) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.52/20.99 | | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/20.99 | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.52/20.99 | | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.99 | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.52/20.99 | | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.52/20.99 | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.52/20.99 | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.52/20.99 | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/20.99 | | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 141.52/20.99 | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 141.52/20.99 | | |
% 141.52/20.99 | | | ALPHA: (44) implies:
% 141.52/20.99 | | | (45) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/20.99 | | | e0) = all_56_15 & $i(all_56_15))
% 141.52/20.99 | | |
% 141.52/20.99 | | | REF_CLOSE: (13), (14), (16), (22), (45) are inconsistent by sub-proof
% 141.52/20.99 | | | #432.
% 141.52/20.99 | | |
% 141.52/20.99 | | Case 2:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (46) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.52/20.99 | | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.52/20.99 | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.52/20.99 | | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/20.99 | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.52/20.99 | | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.52/20.99 | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.52/20.99 | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.52/20.99 | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.52/20.99 | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.52/20.99 | | | e0) = all_56_8 & $i(all_56_8)))
% 141.52/20.99 | | |
% 141.52/20.99 | | | ALPHA: (46) implies:
% 141.52/20.99 | | | (47) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.52/20.99 | | | e1) = all_56_13 & $i(all_56_13))
% 141.52/20.99 | | |
% 141.52/20.99 | | | BETA: splitting (47) gives:
% 141.52/20.99 | | |
% 141.52/20.99 | | | Case 1:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | (48) all_56_8 = e1 & op(e1, e0) = e1
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | ALPHA: (48) implies:
% 141.52/20.99 | | | | (49) op(e1, e0) = e1
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | REF_CLOSE: (1), (16), (24), (49) are inconsistent by sub-proof #459.
% 141.52/20.99 | | | |
% 141.52/20.99 | | | Case 2:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | (50) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | ALPHA: (50) implies:
% 141.52/20.99 | | | | (51) ~ (all_56_13 = e0)
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | BETA: splitting (17) gives:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | Case 1:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | (52) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | ALPHA: (52) implies:
% 141.52/20.99 | | | | | (53) op(e0, e0) = e0
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | REF_CLOSE: (4), (6), (8), (9), (11), (12), (13), (14), (15), (16),
% 141.52/20.99 | | | | | (18), (21), (23), (25), (53) are inconsistent by sub-proof
% 141.52/20.99 | | | | | #518.
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | Case 2:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | (54) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 141.52/20.99 | | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 141.52/20.99 | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.99 | | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | ALPHA: (54) implies:
% 141.52/20.99 | | | | | (55) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 141.52/20.99 | | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | BETA: splitting (55) gives:
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | | Case 1:
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | (56) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | ALPHA: (56) implies:
% 141.52/20.99 | | | | | | (57) op(e0, e3) = e0
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | REF_CLOSE: (2), (4), (16), (22), (51), (57) are inconsistent by
% 141.52/20.99 | | | | | | sub-proof #420.
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | Case 2:
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | (58) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 141.52/20.99 | | | | | | op(e0, e1) = e0)
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | | REF_CLOSE: (3), (13), (14), (16), (20), (58) are inconsistent by
% 141.52/20.99 | | | | | | sub-proof #885.
% 141.52/20.99 | | | | | |
% 141.52/20.99 | | | | | End of split
% 141.52/20.99 | | | | |
% 141.52/20.99 | | | | End of split
% 141.52/20.99 | | | |
% 141.52/20.99 | | | End of split
% 141.52/20.99 | | |
% 141.52/20.99 | | End of split
% 141.52/20.99 | |
% 141.52/20.99 | End of split
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #420 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) ~ (e2 = e1)
% 141.52/20.99 (2) ~ (all_56_13 = e0)
% 141.52/20.99 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.99 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.99 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.99 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.99 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.99 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.99 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.99 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.99 (5) all_56_15 = e1
% 141.52/20.99 (6) op(e0, e3) = e0
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | BETA: splitting (3) gives:
% 141.52/20.99 |
% 141.52/20.99 | Case 1:
% 141.52/20.99 | |
% 141.52/20.99 | | (7) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.99 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 141.52/20.99 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 141.52/20.99 | | = all_56_12 & $i(all_56_12))
% 141.52/20.99 | |
% 141.52/20.99 | | BETA: splitting (7) gives:
% 141.52/20.99 | |
% 141.52/20.99 | | Case 1:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (8) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 141.52/20.99 | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/20.99 | | |
% 141.52/20.99 | | | ALPHA: (8) implies:
% 141.52/20.99 | | | (9) ~ (all_56_10 = e0)
% 141.52/20.99 | | | (10) op(e0, e3) = all_56_10
% 141.52/20.99 | | |
% 141.52/20.99 | | | REF_CLOSE: (4), (6), (9), (10) are inconsistent by sub-proof #954.
% 141.52/20.99 | | |
% 141.52/20.99 | | Case 2:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (11) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.52/20.99 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/20.99 | | |
% 141.52/20.99 | | | REF_CLOSE: (1), (5), (11) are inconsistent by sub-proof #458.
% 141.52/20.99 | | |
% 141.52/20.99 | | End of split
% 141.52/20.99 | |
% 141.52/20.99 | Case 2:
% 141.52/20.99 | |
% 141.52/20.99 | | (12) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/20.99 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 141.52/20.99 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.99 | | e1) = all_56_14 & $i(all_56_14))
% 141.52/20.99 | |
% 141.52/20.99 | | REF_CLOSE: (2), (12) are inconsistent by sub-proof #947.
% 141.52/20.99 | |
% 141.52/20.99 | End of split
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #421 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) op(e1, e2) = e1
% 141.52/20.99 (2) (all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 141.52/20.99 all_56_7 & $i(all_56_7))
% 141.52/20.99 (3) op(e1, e1) = all_4_2
% 141.52/20.99 (4) ~ (all_4_2 = e2)
% 141.52/20.99 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | BETA: splitting (2) gives:
% 141.52/20.99 |
% 141.52/20.99 | Case 1:
% 141.52/20.99 | |
% 141.52/20.99 | | (6) all_56_13 = e2 & op(e1, e1) = e2
% 141.52/20.99 | |
% 141.52/20.99 | | ALPHA: (6) implies:
% 141.52/20.99 | | (7) op(e1, e1) = e2
% 141.52/20.99 | |
% 141.52/20.99 | | REF_CLOSE: (3), (4), (5), (7) are inconsistent by sub-proof #1124.
% 141.52/20.99 | |
% 141.52/20.99 | Case 2:
% 141.52/20.99 | |
% 141.52/20.99 | | (8) ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)
% 141.52/20.99 | |
% 141.52/20.99 | | ALPHA: (8) implies:
% 141.52/20.99 | | (9) ~ (all_56_7 = e1)
% 141.52/20.99 | | (10) op(e1, e2) = all_56_7
% 141.52/20.99 | |
% 141.52/20.99 | | REF_CLOSE: (1), (5), (9), (10) are inconsistent by sub-proof #422.
% 141.52/20.99 | |
% 141.52/20.99 | End of split
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #422 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.99 (2) op(e1, e2) = all_56_7
% 141.52/20.99 (3) op(e1, e2) = e1
% 141.52/20.99 (4) ~ (all_56_7 = e1)
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | GROUND_INST: instantiating (1) with e1, all_56_7, e2, e1, simplifying with
% 141.52/20.99 | (2), (3) gives:
% 141.52/20.99 | (5) all_56_7 = e1
% 141.52/20.99 |
% 141.52/20.99 | REDUCE: (4), (5) imply:
% 141.52/20.99 | (6) $false
% 141.52/20.99 |
% 141.52/20.99 | CLOSE: (6) is inconsistent.
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #423 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) all_54_1 = all_52_4
% 141.52/20.99 (2) all_54_1 = e2
% 141.52/20.99 (3) ~ (all_52_4 = e2)
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.99 | (4) all_52_4 = e2
% 141.52/20.99 |
% 141.52/20.99 | SIMP: (4) implies:
% 141.52/20.99 | (5) all_52_4 = e2
% 141.52/20.99 |
% 141.52/20.99 | REDUCE: (3), (5) imply:
% 141.52/20.99 | (6) $false
% 141.52/20.99 |
% 141.52/20.99 | CLOSE: (6) is inconsistent.
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #424 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) all_54_1 = all_52_4
% 141.52/20.99 (2) all_54_1 = e3
% 141.52/20.99 (3) ~ (all_52_4 = e3)
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | COMBINE_EQS: (1), (2) imply:
% 141.52/20.99 | (4) all_52_4 = e3
% 141.52/20.99 |
% 141.52/20.99 | SIMP: (4) implies:
% 141.52/20.99 | (5) all_52_4 = e3
% 141.52/20.99 |
% 141.52/20.99 | REDUCE: (3), (5) imply:
% 141.52/20.99 | (6) $false
% 141.52/20.99 |
% 141.52/20.99 | CLOSE: (6) is inconsistent.
% 141.52/20.99 |
% 141.52/20.99 End of proof
% 141.52/20.99
% 141.52/20.99 Sub-proof #425 shows that the following formulas are inconsistent:
% 141.52/20.99 ----------------------------------------------------------------
% 141.52/20.99 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/20.99 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/20.99 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/20.99 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/20.99 (3) ~ (all_52_8 = e3)
% 141.52/20.99 (4) ~ (e2 = e1)
% 141.52/20.99 (5) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/20.99 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/20.99 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/20.99 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/20.99 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/20.99 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/20.99 e1) = all_56_14 & $i(all_56_14))
% 141.52/20.99 (6) op(e1, e1) = all_4_2
% 141.52/20.99 (7) op(e3, e1) = all_52_8
% 141.52/20.99 (8) ~ (all_4_2 = e3)
% 141.52/20.99 (9) op(e2, e2) = e2
% 141.52/20.99 (10) ~ (e2 = e0)
% 141.52/20.99 (11) ~ (e3 = e2)
% 141.52/20.99 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/20.99 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/20.99 (13) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/20.99 (14) ~ (e3 = e1)
% 141.52/20.99 (15) op(e0, e0) = all_56_15
% 141.52/20.99 (16) ~ (all_52_13 = e1)
% 141.52/20.99 (17) all_57_2 = e3
% 141.52/20.99 (18) op(e2, e0) = all_52_13
% 141.52/20.99
% 141.52/20.99 Begin of proof
% 141.52/20.99 |
% 141.52/20.99 | BETA: splitting (13) gives:
% 141.52/20.99 |
% 141.52/20.99 | Case 1:
% 141.52/20.99 | |
% 141.52/20.99 | | (19) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/20.99 | |
% 141.52/20.99 | | ALPHA: (19) implies:
% 141.52/20.99 | | (20) all_57_14 = e2
% 141.52/20.99 | |
% 141.52/20.99 | | BETA: splitting (2) gives:
% 141.52/20.99 | |
% 141.52/20.99 | | Case 1:
% 141.52/20.99 | | |
% 141.52/20.99 | | | (21) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 141.52/20.99 | | | e1)
% 141.52/20.99 | | |
% 141.52/20.99 | | | BETA: splitting (21) gives:
% 141.52/20.99 | | |
% 141.52/20.99 | | | Case 1:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | (22) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | REF_CLOSE: (14), (17), (22) are inconsistent by sub-proof #939.
% 141.52/20.99 | | | |
% 141.52/20.99 | | | Case 2:
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | (23) all_57_3 = e1 & op(e2, e2) = e1
% 141.52/20.99 | | | |
% 141.52/20.99 | | | | ALPHA: (23) implies:
% 141.52/21.00 | | | | (24) op(e2, e2) = e1
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | REF_CLOSE: (4), (9), (12), (24) are inconsistent by sub-proof #749.
% 141.52/21.00 | | | |
% 141.52/21.00 | | | End of split
% 141.52/21.00 | | |
% 141.52/21.00 | | Case 2:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (25) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 141.52/21.00 | | | e1)
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (1), (3), (6), (7), (8), (11), (12), (14), (16), (18), (20),
% 141.52/21.00 | | | (25) are inconsistent by sub-proof #444.
% 141.52/21.00 | | |
% 141.52/21.00 | | End of split
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (26) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (26) implies:
% 141.52/21.00 | | (27) op(e0, e0) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (4), (5), (9), (10), (11), (12), (15), (27) are inconsistent by
% 141.52/21.00 | | sub-proof #643.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #426 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/21.00 (2) ~ (all_52_7 = e2)
% 141.52/21.00 (3) ~ (e2 = e0)
% 141.52/21.00 (4) all_57_12 = e0
% 141.52/21.00 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (6) op(e0, e2) = all_52_7
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (1) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (7) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (7) implies:
% 141.52/21.00 | | (8) all_57_12 = e2
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #1025.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (9) all_57_13 = e2 & op(e0, e2) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #446.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #427 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) all_57_6 = e0 & op(e1, e3) = e0
% 141.52/21.00 (2) all_57_6 = e1
% 141.52/21.00 (3) ~ (e1 = e0)
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | ALPHA: (1) implies:
% 141.52/21.00 | (4) all_57_6 = e0
% 141.52/21.00 |
% 141.52/21.00 | COMBINE_EQS: (2), (4) imply:
% 141.52/21.00 | (5) e1 = e0
% 141.52/21.00 |
% 141.52/21.00 | REDUCE: (3), (5) imply:
% 141.52/21.00 | (6) $false
% 141.52/21.00 |
% 141.52/21.00 | CLOSE: (6) is inconsistent.
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #428 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ~ (all_50_2 = e0) | ( ~ (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 &
% 141.52/21.00 op(e1, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 141.52/21.00 e3) & op(e1, e0) = all_50_1 & $i(all_50_1))
% 141.52/21.00 (2) ~ (all_52_9 = e2)
% 141.52/21.00 (3) op(e1, e1) = all_4_2
% 141.52/21.00 (4) all_57_14 = e3
% 141.52/21.00 (5) op(e3, e1) = all_52_8
% 141.52/21.00 (6) op(e1, e0) = e3
% 141.52/21.00 (7) all_50_2 = e0
% 141.52/21.00 (8) ~ (e3 = e2)
% 141.52/21.00 (9) ~ (all_4_2 = e2)
% 141.52/21.00 (10) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.52/21.00 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.52/21.00 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (12) op(e2, e1) = all_52_9
% 141.52/21.00 (13) op(e1, e0) = all_52_14
% 141.52/21.00 (14) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 141.52/21.00 all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1,
% 141.52/21.00 e0) = all_48_1 & $i(all_48_1))
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (10) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (15) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 141.52/21.00 | | e2)
% 141.52/21.00 | |
% 141.52/21.00 | | BETA: splitting (15) gives:
% 141.52/21.00 | |
% 141.52/21.00 | | Case 1:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (16) all_57_4 = e2 & op(e3, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (16) implies:
% 141.52/21.00 | | | (17) op(e3, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (1), (5), (6), (7), (11), (13), (14), (17) are inconsistent by
% 141.52/21.00 | | | sub-proof #893.
% 141.52/21.00 | | |
% 141.52/21.00 | | Case 2:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (18) all_57_5 = e2 & op(e2, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (18) implies:
% 141.52/21.00 | | | (19) op(e2, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (2), (11), (12), (19) are inconsistent by sub-proof #890.
% 141.52/21.00 | | |
% 141.52/21.00 | | End of split
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (20) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 141.52/21.00 | | e2)
% 141.52/21.00 | |
% 141.52/21.00 | | BETA: splitting (20) gives:
% 141.52/21.00 | |
% 141.52/21.00 | | Case 1:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (21) all_57_8 = e2 & op(e1, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (21) implies:
% 141.52/21.00 | | | (22) op(e1, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (3), (9), (11), (22) are inconsistent by sub-proof #1124.
% 141.52/21.00 | | |
% 141.52/21.00 | | Case 2:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (23) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (4), (8), (23) are inconsistent by sub-proof #704.
% 141.52/21.00 | | |
% 141.52/21.00 | | End of split
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #429 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) all_54_11 = e1 | all_54_11 = e0
% 141.52/21.00 (2) all_54_11 = all_52_14
% 141.52/21.00 (3) ~ (all_52_14 = e1)
% 141.52/21.00 (4) ~ (all_52_14 = e0)
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (1) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (5) all_54_11 = e1
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #942.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (6) all_54_11 = e0
% 141.52/21.00 | |
% 141.52/21.00 | | COMBINE_EQS: (2), (6) imply:
% 141.52/21.00 | | (7) all_52_14 = e0
% 141.52/21.00 | |
% 141.52/21.00 | | SIMP: (7) implies:
% 141.52/21.00 | | (8) all_52_14 = e0
% 141.52/21.00 | |
% 141.52/21.00 | | REDUCE: (4), (8) imply:
% 141.52/21.00 | | (9) $false
% 141.52/21.00 | |
% 141.52/21.00 | | CLOSE: (9) is inconsistent.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #430 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ~ (all_52_14 = e1)
% 141.52/21.00 (2) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 141.52/21.00 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/21.00 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 141.52/21.00 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 141.52/21.00 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 141.52/21.00 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 141.52/21.00 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 141.52/21.00 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 141.52/21.00 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 141.52/21.00 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 141.52/21.00 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.52/21.00 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 141.52/21.00 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 141.52/21.00 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 141.52/21.00 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 141.52/21.00 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 141.52/21.00 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 141.52/21.00 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 141.52/21.00 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 141.52/21.00 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 141.52/21.00 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/21.00 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/21.00 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/21.00 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/21.00 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/21.00 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/21.00 e1) = all_56_14 & $i(all_56_14))
% 141.52/21.00 (4) ~ (all_52_11 = e0)
% 141.52/21.00 (5) op(e0, e1) = all_52_11
% 141.52/21.00 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (7) ~ (all_52_13 = e2)
% 141.52/21.00 (8) all_56_15 = e1
% 141.52/21.00 (9) op(e3, e3) = all_14_2
% 141.52/21.00 (10) op(e2, e0) = all_52_13
% 141.52/21.00 (11) ~ (all_14_2 = e0)
% 141.52/21.00 (12) op(e1, e0) = all_52_14
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (2) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (13) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3,
% 141.52/21.00 | | e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 141.52/21.00 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 141.52/21.00 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/21.00 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3,
% 141.52/21.00 | | e1) = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 141.52/21.00 | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 141.52/21.00 | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 141.52/21.00 | | (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 141.52/21.00 | | ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 141.52/21.00 | | e1) = all_56_14 & $i(all_56_14)))
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (13) implies:
% 141.52/21.00 | | (14) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 141.52/21.00 | | e0) = all_56_15 & $i(all_56_15))
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (4), (5), (6), (8), (14) are inconsistent by sub-proof #432.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (15) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 141.52/21.00 | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 141.52/21.00 | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 141.52/21.00 | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 141.52/21.00 | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 141.52/21.00 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 141.52/21.00 | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 141.52/21.00 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.52/21.00 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.52/21.00 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 141.52/21.00 | | e0) = all_56_8 & $i(all_56_8)))
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (1), (3), (6), (7), (9), (10), (11), (12), (15) are inconsistent
% 141.52/21.00 | | by sub-proof #431.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #431 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ~ (all_52_14 = e1)
% 141.52/21.00 (2) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 141.52/21.00 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.52/21.00 ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 141.52/21.00 all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 141.52/21.00 ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 141.52/21.00 ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 141.52/21.00 all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 141.52/21.00 (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 141.52/21.00 ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 141.52/21.00 all_56_8 & $i(all_56_8)))
% 141.52/21.00 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/21.00 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/21.00 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/21.00 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/21.00 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/21.00 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/21.00 e1) = all_56_14 & $i(all_56_14))
% 141.52/21.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (5) ~ (all_52_13 = e2)
% 141.52/21.00 (6) op(e3, e3) = all_14_2
% 141.52/21.00 (7) op(e2, e0) = all_52_13
% 141.52/21.00 (8) ~ (all_14_2 = e0)
% 141.52/21.00 (9) op(e1, e0) = all_52_14
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | ALPHA: (2) implies:
% 141.52/21.00 | (10) (all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 141.52/21.00 | = all_56_13 & $i(all_56_13))
% 141.52/21.00 | (11) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2)
% 141.52/21.00 | = all_56_11 & $i(all_56_11))
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (11) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (12) all_56_5 = e2 & op(e2, e0) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (12) implies:
% 141.52/21.00 | | (13) op(e2, e0) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (4), (5), (7), (13) are inconsistent by sub-proof #1030.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (14) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (14) implies:
% 141.52/21.00 | | (15) ~ (all_56_11 = e0)
% 141.52/21.00 | | (16) op(e2, e2) = all_56_11
% 141.52/21.00 | |
% 141.52/21.00 | | BETA: splitting (10) gives:
% 141.52/21.00 | |
% 141.52/21.00 | | Case 1:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (17) all_56_8 = e1 & op(e1, e0) = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (17) implies:
% 141.52/21.00 | | | (18) op(e1, e0) = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (1), (4), (9), (18) are inconsistent by sub-proof #459.
% 141.52/21.00 | | |
% 141.52/21.00 | | Case 2:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (19) ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (19) implies:
% 141.52/21.00 | | | (20) ~ (all_56_13 = e0)
% 141.52/21.00 | | |
% 141.52/21.00 | | | BETA: splitting (3) gives:
% 141.52/21.00 | | |
% 141.52/21.00 | | | Case 1:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | (21) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.52/21.00 | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/21.00 | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/21.00 | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | BETA: splitting (21) gives:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | Case 1:
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | (22) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.52/21.00 | | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | ALPHA: (22) implies:
% 141.52/21.00 | | | | | (23) op(e3, e3) = e0
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | REF_CLOSE: (4), (6), (8), (23) are inconsistent by sub-proof #1125.
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | Case 2:
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | (24) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/21.00 | | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | ALPHA: (24) implies:
% 141.52/21.00 | | | | | (25) op(e2, e2) = e0
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | REF_CLOSE: (4), (15), (16), (25) are inconsistent by sub-proof #857.
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | End of split
% 141.52/21.00 | | | |
% 141.52/21.00 | | | Case 2:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | (26) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.52/21.00 | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.52/21.00 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 141.52/21.00 | | | | e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | REF_CLOSE: (20), (26) are inconsistent by sub-proof #947.
% 141.52/21.00 | | | |
% 141.52/21.00 | | | End of split
% 141.52/21.00 | | |
% 141.52/21.00 | | End of split
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #432 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ~ (all_52_11 = e0)
% 141.52/21.00 (2) op(e0, e1) = all_52_11
% 141.52/21.00 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (4) all_56_15 = e1
% 141.52/21.00 (5) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 141.52/21.00 all_56_15 & $i(all_56_15))
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (5) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (6) all_56_14 = e0 & op(e0, e1) = e0
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (6) implies:
% 141.52/21.00 | | (7) op(e0, e1) = e0
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (1), (2), (3), (7) are inconsistent by sub-proof #886.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (8) ~ (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (8) implies:
% 141.52/21.00 | | (9) ~ (all_56_15 = e1)
% 141.52/21.00 | |
% 141.52/21.00 | | REDUCE: (4), (9) imply:
% 141.52/21.00 | | (10) $false
% 141.52/21.00 | |
% 141.52/21.00 | | CLOSE: (10) is inconsistent.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #433 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ~ (e2 = e1)
% 141.52/21.00 (2) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 141.52/21.00 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 141.52/21.00 ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 141.52/21.00 all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | (
% 141.52/21.00 ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 141.52/21.00 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 141.52/21.00 all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | (
% 141.52/21.00 ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7))) &
% 141.52/21.00 ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 141.52/21.00 all_56_12 & $i(all_56_12)))
% 141.52/21.00 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/21.00 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/21.00 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/21.00 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/21.00 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/21.00 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/21.00 e1) = all_56_14 & $i(all_56_14))
% 141.52/21.00 (4) op(e0, e2) = e0
% 141.52/21.00 (5) op(e2, e2) = e2
% 141.52/21.00 (6) ~ (e2 = e0)
% 141.52/21.00 (7) ~ (e3 = e2)
% 141.52/21.00 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (9) op(e0, e0) = all_56_15
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | ALPHA: (2) implies:
% 141.52/21.00 | (10) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2)
% 141.52/21.00 | = all_56_12 & $i(all_56_12))
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (10) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (11) all_56_15 = e2 & op(e0, e0) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (11) implies:
% 141.52/21.00 | | (12) op(e0, e0) = e2
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (12) are inconsistent by
% 141.52/21.00 | | sub-proof #643.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (13) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (13) implies:
% 141.52/21.00 | | (14) ~ (all_56_12 = e0)
% 141.52/21.00 | | (15) op(e0, e2) = all_56_12
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (4), (8), (14), (15) are inconsistent by sub-proof #738.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #434 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) (all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 141.52/21.00 all_56_6 & $i(all_56_6))
% 141.52/21.00 (2) op(e1, e1) = all_4_2
% 141.52/21.00 (3) ~ (all_4_2 = e3)
% 141.52/21.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (5) op(e1, e3) = e1
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (1) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (6) all_56_13 = e3 & op(e1, e1) = e3
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (6) implies:
% 141.52/21.00 | | (7) op(e1, e1) = e3
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1127.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (8) ~ (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6)
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (8) implies:
% 141.52/21.00 | | (9) ~ (all_56_6 = e1)
% 141.52/21.00 | | (10) op(e1, e3) = all_56_6
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (4), (5), (9), (10) are inconsistent by sub-proof #435.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #435 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (2) op(e1, e3) = all_56_6
% 141.52/21.00 (3) op(e1, e3) = e1
% 141.52/21.00 (4) ~ (all_56_6 = e1)
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | GROUND_INST: instantiating (1) with e1, all_56_6, e3, e1, simplifying with
% 141.52/21.00 | (2), (3) gives:
% 141.52/21.00 | (5) all_56_6 = e1
% 141.52/21.00 |
% 141.52/21.00 | REDUCE: (4), (5) imply:
% 141.52/21.00 | (6) $false
% 141.52/21.00 |
% 141.52/21.00 | CLOSE: (6) is inconsistent.
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #436 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) ~ (e2 = e1)
% 141.52/21.00 (2) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/21.00 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/21.00 (3) all_57_8 = e0
% 141.52/21.00 (4) ~ (e3 = e0)
% 141.52/21.00 (5) all_57_11 = e2
% 141.52/21.00 (6) ~ (e1 = e0)
% 141.52/21.00 (7) ~ (e3 = e2)
% 141.52/21.00 (8) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/21.00 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/21.00 (9) ~ (e3 = e1)
% 141.52/21.00 (10) all_57_7 = e0
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (2) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.52/21.00 | | e1)
% 141.52/21.00 | |
% 141.52/21.00 | | BETA: splitting (11) gives:
% 141.52/21.00 | |
% 141.52/21.00 | | Case 1:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (12) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (12) implies:
% 141.52/21.00 | | | (13) all_57_6 = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | BETA: splitting (8) gives:
% 141.52/21.00 | | |
% 141.52/21.00 | | | Case 1:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 141.52/21.00 | | | | = e3)
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | BETA: splitting (14) gives:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | Case 1:
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | (15) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | REF_CLOSE: (9), (13), (15) are inconsistent by sub-proof #1099.
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | Case 2:
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | (16) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | REF_CLOSE: (4), (10), (16) are inconsistent by sub-proof #713.
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | End of split
% 141.52/21.00 | | | |
% 141.52/21.00 | | | Case 2:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | (17) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 141.52/21.00 | | | | = e3)
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | BETA: splitting (17) gives:
% 141.52/21.00 | | | |
% 141.52/21.00 | | | | Case 1:
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | (18) all_57_8 = e3 & op(e1, e1) = e3
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | ALPHA: (18) implies:
% 141.52/21.00 | | | | | (19) all_57_8 = e3
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | COMBINE_EQS: (3), (19) imply:
% 141.52/21.00 | | | | | (20) e3 = e0
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | SIMP: (20) implies:
% 141.52/21.00 | | | | | (21) e3 = e0
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | REDUCE: (4), (21) imply:
% 141.52/21.00 | | | | | (22) $false
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | CLOSE: (22) is inconsistent.
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | Case 2:
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | (23) all_57_11 = e3 & op(e1, e0) = e3
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | ALPHA: (23) implies:
% 141.52/21.00 | | | | | (24) all_57_11 = e3
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | | REF_CLOSE: (5), (7), (24) are inconsistent by sub-proof #1055.
% 141.52/21.00 | | | | |
% 141.52/21.00 | | | | End of split
% 141.52/21.00 | | | |
% 141.52/21.00 | | | End of split
% 141.52/21.00 | | |
% 141.52/21.00 | | Case 2:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (25) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (25) implies:
% 141.52/21.00 | | | (26) all_57_7 = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (6), (10), (26) are inconsistent by sub-proof #712.
% 141.52/21.00 | | |
% 141.52/21.00 | | End of split
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (27) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.52/21.00 | | e1)
% 141.52/21.00 | |
% 141.52/21.00 | | BETA: splitting (27) gives:
% 141.52/21.00 | |
% 141.52/21.00 | | Case 1:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (28) all_57_8 = e1 & op(e1, e1) = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | ALPHA: (28) implies:
% 141.52/21.00 | | | (29) all_57_8 = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | COMBINE_EQS: (3), (29) imply:
% 141.52/21.00 | | | (30) e1 = e0
% 141.52/21.00 | | |
% 141.52/21.00 | | | SIMP: (30) implies:
% 141.52/21.00 | | | (31) e1 = e0
% 141.52/21.00 | | |
% 141.52/21.00 | | | REDUCE: (6), (31) imply:
% 141.52/21.00 | | | (32) $false
% 141.52/21.00 | | |
% 141.52/21.00 | | | CLOSE: (32) is inconsistent.
% 141.52/21.00 | | |
% 141.52/21.00 | | Case 2:
% 141.52/21.00 | | |
% 141.52/21.00 | | | (33) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/21.00 | | |
% 141.52/21.00 | | | REF_CLOSE: (1), (5), (33) are inconsistent by sub-proof #862.
% 141.52/21.00 | | |
% 141.52/21.00 | | End of split
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #437 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/21.00 (2) all_57_6 = e2
% 141.52/21.00 (3) ~ (e2 = e1)
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | ALPHA: (1) implies:
% 141.52/21.00 | (4) all_57_6 = e1
% 141.52/21.00 |
% 141.52/21.00 | COMBINE_EQS: (2), (4) imply:
% 141.52/21.00 | (5) e2 = e1
% 141.52/21.00 |
% 141.52/21.00 | REDUCE: (3), (5) imply:
% 141.52/21.00 | (6) $false
% 141.52/21.00 |
% 141.52/21.00 | CLOSE: (6) is inconsistent.
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #438 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) op(e3, e3) = e3
% 141.52/21.00 (2) ~ (all_52_1 = e1)
% 141.52/21.00 (3) op(e2, e3) = all_52_1
% 141.52/21.00 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.00 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.00 (5) ~ (e3 = e1)
% 141.52/21.00 (6) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | BETA: splitting (6) gives:
% 141.52/21.00 |
% 141.52/21.00 | Case 1:
% 141.52/21.00 | |
% 141.52/21.00 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/21.00 | |
% 141.52/21.00 | | ALPHA: (7) implies:
% 141.52/21.00 | | (8) op(e3, e3) = e1
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #838.
% 141.52/21.00 | |
% 141.52/21.00 | Case 2:
% 141.52/21.00 | |
% 141.52/21.00 | | (9) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/21.00 | |
% 141.52/21.00 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #846.
% 141.52/21.00 | |
% 141.52/21.00 | End of split
% 141.52/21.00 |
% 141.52/21.00 End of proof
% 141.52/21.00
% 141.52/21.00 Sub-proof #439 shows that the following formulas are inconsistent:
% 141.52/21.00 ----------------------------------------------------------------
% 141.52/21.00 (1) all_54_3 = all_52_12
% 141.52/21.00 (2) all_54_3 = e3
% 141.52/21.00 (3) ~ (all_52_12 = e3)
% 141.52/21.00
% 141.52/21.00 Begin of proof
% 141.52/21.00 |
% 141.52/21.00 | COMBINE_EQS: (1), (2) imply:
% 141.52/21.01 | (4) all_52_12 = e3
% 141.52/21.01 |
% 141.52/21.01 | SIMP: (4) implies:
% 141.52/21.01 | (5) all_52_12 = e3
% 141.52/21.01 |
% 141.52/21.01 | REDUCE: (3), (5) imply:
% 141.52/21.01 | (6) $false
% 141.52/21.01 |
% 141.52/21.01 | CLOSE: (6) is inconsistent.
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #440 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/21.01 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/21.01 (2) ~ (e2 = e1)
% 141.52/21.01 (3) all_57_5 = e3
% 141.52/21.01 (4) ~ (all_52_1 = e1)
% 141.52/21.01 (5) op(e2, e3) = all_52_1
% 141.52/21.01 (6) op(e2, e2) = e2
% 141.52/21.01 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (8) ~ (e3 = e1)
% 141.52/21.01 (9) ~ (all_52_13 = e1)
% 141.52/21.01 (10) op(e2, e0) = all_52_13
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (1) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (11) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 141.52/21.01 | | e1)
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (2), (4), (5), (6), (7), (11) are inconsistent by sub-proof #442.
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (12) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 141.52/21.01 | | e1)
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (3), (7), (8), (9), (10), (12) are inconsistent by sub-proof
% 141.52/21.01 | | #441.
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #441 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) all_57_5 = e3
% 141.52/21.01 (2) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/21.01 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (4) ~ (e3 = e1)
% 141.52/21.01 (5) ~ (all_52_13 = e1)
% 141.52/21.01 (6) op(e2, e0) = all_52_13
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (2) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (7) all_57_5 = e1 & op(e2, e1) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | ALPHA: (7) implies:
% 141.52/21.01 | | (8) all_57_5 = e1
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #1035.
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (9) all_57_10 = e1 & op(e2, e0) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (3), (5), (6), (9) are inconsistent by sub-proof #460.
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #442 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) ~ (e2 = e1)
% 141.52/21.01 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 141.52/21.01 (3) ~ (all_52_1 = e1)
% 141.52/21.01 (4) op(e2, e3) = all_52_1
% 141.52/21.01 (5) op(e2, e2) = e2
% 141.52/21.01 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (2) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (7) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (3), (4), (6), (7) are inconsistent by sub-proof #846.
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | ALPHA: (8) implies:
% 141.52/21.01 | | (9) op(e2, e2) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (1), (5), (6), (9) are inconsistent by sub-proof #749.
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #443 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) ~ (all_52_1 = e2)
% 141.52/21.01 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/21.01 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/21.01 (3) ~ (all_52_12 = e3)
% 141.52/21.01 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.52/21.01 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/21.01 (5) ~ (all_52_8 = e3)
% 141.52/21.01 (6) ~ (e2 = e1)
% 141.52/21.01 (7) op(e3, e3) = e3
% 141.52/21.01 (8) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/21.01 (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/21.01 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/21.01 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/21.01 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/21.01 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/21.01 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/21.01 e1) = all_56_14 & $i(all_56_14))
% 141.52/21.01 (10) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.52/21.01 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/21.01 (11) ~ (e3 = e0)
% 141.52/21.01 (12) op(e1, e1) = all_4_2
% 141.52/21.01 (13) ~ (all_52_4 = e3)
% 141.52/21.01 (14) op(e3, e1) = all_52_8
% 141.52/21.01 (15) ~ (all_52_7 = e2)
% 141.52/21.01 (16) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/21.01 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.52/21.01 e2)
% 141.52/21.01 (17) op(e2, e3) = all_52_1
% 141.52/21.01 (18) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.52/21.01 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.52/21.01 (19) ~ (all_4_2 = e3)
% 141.52/21.01 (20) ~ (e1 = e0)
% 141.52/21.01 (21) op(e2, e2) = e2
% 141.52/21.01 (22) op(e3, e2) = all_52_4
% 141.52/21.01 (23) ~ (e2 = e0)
% 141.52/21.01 (24) ~ (e3 = e2)
% 141.52/21.01 (25) op(e3, e0) = all_52_12
% 141.52/21.01 (26) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (27) ~ (e3 = e1)
% 141.52/21.01 (28) op(e0, e2) = all_52_7
% 141.52/21.01 (29) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/21.01 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/21.01 (30) op(e0, e0) = all_56_15
% 141.52/21.01 (31) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/21.01 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/21.01 (32) ~ (all_52_13 = e1)
% 141.52/21.01 (33) op(e2, e0) = all_52_13
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | ALPHA: (8) implies:
% 141.52/21.01 | (34) all_57_6 = e3
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (18) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (35) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 141.52/21.01 | | e1)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (35) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (36) all_57_0 = e1 & op(e3, e3) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (36) implies:
% 141.52/21.01 | | | (37) op(e3, e3) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (7), (26), (27), (37) are inconsistent by sub-proof #838.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (38) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (38) implies:
% 141.52/21.01 | | | (39) all_57_2 = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | BETA: splitting (29) gives:
% 141.52/21.01 | | |
% 141.52/21.01 | | | Case 1:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 141.52/21.01 | | | | = e3)
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | BETA: splitting (40) gives:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | Case 1:
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | (41) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | ALPHA: (41) implies:
% 141.52/21.01 | | | | | (42) all_57_0 = e3
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | REF_CLOSE: (1), (3), (5), (7), (10), (11), (13), (14), (17), (20),
% 141.52/21.01 | | | | | (22), (23), (24), (25), (26), (29), (31), (34), (39), (42)
% 141.52/21.01 | | | | | are inconsistent by sub-proof #447.
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | Case 2:
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | (43) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | ALPHA: (43) implies:
% 141.52/21.01 | | | | | (44) op(e3, e2) = e3
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | REF_CLOSE: (13), (22), (26), (44) are inconsistent by sub-proof #1107.
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | End of split
% 141.52/21.01 | | | |
% 141.52/21.01 | | | Case 2:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | (45) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 141.52/21.01 | | | | = e3)
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | REF_CLOSE: (3), (5), (14), (25), (26), (45) are inconsistent by
% 141.52/21.01 | | | | sub-proof #1104.
% 141.52/21.01 | | | |
% 141.52/21.01 | | | End of split
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (46) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 141.52/21.01 | | e1)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (46) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (47) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (27), (34), (47) are inconsistent by sub-proof #865.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (48) all_57_12 = e1 & op(e0, e3) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (48) implies:
% 141.52/21.01 | | | (49) all_57_12 = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | BETA: splitting (16) gives:
% 141.52/21.01 | | |
% 141.52/21.01 | | | Case 1:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | (50) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 141.52/21.01 | | | | e2) = e2)
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | REF_CLOSE: (6), (15), (26), (28), (49), (50) are inconsistent by
% 141.52/21.01 | | | | sub-proof #445.
% 141.52/21.01 | | | |
% 141.52/21.01 | | | Case 2:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | (51) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 141.52/21.01 | | | | e0) = e2)
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | BETA: splitting (51) gives:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | Case 1:
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | (52) all_57_14 = e2 & op(e0, e1) = e2
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | ALPHA: (52) implies:
% 141.52/21.01 | | | | | (53) all_57_14 = e2
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | BETA: splitting (29) gives:
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | Case 1:
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | | (54) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 141.52/21.01 | | | | | | e2) = e3)
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | | BETA: splitting (54) gives:
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | | Case 1:
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | (55) all_57_0 = e3 & op(e3, e3) = e3
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | ALPHA: (55) implies:
% 141.52/21.01 | | | | | | | (56) all_57_0 = e3
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | BETA: splitting (4) gives:
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | Case 1:
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | | (57) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 141.52/21.01 | | | | | | | | op(e2, e2) = e1)
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | | BETA: splitting (57) gives:
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | | Case 1:
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | | (58) all_57_2 = e1 & op(e2, e3) = e1
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | | ALPHA: (58) implies:
% 141.52/21.01 | | | | | | | | | (59) all_57_2 = e1
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | | REF_CLOSE: (1), (3), (5), (7), (10), (11), (13), (14), (17),
% 141.52/21.01 | | | | | | | | | (20), (22), (23), (24), (25), (26), (29), (31),
% 141.52/21.01 | | | | | | | | | (34), (56), (59) are inconsistent by sub-proof
% 141.52/21.01 | | | | | | | | | #447.
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | Case 2:
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | | (60) all_57_3 = e1 & op(e2, e2) = e1
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | | ALPHA: (60) implies:
% 141.52/21.01 | | | | | | | | | (61) op(e2, e2) = e1
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | | REF_CLOSE: (6), (21), (26), (61) are inconsistent by sub-proof
% 141.52/21.01 | | | | | | | | | #749.
% 141.52/21.01 | | | | | | | | |
% 141.52/21.01 | | | | | | | | End of split
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | Case 2:
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | | (62) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 141.52/21.01 | | | | | | | | op(e2, e0) = e1)
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | | REF_CLOSE: (2), (5), (12), (14), (19), (24), (26), (27), (32),
% 141.52/21.01 | | | | | | | | (33), (53), (62) are inconsistent by sub-proof #444.
% 141.52/21.01 | | | | | | | |
% 141.52/21.01 | | | | | | | End of split
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | Case 2:
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | (63) all_57_1 = e3 & op(e3, e2) = e3
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | ALPHA: (63) implies:
% 141.52/21.01 | | | | | | | (64) op(e3, e2) = e3
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | | REF_CLOSE: (13), (22), (26), (64) are inconsistent by sub-proof
% 141.52/21.01 | | | | | | | #1107.
% 141.52/21.01 | | | | | | |
% 141.52/21.01 | | | | | | End of split
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | Case 2:
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | | (65) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 141.52/21.01 | | | | | | e0) = e3)
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | | REF_CLOSE: (3), (5), (14), (25), (26), (65) are inconsistent by
% 141.52/21.01 | | | | | | sub-proof #1104.
% 141.52/21.01 | | | | | |
% 141.52/21.01 | | | | | End of split
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | Case 2:
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | (66) all_57_15 = e2 & op(e0, e0) = e2
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | ALPHA: (66) implies:
% 141.52/21.01 | | | | | (67) op(e0, e0) = e2
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | | REF_CLOSE: (6), (9), (21), (23), (24), (26), (30), (67) are
% 141.52/21.01 | | | | | inconsistent by sub-proof #643.
% 141.52/21.01 | | | | |
% 141.52/21.01 | | | | End of split
% 141.52/21.01 | | | |
% 141.52/21.01 | | | End of split
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #444 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.52/21.01 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.52/21.01 (2) ~ (all_52_8 = e3)
% 141.52/21.01 (3) all_57_14 = e2
% 141.52/21.01 (4) op(e1, e1) = all_4_2
% 141.52/21.01 (5) op(e3, e1) = all_52_8
% 141.52/21.01 (6) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.52/21.01 (7) ~ (all_4_2 = e3)
% 141.52/21.01 (8) ~ (e3 = e2)
% 141.52/21.01 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (10) ~ (e3 = e1)
% 141.52/21.01 (11) ~ (all_52_13 = e1)
% 141.52/21.01 (12) op(e2, e0) = all_52_13
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (6) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (13) all_57_5 = e1 & op(e2, e1) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | ALPHA: (13) implies:
% 141.52/21.01 | | (14) all_57_5 = e1
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (1) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (15) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 141.52/21.01 | | | e3)
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (2), (5), (9), (10), (14), (15) are inconsistent by sub-proof
% 141.52/21.01 | | | #1034.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (16) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 141.52/21.01 | | | e3)
% 141.52/21.01 | | |
% 141.52/21.01 | | | BETA: splitting (16) gives:
% 141.52/21.01 | | |
% 141.52/21.01 | | | Case 1:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | (17) all_57_8 = e3 & op(e1, e1) = e3
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | ALPHA: (17) implies:
% 141.52/21.01 | | | | (18) op(e1, e1) = e3
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | REF_CLOSE: (4), (7), (9), (18) are inconsistent by sub-proof #1127.
% 141.52/21.01 | | | |
% 141.52/21.01 | | | Case 2:
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | (19) all_57_14 = e3 & op(e0, e1) = e3
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | ALPHA: (19) implies:
% 141.52/21.01 | | | | (20) all_57_14 = e3
% 141.52/21.01 | | | |
% 141.52/21.01 | | | | REF_CLOSE: (3), (8), (20) are inconsistent by sub-proof #1011.
% 141.52/21.01 | | | |
% 141.52/21.01 | | | End of split
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (21) all_57_10 = e1 & op(e2, e0) = e1
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (9), (11), (12), (21) are inconsistent by sub-proof #460.
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #445 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) ~ (e2 = e1)
% 141.52/21.01 (2) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.52/21.01 (3) ~ (all_52_7 = e2)
% 141.52/21.01 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (5) op(e0, e2) = all_52_7
% 141.52/21.01 (6) all_57_12 = e1
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (2) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (7) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/21.01 | |
% 141.52/21.01 | | ALPHA: (7) implies:
% 141.52/21.01 | | (8) all_57_12 = e2
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #970.
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (9) all_57_13 = e2 & op(e0, e2) = e2
% 141.52/21.01 | |
% 141.52/21.01 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #446.
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #446 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) all_57_13 = e2 & op(e0, e2) = e2
% 141.52/21.01 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (3) op(e0, e2) = all_52_7
% 141.52/21.01 (4) ~ (all_52_7 = e2)
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | ALPHA: (1) implies:
% 141.52/21.01 | (5) op(e0, e2) = e2
% 141.52/21.01 |
% 141.52/21.01 | GROUND_INST: instantiating (2) with all_52_7, e2, e2, e0, simplifying with
% 141.52/21.01 | (3), (5) gives:
% 141.52/21.01 | (6) all_52_7 = e2
% 141.52/21.01 |
% 141.52/21.01 | REDUCE: (4), (6) imply:
% 141.52/21.01 | (7) $false
% 141.52/21.01 |
% 141.52/21.01 | CLOSE: (7) is inconsistent.
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #447 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) ~ (all_52_1 = e2)
% 141.52/21.01 (2) all_57_6 = e3
% 141.52/21.01 (3) ~ (all_52_12 = e3)
% 141.52/21.01 (4) ~ (all_52_8 = e3)
% 141.52/21.01 (5) op(e3, e3) = e3
% 141.52/21.01 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.52/21.01 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/21.01 (7) ~ (e3 = e0)
% 141.52/21.01 (8) ~ (all_52_4 = e3)
% 141.52/21.01 (9) op(e3, e1) = all_52_8
% 141.52/21.01 (10) op(e2, e3) = all_52_1
% 141.52/21.01 (11) ~ (e1 = e0)
% 141.52/21.01 (12) op(e3, e2) = all_52_4
% 141.52/21.01 (13) ~ (e2 = e0)
% 141.52/21.01 (14) ~ (e3 = e2)
% 141.52/21.01 (15) all_57_0 = e3
% 141.52/21.01 (16) op(e3, e0) = all_52_12
% 141.52/21.01 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/21.01 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/21.01 (19) all_57_2 = e1
% 141.52/21.01 (20) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.52/21.01 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (20) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (21) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 141.52/21.01 | | e2)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (21) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (22) all_57_0 = e2 & op(e3, e3) = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (22) implies:
% 141.52/21.01 | | | (23) op(e3, e3) = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (5), (14), (17), (23) are inconsistent by sub-proof #450.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (24) all_57_2 = e2 & op(e2, e3) = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (24) implies:
% 141.52/21.01 | | | (25) op(e2, e3) = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (1), (10), (17), (25) are inconsistent by sub-proof #882.
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (26) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 141.52/21.01 | | e2)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (26) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (27) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (2), (14), (27) are inconsistent by sub-proof #998.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (28) all_57_12 = e2 & op(e0, e3) = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (28) implies:
% 141.52/21.01 | | | (29) all_57_12 = e2
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (15),
% 141.52/21.01 | | | (16), (17), (18), (19), (29) are inconsistent by sub-proof
% 141.52/21.01 | | | #448.
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #448 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) all_57_6 = e3
% 141.52/21.01 (2) ~ (all_52_12 = e3)
% 141.52/21.01 (3) ~ (all_52_8 = e3)
% 141.52/21.01 (4) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 141.52/21.01 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 141.52/21.01 (5) ~ (e3 = e0)
% 141.52/21.01 (6) ~ (all_52_4 = e3)
% 141.52/21.01 (7) op(e3, e1) = all_52_8
% 141.52/21.01 (8) ~ (e1 = e0)
% 141.52/21.01 (9) op(e3, e2) = all_52_4
% 141.52/21.01 (10) ~ (e2 = e0)
% 141.52/21.01 (11) all_57_0 = e3
% 141.52/21.01 (12) op(e3, e0) = all_52_12
% 141.52/21.01 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.52/21.01 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.52/21.01 (15) all_57_2 = e1
% 141.52/21.01 (16) all_57_12 = e2
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (4) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (17) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 141.52/21.01 | | e0)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (17) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (18) all_57_0 = e0 & op(e3, e3) = e0
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (18) implies:
% 141.52/21.01 | | | (19) all_57_0 = e0
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (2), (3), (5), (6), (7), (9), (12), (13), (14), (19) are
% 141.52/21.01 | | | inconsistent by sub-proof #1103.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (20) all_57_2 = e0 & op(e2, e3) = e0
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (8), (15), (20) are inconsistent by sub-proof #449.
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.01 | | (21) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 141.52/21.01 | | e0)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (21) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (22) all_57_6 = e0 & op(e1, e3) = e0
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (9), (11), (12), (13), (14), (22)
% 141.52/21.01 | | | are inconsistent by sub-proof #959.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (23) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (10), (16), (23) are inconsistent by sub-proof #958.
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | End of split
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #449 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) all_57_2 = e0 & op(e2, e3) = e0
% 141.52/21.01 (2) all_57_2 = e1
% 141.52/21.01 (3) ~ (e1 = e0)
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | ALPHA: (1) implies:
% 141.52/21.01 | (4) all_57_2 = e0
% 141.52/21.01 |
% 141.52/21.01 | COMBINE_EQS: (2), (4) imply:
% 141.52/21.01 | (5) e1 = e0
% 141.52/21.01 |
% 141.52/21.01 | REDUCE: (3), (5) imply:
% 141.52/21.01 | (6) $false
% 141.52/21.01 |
% 141.52/21.01 | CLOSE: (6) is inconsistent.
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #450 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (2) op(e3, e3) = e3
% 141.52/21.01 (3) op(e3, e3) = e2
% 141.52/21.01 (4) ~ (e3 = e2)
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | GROUND_INST: instantiating (1) with e2, e3, e3, e3, simplifying with (2), (3)
% 141.52/21.01 | gives:
% 141.52/21.01 | (5) e3 = e2
% 141.52/21.01 |
% 141.52/21.01 | REDUCE: (4), (5) imply:
% 141.52/21.01 | (6) $false
% 141.52/21.01 |
% 141.52/21.01 | CLOSE: (6) is inconsistent.
% 141.52/21.01 |
% 141.52/21.01 End of proof
% 141.52/21.01
% 141.52/21.01 Sub-proof #451 shows that the following formulas are inconsistent:
% 141.52/21.01 ----------------------------------------------------------------
% 141.52/21.01 (1) ~ (all_52_14 = e1)
% 141.52/21.01 (2) ~ (e2 = e1)
% 141.52/21.01 (3) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.52/21.01 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/21.01 (4) op(e1, e1) = e0
% 141.52/21.01 (5) ~ (e3 = e0)
% 141.52/21.01 (6) op(e1, e1) = all_4_2
% 141.52/21.01 (7) all_57_6 = e0
% 141.52/21.01 (8) ~ (all_4_2 = e3)
% 141.52/21.01 (9) ~ (e1 = e0)
% 141.52/21.01 (10) ~ (e2 = e0)
% 141.52/21.01 (11) ~ (e3 = e2)
% 141.52/21.01 (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/21.01 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/21.01 (13) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/21.01 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/21.01 (14) ~ (all_4_2 = e2)
% 141.52/21.01 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.01 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.01 (16) ~ (e3 = e1)
% 141.52/21.01 (17) op(e1, e0) = all_52_14
% 141.52/21.01
% 141.52/21.01 Begin of proof
% 141.52/21.01 |
% 141.52/21.01 | BETA: splitting (3) gives:
% 141.52/21.01 |
% 141.52/21.01 | Case 1:
% 141.52/21.01 | |
% 141.52/21.01 | | (18) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.52/21.01 | | e1)
% 141.52/21.01 | |
% 141.52/21.01 | | BETA: splitting (18) gives:
% 141.52/21.01 | |
% 141.52/21.01 | | Case 1:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (19) all_57_6 = e1 & op(e1, e3) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (19) implies:
% 141.52/21.01 | | | (20) all_57_6 = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (7), (9), (20) are inconsistent by sub-proof #1026.
% 141.52/21.01 | | |
% 141.52/21.01 | | Case 2:
% 141.52/21.01 | | |
% 141.52/21.01 | | | (21) all_57_7 = e1 & op(e1, e2) = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | ALPHA: (21) implies:
% 141.52/21.01 | | | (22) all_57_7 = e1
% 141.52/21.01 | | |
% 141.52/21.01 | | | REF_CLOSE: (2), (5), (6), (7), (8), (10), (11), (12), (13), (14), (15),
% 141.52/21.01 | | | (16), (22) are inconsistent by sub-proof #453.
% 141.52/21.01 | | |
% 141.52/21.01 | | End of split
% 141.52/21.01 | |
% 141.52/21.01 | Case 2:
% 141.52/21.01 | |
% 141.52/21.02 | | (23) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.52/21.02 | | e1)
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (4), (9), (15), (17), (23) are inconsistent by sub-proof
% 141.52/21.02 | | #452.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #452 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ~ (all_52_14 = e1)
% 141.52/21.02 (2) op(e1, e1) = e0
% 141.52/21.02 (3) ~ (e1 = e0)
% 141.52/21.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (5) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.52/21.02 (6) op(e1, e0) = all_52_14
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (5) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (7) all_57_8 = e1 & op(e1, e1) = e1
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (7) implies:
% 141.52/21.02 | | (8) op(e1, e1) = e1
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #1089.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (9) all_57_11 = e1 & op(e1, e0) = e1
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (9) implies:
% 141.52/21.02 | | (10) op(e1, e0) = e1
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #459.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #453 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ~ (e2 = e1)
% 141.52/21.02 (2) all_57_7 = e1
% 141.52/21.02 (3) ~ (e3 = e0)
% 141.52/21.02 (4) op(e1, e1) = all_4_2
% 141.52/21.02 (5) all_57_6 = e0
% 141.52/21.02 (6) ~ (all_4_2 = e3)
% 141.52/21.02 (7) ~ (e2 = e0)
% 141.52/21.02 (8) ~ (e3 = e2)
% 141.52/21.02 (9) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/21.02 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/21.02 (10) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.52/21.02 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.52/21.02 (11) ~ (all_4_2 = e2)
% 141.52/21.02 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (13) ~ (e3 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (10) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 141.52/21.02 | | e2)
% 141.52/21.02 | |
% 141.52/21.02 | | BETA: splitting (14) gives:
% 141.52/21.02 | |
% 141.52/21.02 | | Case 1:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (15) all_57_6 = e2 & op(e1, e3) = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (15) implies:
% 141.52/21.02 | | | (16) all_57_6 = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (5), (7), (16) are inconsistent by sub-proof #811.
% 141.52/21.02 | | |
% 141.52/21.02 | | Case 2:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (17) all_57_7 = e2 & op(e1, e2) = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (17) implies:
% 141.52/21.02 | | | (18) all_57_7 = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (1), (2), (18) are inconsistent by sub-proof #872.
% 141.52/21.02 | | |
% 141.52/21.02 | | End of split
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (19) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 141.52/21.02 | | e2)
% 141.52/21.02 | |
% 141.52/21.02 | | BETA: splitting (19) gives:
% 141.52/21.02 | |
% 141.52/21.02 | | Case 1:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (20) all_57_8 = e2 & op(e1, e1) = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (20) implies:
% 141.52/21.02 | | | (21) op(e1, e1) = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (4), (11), (12), (21) are inconsistent by sub-proof #1124.
% 141.52/21.02 | | |
% 141.52/21.02 | | Case 2:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (22) all_57_11 = e2 & op(e1, e0) = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (22) implies:
% 141.52/21.02 | | | (23) all_57_11 = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (12), (13), (23) are
% 141.52/21.02 | | | inconsistent by sub-proof #454.
% 141.52/21.02 | | |
% 141.52/21.02 | | End of split
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #454 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) all_57_7 = e1
% 141.52/21.02 (2) ~ (e3 = e0)
% 141.52/21.02 (3) op(e1, e1) = all_4_2
% 141.52/21.02 (4) all_57_6 = e0
% 141.52/21.02 (5) ~ (all_4_2 = e3)
% 141.52/21.02 (6) all_57_11 = e2
% 141.52/21.02 (7) ~ (e3 = e2)
% 141.52/21.02 (8) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.52/21.02 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.52/21.02 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (10) ~ (e3 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (8) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 141.52/21.02 | | e3)
% 141.52/21.02 | |
% 141.52/21.02 | | BETA: splitting (11) gives:
% 141.52/21.02 | |
% 141.52/21.02 | | Case 1:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (12) all_57_6 = e3 & op(e1, e3) = e3
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (12) implies:
% 141.52/21.02 | | | (13) all_57_6 = e3
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (2), (4), (13) are inconsistent by sub-proof #873.
% 141.52/21.02 | | |
% 141.52/21.02 | | Case 2:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (14) all_57_7 = e3 & op(e1, e2) = e3
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (14) implies:
% 141.52/21.02 | | | (15) all_57_7 = e3
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (1), (10), (15) are inconsistent by sub-proof #915.
% 141.52/21.02 | | |
% 141.52/21.02 | | End of split
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (16) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 141.52/21.02 | | e3)
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (3), (5), (6), (7), (9), (16) are inconsistent by sub-proof #861.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #455 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ~ (all_4_2 = e0)
% 141.52/21.02 (2) ~ (e2 = e1)
% 141.52/21.02 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 141.52/21.02 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 141.52/21.02 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 141.52/21.02 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 141.52/21.02 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 141.52/21.02 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 141.52/21.02 e1) = all_56_14 & $i(all_56_14))
% 141.52/21.02 (4) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/21.02 (5) op(e1, e1) = all_4_2
% 141.52/21.02 (6) ~ (all_4_2 = e3)
% 141.52/21.02 (7) ~ (all_4_2 = e2)
% 141.52/21.02 (8) all_54_10 = all_4_2
% 141.52/21.02 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (10) all_56_15 = e1
% 141.52/21.02 (11) op(e3, e3) = all_14_2
% 141.52/21.02 (12) ~ (all_14_2 = e0)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (4) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (13) all_54_10 = e3
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (6), (8), (13) are inconsistent by sub-proof #1112.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (14) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 141.52/21.02 | |
% 141.52/21.02 | | BETA: splitting (14) gives:
% 141.52/21.02 | |
% 141.52/21.02 | | Case 1:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (15) all_54_10 = e2
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (7), (8), (15) are inconsistent by sub-proof #1111.
% 141.52/21.02 | | |
% 141.52/21.02 | | Case 2:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (16) all_54_10 = e1 | all_54_10 = e0
% 141.52/21.02 | | |
% 141.52/21.02 | | | BETA: splitting (3) gives:
% 141.52/21.02 | | |
% 141.52/21.02 | | | Case 1:
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | (17) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.52/21.02 | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.52/21.02 | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/21.02 | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | BETA: splitting (17) gives:
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | Case 1:
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | | (18) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 141.52/21.02 | | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | | ALPHA: (18) implies:
% 141.52/21.02 | | | | | (19) op(e3, e3) = e0
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | | REF_CLOSE: (9), (11), (12), (19) are inconsistent by sub-proof #1125.
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | Case 2:
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | | (20) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 141.52/21.02 | | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | | REF_CLOSE: (2), (10), (20) are inconsistent by sub-proof #458.
% 141.52/21.02 | | | | |
% 141.52/21.02 | | | | End of split
% 141.52/21.02 | | | |
% 141.52/21.02 | | | Case 2:
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | (21) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 141.52/21.02 | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 141.52/21.02 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 141.52/21.02 | | | | e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | REF_CLOSE: (1), (5), (8), (9), (16), (21) are inconsistent by sub-proof
% 141.52/21.02 | | | | #456.
% 141.52/21.02 | | | |
% 141.52/21.02 | | | End of split
% 141.52/21.02 | | |
% 141.52/21.02 | | End of split
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #456 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ~ (all_4_2 = e0)
% 141.52/21.02 (2) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 141.52/21.02 op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 141.52/21.02 e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.52/21.02 $i(all_56_14))
% 141.52/21.02 (3) all_54_10 = e1 | all_54_10 = e0
% 141.52/21.02 (4) op(e1, e1) = all_4_2
% 141.52/21.02 (5) all_54_10 = all_4_2
% 141.52/21.02 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (2) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (7) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 141.52/21.02 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (7) implies:
% 141.52/21.02 | | (8) op(e1, e1) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (3), (4), (5), (6), (8) are inconsistent by sub-proof #457.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (9) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 141.52/21.02 | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (9) implies:
% 141.52/21.02 | | (10) op(e1, e1) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (3), (4), (5), (6), (10) are inconsistent by sub-proof #457.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #457 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ~ (all_4_2 = e0)
% 141.52/21.02 (2) op(e1, e1) = e0
% 141.52/21.02 (3) all_54_10 = e1 | all_54_10 = e0
% 141.52/21.02 (4) op(e1, e1) = all_4_2
% 141.52/21.02 (5) all_54_10 = all_4_2
% 141.52/21.02 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (3) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (7) all_54_10 = e1
% 141.52/21.02 | |
% 141.52/21.02 | | COMBINE_EQS: (5), (7) imply:
% 141.52/21.02 | | (8) all_4_2 = e1
% 141.52/21.02 | |
% 141.52/21.02 | | SIMP: (8) implies:
% 141.52/21.02 | | (9) all_4_2 = e1
% 141.52/21.02 | |
% 141.52/21.02 | | REDUCE: (1), (9) imply:
% 141.52/21.02 | | (10) ~ (e1 = e0)
% 141.52/21.02 | |
% 141.52/21.02 | | REDUCE: (4), (9) imply:
% 141.52/21.02 | | (11) op(e1, e1) = e1
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (2), (6), (10), (11) are inconsistent by sub-proof #1089.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (12) all_54_10 = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #899.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #458 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 141.52/21.02 op(e0, e2) = all_56_12 & $i(all_56_12)
% 141.52/21.02 (2) all_56_15 = e1
% 141.52/21.02 (3) ~ (e2 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | ALPHA: (1) implies:
% 141.52/21.02 | (4) all_56_15 = e2
% 141.52/21.02 |
% 141.52/21.02 | COMBINE_EQS: (2), (4) imply:
% 141.52/21.02 | (5) e2 = e1
% 141.52/21.02 |
% 141.52/21.02 | SIMP: (5) implies:
% 141.52/21.02 | (6) e2 = e1
% 141.52/21.02 |
% 141.52/21.02 | REDUCE: (3), (6) imply:
% 141.52/21.02 | (7) $false
% 141.52/21.02 |
% 141.52/21.02 | CLOSE: (7) is inconsistent.
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #459 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (2) op(e1, e0) = all_52_14
% 141.52/21.02 (3) op(e1, e0) = e1
% 141.52/21.02 (4) ~ (all_52_14 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | GROUND_INST: instantiating (1) with all_52_14, e1, e0, e1, simplifying with
% 141.52/21.02 | (2), (3) gives:
% 141.52/21.02 | (5) all_52_14 = e1
% 141.52/21.02 |
% 141.52/21.02 | REDUCE: (4), (5) imply:
% 141.52/21.02 | (6) $false
% 141.52/21.02 |
% 141.52/21.02 | CLOSE: (6) is inconsistent.
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #460 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) all_57_10 = e1 & op(e2, e0) = e1
% 141.52/21.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (3) op(e2, e0) = all_52_13
% 141.52/21.02 (4) ~ (all_52_13 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | ALPHA: (1) implies:
% 141.52/21.02 | (5) op(e2, e0) = e1
% 141.52/21.02 |
% 141.52/21.02 | GROUND_INST: instantiating (2) with all_52_13, e1, e0, e2, simplifying with
% 141.52/21.02 | (3), (5) gives:
% 141.52/21.02 | (6) all_52_13 = e1
% 141.52/21.02 |
% 141.52/21.02 | REDUCE: (4), (6) imply:
% 141.52/21.02 | (7) $false
% 141.52/21.02 |
% 141.52/21.02 | CLOSE: (7) is inconsistent.
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #461 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) all_57_9 = e1 & op(e3, e0) = e1
% 141.52/21.02 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (3) op(e3, e0) = all_52_12
% 141.52/21.02 (4) ~ (all_52_12 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | ALPHA: (1) implies:
% 141.52/21.02 | (5) op(e3, e0) = e1
% 141.52/21.02 |
% 141.52/21.02 | GROUND_INST: instantiating (2) with all_52_12, e1, e0, e3, simplifying with
% 141.52/21.02 | (3), (5) gives:
% 141.52/21.02 | (6) all_52_12 = e1
% 141.52/21.02 |
% 141.52/21.02 | REDUCE: (4), (6) imply:
% 141.52/21.02 | (7) $false
% 141.52/21.02 |
% 141.52/21.02 | CLOSE: (7) is inconsistent.
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #462 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) op(e1, e1) = all_4_2
% 141.52/21.02 (2) op(e0, e0) = e1
% 141.52/21.02 (3) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 141.52/21.02 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 141.52/21.02 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 141.52/21.02 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 141.52/21.02 (4) ~ (all_4_2 = e2)
% 141.52/21.02 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (6) ~ (e3 = e1)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (3) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (7) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 141.52/21.02 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (7) implies:
% 141.52/21.02 | | (8) op(e0, e0) = e3
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #732.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (9) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 141.52/21.02 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (9) implies:
% 141.52/21.02 | | (10) op(e1, e1) = e2
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #1124.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #463 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) op(e3, e1) = all_52_8
% 141.52/21.02 (2) ~ (all_52_12 = e0)
% 141.52/21.02 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/21.02 (4) op(e3, e0) = all_52_12
% 141.52/21.02 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (6) ~ (all_52_8 = e0)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (3) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (7) all_57_4 = e0 & op(e3, e1) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (5), (6), (7) are inconsistent by sub-proof #981.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (8) all_57_9 = e0 & op(e3, e0) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (8) implies:
% 141.52/21.02 | | (9) op(e3, e0) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #941.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #464 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) op(e1, e2) = all_52_6
% 141.52/21.02 (2) ~ (all_52_7 = e0)
% 141.52/21.02 (3) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.52/21.02 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (5) op(e0, e2) = all_52_7
% 141.52/21.02 (6) ~ (all_52_6 = e0)
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (3) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (7) all_57_7 = e0 & op(e1, e2) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (7) implies:
% 141.52/21.02 | | (8) op(e1, e2) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (1), (4), (6), (8) are inconsistent by sub-proof #999.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (9) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (9) implies:
% 141.52/21.02 | | (10) op(e0, e2) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #977.
% 141.52/21.02 | |
% 141.52/21.02 | End of split
% 141.52/21.02 |
% 141.52/21.02 End of proof
% 141.52/21.02
% 141.52/21.02 Sub-proof #465 shows that the following formulas are inconsistent:
% 141.52/21.02 ----------------------------------------------------------------
% 141.52/21.02 (1) ~ (all_52_13 = e0)
% 141.52/21.02 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.52/21.02 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/21.02 (3) ~ (e2 = e1)
% 141.52/21.02 (4) ~ (all_52_7 = e0)
% 141.52/21.02 (5) op(e0, e3) = all_52_3
% 141.52/21.02 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.52/21.02 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/21.02 (7) ~ (e3 = e0)
% 141.52/21.02 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.52/21.02 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.52/21.02 (9) all_57_13 = e2
% 141.52/21.02 (10) ~ (all_52_12 = e0)
% 141.52/21.02 (11) ~ (e1 = e0)
% 141.52/21.02 (12) all_57_9 = e2
% 141.52/21.02 (13) ~ (e2 = e0)
% 141.52/21.02 (14) ~ (e3 = e2)
% 141.52/21.02 (15) op(e3, e0) = all_52_12
% 141.52/21.02 (16) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.52/21.02 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.52/21.02 (17) op(e0, e0) = e2
% 141.52/21.02 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.52/21.02 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.52/21.02 (19) ~ (all_52_3 = e0)
% 141.52/21.02 (20) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.52/21.02 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.52/21.02 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.52/21.02 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.52/21.02 (21) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.52/21.02 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.52/21.02 (22) ~ (e3 = e1)
% 141.52/21.02 (23) op(e0, e2) = all_52_7
% 141.52/21.02 (24) op(e2, e0) = all_52_13
% 141.52/21.02
% 141.52/21.02 Begin of proof
% 141.52/21.02 |
% 141.52/21.02 | BETA: splitting (20) gives:
% 141.52/21.02 |
% 141.52/21.02 | Case 1:
% 141.52/21.02 | |
% 141.52/21.02 | | (25) all_57_15 = e0 & op(e0, e0) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (25) implies:
% 141.52/21.02 | | (26) op(e0, e0) = e0
% 141.52/21.02 | |
% 141.52/21.02 | | REF_CLOSE: (13), (17), (18), (26) are inconsistent by sub-proof #1094.
% 141.52/21.02 | |
% 141.52/21.02 | Case 2:
% 141.52/21.02 | |
% 141.52/21.02 | | (27) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.52/21.02 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 141.52/21.02 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.52/21.02 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.52/21.02 | |
% 141.52/21.02 | | ALPHA: (27) implies:
% 141.52/21.02 | | (28) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.52/21.02 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.52/21.02 | | (29) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.52/21.02 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 141.52/21.02 | |
% 141.52/21.02 | | BETA: splitting (28) gives:
% 141.52/21.02 | |
% 141.52/21.02 | | Case 1:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (30) all_57_12 = e0 & op(e0, e3) = e0
% 141.52/21.02 | | |
% 141.52/21.02 | | | ALPHA: (30) implies:
% 141.52/21.02 | | | (31) op(e0, e3) = e0
% 141.52/21.02 | | |
% 141.52/21.02 | | | REF_CLOSE: (5), (18), (19), (31) are inconsistent by sub-proof #986.
% 141.52/21.02 | | |
% 141.52/21.02 | | Case 2:
% 141.52/21.02 | | |
% 141.52/21.02 | | | (32) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 141.52/21.02 | | | = e0)
% 141.52/21.02 | | |
% 141.52/21.02 | | | BETA: splitting (32) gives:
% 141.52/21.02 | | |
% 141.52/21.02 | | | Case 1:
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | (33) all_57_13 = e0 & op(e0, e2) = e0
% 141.52/21.02 | | | |
% 141.52/21.02 | | | | ALPHA: (33) implies:
% 141.59/21.02 | | | | (34) op(e0, e2) = e0
% 141.59/21.02 | | | |
% 141.59/21.02 | | | | REF_CLOSE: (4), (18), (23), (34) are inconsistent by sub-proof #977.
% 141.59/21.02 | | | |
% 141.59/21.02 | | | Case 2:
% 141.59/21.02 | | | |
% 141.59/21.02 | | | | (35) all_57_14 = e0 & op(e0, e1) = e0
% 141.59/21.02 | | | |
% 141.59/21.02 | | | | ALPHA: (35) implies:
% 141.59/21.02 | | | | (36) all_57_14 = e0
% 141.59/21.02 | | | |
% 141.59/21.02 | | | | BETA: splitting (2) gives:
% 141.59/21.02 | | | |
% 141.59/21.02 | | | | Case 1:
% 141.59/21.02 | | | | |
% 141.59/21.02 | | | | | (37) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 141.59/21.02 | | | | | e2) = e3)
% 141.59/21.02 | | | | |
% 141.59/21.02 | | | | | BETA: splitting (37) gives:
% 141.59/21.02 | | | | |
% 141.59/21.02 | | | | | Case 1:
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | (38) all_57_12 = e3 & op(e0, e3) = e3
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | ALPHA: (38) implies:
% 141.59/21.02 | | | | | | (39) all_57_12 = e3
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | BETA: splitting (29) gives:
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | Case 1:
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | | (40) all_57_9 = e0 & op(e3, e0) = e0
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | | ALPHA: (40) implies:
% 141.59/21.02 | | | | | | | (41) op(e3, e0) = e0
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | | REF_CLOSE: (10), (15), (18), (41) are inconsistent by sub-proof
% 141.59/21.02 | | | | | | | #941.
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | Case 2:
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | | (42) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 141.59/21.02 | | | | | | | op(e1, e0) = e0)
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | | BETA: splitting (42) gives:
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | | Case 1:
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | | (43) all_57_10 = e0 & op(e2, e0) = e0
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | | REF_CLOSE: (1), (18), (24), (43) are inconsistent by sub-proof
% 141.59/21.02 | | | | | | | | #1078.
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | Case 2:
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | | (44) all_57_11 = e0 & op(e1, e0) = e0
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | | ALPHA: (44) implies:
% 141.59/21.02 | | | | | | | | (45) all_57_11 = e0
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | | BETA: splitting (21) gives:
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | | Case 1:
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | | (46) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 141.59/21.02 | | | | | | | | | op(e2, e0) = e1)
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | | BETA: splitting (46) gives:
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | | Case 1:
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | | (47) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | | REF_CLOSE: (3), (12), (47) are inconsistent by sub-proof
% 141.59/21.02 | | | | | | | | | | #691.
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | Case 2:
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | | (48) all_57_10 = e1 & op(e2, e0) = e1
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | | ALPHA: (48) implies:
% 141.59/21.02 | | | | | | | | | | (49) all_57_10 = e1
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (11), (12), (13), (14),
% 141.59/21.02 | | | | | | | | | | (16), (18), (20), (22), (23), (39), (45), (49) are
% 141.59/21.02 | | | | | | | | | | inconsistent by sub-proof #466.
% 141.59/21.02 | | | | | | | | | |
% 141.59/21.02 | | | | | | | | | End of split
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | Case 2:
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | | (50) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 141.59/21.02 | | | | | | | | | op(e0, e0) = e1)
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | | REF_CLOSE: (3), (11), (17), (18), (45), (50) are inconsistent
% 141.59/21.02 | | | | | | | | | by sub-proof #498.
% 141.59/21.02 | | | | | | | | |
% 141.59/21.02 | | | | | | | | End of split
% 141.59/21.02 | | | | | | | |
% 141.59/21.02 | | | | | | | End of split
% 141.59/21.02 | | | | | | |
% 141.59/21.02 | | | | | | End of split
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | Case 2:
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | (51) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | ALPHA: (51) implies:
% 141.59/21.02 | | | | | | (52) all_57_13 = e3
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | | REF_CLOSE: (9), (14), (52) are inconsistent by sub-proof #1068.
% 141.59/21.02 | | | | | |
% 141.59/21.02 | | | | | End of split
% 141.59/21.02 | | | | |
% 141.59/21.02 | | | | Case 2:
% 141.59/21.02 | | | | |
% 141.59/21.02 | | | | | (53) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 141.59/21.02 | | | | | e0) = e3)
% 141.59/21.02 | | | | |
% 141.59/21.02 | | | | | REF_CLOSE: (7), (14), (17), (18), (36), (53) are inconsistent by
% 141.59/21.02 | | | | | sub-proof #1065.
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | End of split
% 141.59/21.03 | | | |
% 141.59/21.03 | | | End of split
% 141.59/21.03 | | |
% 141.59/21.03 | | End of split
% 141.59/21.03 | |
% 141.59/21.03 | End of split
% 141.59/21.03 |
% 141.59/21.03 End of proof
% 141.59/21.03
% 141.59/21.03 Sub-proof #466 shows that the following formulas are inconsistent:
% 141.59/21.03 ----------------------------------------------------------------
% 141.59/21.03 (1) all_57_11 = e0
% 141.59/21.03 (2) ~ (e2 = e1)
% 141.59/21.03 (3) ~ (all_52_7 = e0)
% 141.59/21.03 (4) all_57_12 = e3
% 141.59/21.03 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.59/21.03 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.03 (6) ~ (e3 = e0)
% 141.59/21.03 (7) all_57_10 = e1
% 141.59/21.03 (8) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.59/21.03 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.03 (9) ~ (e1 = e0)
% 141.59/21.03 (10) all_57_9 = e2
% 141.59/21.03 (11) ~ (e2 = e0)
% 141.59/21.03 (12) ~ (e3 = e2)
% 141.59/21.03 (13) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.59/21.03 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.03 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.03 (15) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.59/21.03 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.59/21.03 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.59/21.03 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.59/21.03 (16) ~ (e3 = e1)
% 141.59/21.03 (17) op(e0, e2) = all_52_7
% 141.59/21.03
% 141.59/21.03 Begin of proof
% 141.59/21.03 |
% 141.59/21.03 | BETA: splitting (13) gives:
% 141.59/21.03 |
% 141.59/21.03 | Case 1:
% 141.59/21.03 | |
% 141.59/21.03 | | (18) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 141.59/21.03 | | e3)
% 141.59/21.03 | |
% 141.59/21.03 | | BETA: splitting (18) gives:
% 141.59/21.03 | |
% 141.59/21.03 | | Case 1:
% 141.59/21.03 | | |
% 141.59/21.03 | | | (19) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | ALPHA: (19) implies:
% 141.59/21.03 | | | (20) all_57_9 = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | REF_CLOSE: (10), (12), (20) are inconsistent by sub-proof #581.
% 141.59/21.03 | | |
% 141.59/21.03 | | Case 2:
% 141.59/21.03 | | |
% 141.59/21.03 | | | (21) all_57_10 = e3 & op(e2, e0) = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | ALPHA: (21) implies:
% 141.59/21.03 | | | (22) all_57_10 = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | REF_CLOSE: (7), (16), (22) are inconsistent by sub-proof #877.
% 141.59/21.03 | | |
% 141.59/21.03 | | End of split
% 141.59/21.03 | |
% 141.59/21.03 | Case 2:
% 141.59/21.03 | |
% 141.59/21.03 | | (23) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.59/21.03 | | e3)
% 141.59/21.03 | |
% 141.59/21.03 | | BETA: splitting (23) gives:
% 141.59/21.03 | |
% 141.59/21.03 | | Case 1:
% 141.59/21.03 | | |
% 141.59/21.03 | | | (24) all_57_11 = e3 & op(e1, e0) = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | ALPHA: (24) implies:
% 141.59/21.03 | | | (25) all_57_11 = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | REF_CLOSE: (1), (6), (25) are inconsistent by sub-proof #858.
% 141.59/21.03 | | |
% 141.59/21.03 | | Case 2:
% 141.59/21.03 | | |
% 141.59/21.03 | | | (26) all_57_15 = e3 & op(e0, e0) = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (11), (12), (14), (15),
% 141.59/21.03 | | | (16), (17), (26) are inconsistent by sub-proof #467.
% 141.59/21.03 | | |
% 141.59/21.03 | | End of split
% 141.59/21.03 | |
% 141.59/21.03 | End of split
% 141.59/21.03 |
% 141.59/21.03 End of proof
% 141.59/21.03
% 141.59/21.03 Sub-proof #467 shows that the following formulas are inconsistent:
% 141.59/21.03 ----------------------------------------------------------------
% 141.59/21.03 (1) ~ (e2 = e1)
% 141.59/21.03 (2) ~ (all_52_7 = e0)
% 141.59/21.03 (3) all_57_12 = e3
% 141.59/21.03 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.59/21.03 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.03 (5) ~ (e3 = e0)
% 141.59/21.03 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.59/21.03 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.03 (7) ~ (e1 = e0)
% 141.59/21.03 (8) ~ (e2 = e0)
% 141.59/21.03 (9) ~ (e3 = e2)
% 141.59/21.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.03 (11) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.59/21.03 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.59/21.03 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.59/21.03 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.59/21.03 (12) ~ (e3 = e1)
% 141.59/21.03 (13) op(e0, e2) = all_52_7
% 141.59/21.03 (14) all_57_15 = e3 & op(e0, e0) = e3
% 141.59/21.03
% 141.59/21.03 Begin of proof
% 141.59/21.03 |
% 141.59/21.03 | ALPHA: (14) implies:
% 141.59/21.03 | (15) op(e0, e0) = e3
% 141.59/21.03 |
% 141.59/21.03 | BETA: splitting (11) gives:
% 141.59/21.03 |
% 141.59/21.03 | Case 1:
% 141.59/21.03 | |
% 141.59/21.03 | | (16) all_57_15 = e0 & op(e0, e0) = e0
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (16) implies:
% 141.59/21.03 | | (17) op(e0, e0) = e0
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (5), (10), (15), (17) are inconsistent by sub-proof #751.
% 141.59/21.03 | |
% 141.59/21.03 | Case 2:
% 141.59/21.03 | |
% 141.59/21.03 | | (18) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.59/21.03 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 141.59/21.03 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.59/21.03 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (18) implies:
% 141.59/21.03 | | (19) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.59/21.03 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12), (13),
% 141.59/21.03 | | (15), (19) are inconsistent by sub-proof #656.
% 141.59/21.03 | |
% 141.59/21.03 | End of split
% 141.59/21.03 |
% 141.59/21.03 End of proof
% 141.59/21.03
% 141.59/21.03 Sub-proof #468 shows that the following formulas are inconsistent:
% 141.59/21.03 ----------------------------------------------------------------
% 141.59/21.03 (1) all_57_11 = e0
% 141.59/21.03 (2) ~ (e2 = e1)
% 141.59/21.03 (3) ~ (all_52_7 = e0)
% 141.59/21.03 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.59/21.03 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.03 (5) ~ (e3 = e0)
% 141.59/21.03 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.59/21.03 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.03 (7) ~ (e1 = e0)
% 141.59/21.03 (8) ~ (e2 = e0)
% 141.59/21.03 (9) ~ (e3 = e2)
% 141.59/21.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.03 (11) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.59/21.03 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.59/21.03 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.59/21.03 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.59/21.03 (12) ~ (e3 = e1)
% 141.59/21.03 (13) all_57_13 = e3
% 141.59/21.03 (14) op(e0, e2) = all_52_7
% 141.59/21.03 (15) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.03
% 141.59/21.03 Begin of proof
% 141.59/21.03 |
% 141.59/21.03 | BETA: splitting (15) gives:
% 141.59/21.03 |
% 141.59/21.03 | Case 1:
% 141.59/21.03 | |
% 141.59/21.03 | | (16) all_57_11 = e3 & op(e1, e0) = e3
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (16) implies:
% 141.59/21.03 | | (17) all_57_11 = e3
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (1), (5), (17) are inconsistent by sub-proof #858.
% 141.59/21.03 | |
% 141.59/21.03 | Case 2:
% 141.59/21.03 | |
% 141.59/21.03 | | (18) all_57_15 = e3 & op(e0, e0) = e3
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (18) implies:
% 141.59/21.03 | | (19) op(e0, e0) = e3
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.59/21.03 | | (14), (19) are inconsistent by sub-proof #469.
% 141.59/21.03 | |
% 141.59/21.03 | End of split
% 141.59/21.03 |
% 141.59/21.03 End of proof
% 141.59/21.03
% 141.59/21.03 Sub-proof #469 shows that the following formulas are inconsistent:
% 141.59/21.03 ----------------------------------------------------------------
% 141.59/21.03 (1) ~ (e2 = e1)
% 141.59/21.03 (2) op(e0, e0) = e3
% 141.59/21.03 (3) ~ (all_52_7 = e0)
% 141.59/21.03 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.59/21.03 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.03 (5) ~ (e3 = e0)
% 141.59/21.03 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 141.59/21.03 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.03 (7) ~ (e1 = e0)
% 141.59/21.03 (8) ~ (e2 = e0)
% 141.59/21.03 (9) ~ (e3 = e2)
% 141.59/21.03 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.03 (11) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 141.59/21.03 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 141.59/21.03 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 141.59/21.03 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 141.59/21.03 (12) ~ (e3 = e1)
% 141.59/21.03 (13) all_57_13 = e3
% 141.59/21.03 (14) op(e0, e2) = all_52_7
% 141.59/21.03
% 141.59/21.03 Begin of proof
% 141.59/21.03 |
% 141.59/21.03 | BETA: splitting (11) gives:
% 141.59/21.03 |
% 141.59/21.03 | Case 1:
% 141.59/21.03 | |
% 141.59/21.03 | | (15) all_57_15 = e0 & op(e0, e0) = e0
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (15) implies:
% 141.59/21.03 | | (16) op(e0, e0) = e0
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (2), (5), (10), (16) are inconsistent by sub-proof #751.
% 141.59/21.03 | |
% 141.59/21.03 | Case 2:
% 141.59/21.03 | |
% 141.59/21.03 | | (17) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 141.59/21.03 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 141.59/21.03 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.59/21.03 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (17) implies:
% 141.59/21.03 | | (18) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 141.59/21.03 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (12), (13), (14),
% 141.59/21.03 | | (18) are inconsistent by sub-proof #665.
% 141.59/21.03 | |
% 141.59/21.03 | End of split
% 141.59/21.03 |
% 141.59/21.03 End of proof
% 141.59/21.03
% 141.59/21.03 Sub-proof #470 shows that the following formulas are inconsistent:
% 141.59/21.03 ----------------------------------------------------------------
% 141.59/21.03 (1) all_57_14 = e0
% 141.59/21.03 (2) ~ (e2 = e1)
% 141.59/21.03 (3) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.03 (4) ~ (e1 = e0)
% 141.59/21.03 (5) op(e0, e0) = e2
% 141.59/21.03 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.03
% 141.59/21.03 Begin of proof
% 141.59/21.03 |
% 141.59/21.03 | BETA: splitting (3) gives:
% 141.59/21.03 |
% 141.59/21.03 | Case 1:
% 141.59/21.03 | |
% 141.59/21.03 | | (7) all_57_14 = e1 & op(e0, e1) = e1
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #668.
% 141.59/21.03 | |
% 141.59/21.03 | Case 2:
% 141.59/21.03 | |
% 141.59/21.03 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 141.59/21.03 | |
% 141.59/21.03 | | ALPHA: (8) implies:
% 141.59/21.03 | | (9) op(e0, e0) = e1
% 141.59/21.03 | |
% 141.59/21.03 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #1070.
% 141.59/21.03 | |
% 141.59/21.03 | End of split
% 141.59/21.03 |
% 141.59/21.03 End of proof
% 141.59/21.03
% 141.59/21.03 Sub-proof #471 shows that the following formulas are inconsistent:
% 141.59/21.03 ----------------------------------------------------------------
% 141.59/21.03 (1) ~ (all_52_1 = e2)
% 141.59/21.03 (2) all_57_14 = e0
% 141.59/21.03 (3) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.59/21.03 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.59/21.03 (4) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.03 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.59/21.03 (5) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.03 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.03 (6) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.03 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.03 (7) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.03 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.03 (8) op(e1, e3) = all_52_2
% 141.59/21.03 (9) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.03 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.59/21.03 (10) all_57_11 = e0
% 141.59/21.03 (11) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.03 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 141.59/21.03 (12) ~ (e2 = e1)
% 141.59/21.03 (13) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.03 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.03 (14) ~ (all_52_7 = e0)
% 141.59/21.03 (15) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 141.59/21.03 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 141.59/21.03 e0) = all_16_1 & $i(all_16_1))
% 141.59/21.03 (16) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 141.59/21.03 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2,
% 141.59/21.03 e0) = all_18_1 & $i(all_18_1))
% 141.59/21.03 (17) op(e0, e3) = all_52_3
% 141.59/21.03 (18) op(e0, e1) = e0
% 141.59/21.03 (19) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.03 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.59/21.03 e1)
% 141.59/21.03 (20) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.59/21.03 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.03 (21) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.03 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.03 (22) ~ (e3 = e0)
% 141.59/21.03 (23) op(e1, e1) = e1
% 141.59/21.03 (24) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.03 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.59/21.03 e2)
% 141.59/21.03 (25) op(e2, e3) = all_52_1
% 141.59/21.03 (26) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 141.59/21.03 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 141.59/21.03 e0) = all_14_1 & $i(all_14_1))
% 141.59/21.03 (27) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 141.59/21.03 (all_57_11 = e0 & op(e1, e0) = e0)
% 141.59/21.03 (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 141.59/21.03 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 141.59/21.03 (29) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.59/21.03 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.59/21.03 (30) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.59/21.03 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.59/21.03 (31) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.59/21.03 all_56_15 & $i(all_56_15))
% 141.59/21.03 (32) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.59/21.03 | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.03 (33) all_28_2 = e0
% 141.59/21.03 (34) ~ (e1 = e0)
% 141.59/21.03 (35) ~ (e2 = e0)
% 141.59/21.03 (36) ~ (e3 = e2)
% 141.59/21.03 (37) op(e3, e0) = all_52_12
% 141.59/21.03 (38) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.59/21.03 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.59/21.03 (39) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.59/21.03 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.03 (40) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.03 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.03 (41) op(e0, e0) = e2
% 141.59/21.03 (42) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.03 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.03 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.03 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.03 (44) all_57_5 = e2
% 141.59/21.03 (45) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 141.59/21.03 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 141.59/21.03 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 141.59/21.03 (46) ~ (all_52_3 = e0)
% 141.59/21.03 (47) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.03 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.03 (48) ~ (e3 = e1)
% 141.59/21.03 (49) op(e0, e2) = all_52_7
% 141.59/21.03 (50) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.03 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.03 (51) op(e2, e2) = e0
% 141.59/21.03 (52) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.59/21.03 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.59/21.03 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.59/21.03 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.59/21.03 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.59/21.03 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.59/21.03 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.59/21.03 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.59/21.03 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.59/21.03 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.59/21.03 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.59/21.03 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.59/21.03 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.59/21.03 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.59/21.03 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.59/21.03 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.59/21.03 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.59/21.03 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.59/21.03 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.59/21.03 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.59/21.03 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.59/21.03 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.59/21.03 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.59/21.03 $i(all_56_14))))
% 141.59/21.03 (53) all_57_0 = e0
% 141.59/21.03 (54) op(e3, e3) = e0
% 141.59/21.03 (55) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 141.59/21.03 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 141.59/21.03 (56) all_57_3 = e0
% 141.59/21.03 (57) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.59/21.03 all_56_13 & $i(all_56_13))
% 141.59/21.03 (58) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.03 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.03 (59) all_57_8 = e1
% 141.59/21.03
% 141.59/21.03 Begin of proof
% 141.59/21.03 |
% 141.59/21.03 | BETA: splitting (7) gives:
% 141.59/21.03 |
% 141.59/21.03 | Case 1:
% 141.59/21.03 | |
% 141.59/21.03 | | (60) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 141.59/21.03 | | e3)
% 141.59/21.03 | |
% 141.59/21.03 | | BETA: splitting (60) gives:
% 141.59/21.03 | |
% 141.59/21.03 | | Case 1:
% 141.59/21.03 | | |
% 141.59/21.03 | | | (61) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | ALPHA: (61) implies:
% 141.59/21.03 | | | (62) all_57_4 = e3
% 141.59/21.03 | | |
% 141.59/21.03 | | | BETA: splitting (3) gives:
% 141.59/21.03 | | |
% 141.59/21.03 | | | Case 1:
% 141.59/21.03 | | | |
% 141.59/21.03 | | | | (63) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2)
% 141.59/21.03 | | | | = e2)
% 141.59/21.03 | | | |
% 141.59/21.03 | | | | BETA: splitting (63) gives:
% 141.59/21.03 | | | |
% 141.59/21.03 | | | | Case 1:
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | (64) all_57_0 = e2 & op(e3, e3) = e2
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | ALPHA: (64) implies:
% 141.59/21.03 | | | | | (65) op(e3, e3) = e2
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | REF_CLOSE: (35), (43), (54), (65) are inconsistent by sub-proof #880.
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | Case 2:
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | (66) all_57_1 = e2 & op(e3, e2) = e2
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | ALPHA: (66) implies:
% 141.59/21.03 | | | | | (67) all_57_1 = e2
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | BETA: splitting (5) gives:
% 141.59/21.03 | | | | |
% 141.59/21.03 | | | | | Case 1:
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | | (68) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 141.59/21.03 | | | | | | e2) = e1)
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | | BETA: splitting (68) gives:
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | | Case 1:
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | (69) all_57_1 = e1 & op(e3, e2) = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | REF_CLOSE: (2), (12), (35), (36), (42), (44), (59), (62), (67),
% 141.59/21.03 | | | | | | | (69) are inconsistent by sub-proof #474.
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | Case 2:
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | (70) all_57_3 = e1 & op(e2, e2) = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | ALPHA: (70) implies:
% 141.59/21.03 | | | | | | | (71) op(e2, e2) = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | REF_CLOSE: (34), (43), (51), (71) are inconsistent by sub-proof
% 141.59/21.03 | | | | | | | #1117.
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | End of split
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | Case 2:
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | | (72) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 141.59/21.03 | | | | | | e2) = e1)
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | | BETA: splitting (72) gives:
% 141.59/21.03 | | | | | |
% 141.59/21.03 | | | | | | Case 1:
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | (73) all_57_7 = e1 & op(e1, e2) = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | ALPHA: (73) implies:
% 141.59/21.03 | | | | | | | (74) all_57_7 = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | BETA: splitting (40) gives:
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | (75) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 141.59/21.03 | | | | | | | | op(e1, e2) = e2)
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | BETA: splitting (75) gives:
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | (76) all_57_6 = e2 & op(e1, e3) = e2
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | ALPHA: (76) implies:
% 141.59/21.03 | | | | | | | | | (77) op(e1, e3) = e2
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | BETA: splitting (28) gives:
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | (78) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 &
% 141.59/21.03 | | | | | | | | | | op(e3, e2) = e1)
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | BETA: splitting (78) gives:
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | (79) all_57_0 = e1 & op(e3, e3) = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | ALPHA: (79) implies:
% 141.59/21.03 | | | | | | | | | | | (80) op(e3, e3) = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | REF_CLOSE: (34), (43), (54), (80) are inconsistent by
% 141.59/21.03 | | | | | | | | | | | sub-proof #840.
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | Case 2:
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | (81) all_57_1 = e1 & op(e3, e2) = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | REF_CLOSE: (2), (12), (35), (36), (42), (44), (59), (62),
% 141.59/21.03 | | | | | | | | | | | (67), (81) are inconsistent by sub-proof #474.
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | End of split
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | Case 2:
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | (82) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 &
% 141.59/21.03 | | | | | | | | | | op(e3, e0) = e1)
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | BETA: splitting (82) gives:
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | (83) all_57_4 = e1 & op(e3, e1) = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | ALPHA: (83) implies:
% 141.59/21.03 | | | | | | | | | | | (84) all_57_4 = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (12),
% 141.59/21.03 | | | | | | | | | | | (13), (14), (17), (18), (19), (20), (21), (22),
% 141.59/21.03 | | | | | | | | | | | (23), (24), (27), (29), (30), (31), (32), (34),
% 141.59/21.03 | | | | | | | | | | | (35), (36), (38), (39), (40), (41), (42), (43),
% 141.59/21.03 | | | | | | | | | | | (44), (46), (47), (48), (49), (50), (51), (52),
% 141.59/21.03 | | | | | | | | | | | (53), (54), (56), (57), (58), (67), (74), (84) are
% 141.59/21.03 | | | | | | | | | | | inconsistent by sub-proof #477.
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | Case 2:
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | (85) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | ALPHA: (85) implies:
% 141.59/21.03 | | | | | | | | | | | (86) op(e3, e0) = e1
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | | REF_CLOSE: (8), (26), (33), (37), (43), (45), (77), (86) are
% 141.59/21.03 | | | | | | | | | | | inconsistent by sub-proof #654.
% 141.59/21.03 | | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | | End of split
% 141.59/21.03 | | | | | | | | | |
% 141.59/21.03 | | | | | | | | | End of split
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | Case 2:
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | (87) all_57_7 = e2 & op(e1, e2) = e2
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | ALPHA: (87) implies:
% 141.59/21.03 | | | | | | | | | (88) all_57_7 = e2
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | COMBINE_EQS: (74), (88) imply:
% 141.59/21.03 | | | | | | | | | (89) e2 = e1
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | COMBINE_EQS: (44), (89) imply:
% 141.59/21.03 | | | | | | | | | (90) all_57_5 = e1
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | REF_CLOSE: (2), (12), (35), (36), (42), (59), (62), (90) are
% 141.59/21.03 | | | | | | | | | inconsistent by sub-proof #870.
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | End of split
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | Case 2:
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | (91) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 141.59/21.03 | | | | | | | | op(e1, e0) = e2)
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | REF_CLOSE: (10), (12), (23), (35), (43), (91) are inconsistent
% 141.59/21.03 | | | | | | | | by sub-proof #497.
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | End of split
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | Case 2:
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | (92) all_57_13 = e1 & op(e0, e2) = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | ALPHA: (92) implies:
% 141.59/21.03 | | | | | | | (93) all_57_13 = e1
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | BETA: splitting (55) gives:
% 141.59/21.03 | | | | | | |
% 141.59/21.03 | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | (94) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 141.59/21.03 | | | | | | | | op(e2, e3) = e2)
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | REF_CLOSE: (1), (25), (35), (43), (54), (94) are inconsistent by
% 141.59/21.03 | | | | | | | | sub-proof #707.
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | Case 2:
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | (95) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 141.59/21.03 | | | | | | | | op(e0, e3) = e2)
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | BETA: splitting (95) gives:
% 141.59/21.03 | | | | | | | |
% 141.59/21.03 | | | | | | | | Case 1:
% 141.59/21.03 | | | | | | | | |
% 141.59/21.03 | | | | | | | | | (96) all_57_6 = e2 & op(e1, e3) = e2
% 141.59/21.03 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | ALPHA: (96) implies:
% 141.59/21.04 | | | | | | | | | (97) op(e1, e3) = e2
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | BETA: splitting (58) gives:
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | (98) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 141.59/21.04 | | | | | | | | | | op(e2, e2) = e3)
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | REF_CLOSE: (22), (36), (43), (51), (67), (98) are
% 141.59/21.04 | | | | | | | | | | inconsistent by sub-proof #841.
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | (99) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 141.59/21.04 | | | | | | | | | | & op(e0, e2) = e3)
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | BETA: splitting (99) gives:
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | (100) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | REF_CLOSE: (8), (10), (12), (15), (16), (26), (33), (34),
% 141.59/21.04 | | | | | | | | | | | (37), (41), (43), (45), (47), (97), (100) are
% 141.59/21.04 | | | | | | | | | | | inconsistent by sub-proof #473.
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | (101) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (10), (12), (13), (21), (22), (23),
% 141.59/21.04 | | | | | | | | | | | (34), (35), (36), (40), (43), (44), (48), (50),
% 141.59/21.04 | | | | | | | | | | | (51), (53), (56), (58), (62), (67), (93), (101)
% 141.59/21.04 | | | | | | | | | | | are inconsistent by sub-proof #472.
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | (102) all_57_12 = e2 & op(e0, e3) = e2
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | ALPHA: (102) implies:
% 141.59/21.04 | | | | | | | | | (103) all_57_12 = e2
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | BETA: splitting (58) gives:
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | (104) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3
% 141.59/21.04 | | | | | | | | | | & op(e2, e2) = e3)
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | REF_CLOSE: (22), (36), (43), (51), (67), (104) are
% 141.59/21.04 | | | | | | | | | | inconsistent by sub-proof #841.
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | (105) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 141.59/21.04 | | | | | | | | | | & op(e0, e2) = e3)
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | BETA: splitting (105) gives:
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | (106) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | ALPHA: (106) implies:
% 141.59/21.04 | | | | | | | | | | | (107) all_57_7 = e3
% 141.59/21.04 | | | | | | | | | | | (108) op(e1, e2) = e3
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | BETA: splitting (6) gives:
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | (109) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 141.59/21.04 | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | BETA: splitting (109) gives:
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | (110) all_57_12 = e3 & op(e0, e3) = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | ALPHA: (110) implies:
% 141.59/21.04 | | | | | | | | | | | | | (111) all_57_12 = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | REF_CLOSE: (36), (103), (111) are inconsistent by sub-proof
% 141.59/21.04 | | | | | | | | | | | | | #772.
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | (112) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (10), (12), (13), (21), (22), (23),
% 141.59/21.04 | | | | | | | | | | | | | (34), (35), (36), (40), (43), (44), (48), (50),
% 141.59/21.04 | | | | | | | | | | | | | (51), (53), (56), (58), (62), (67), (93), (112)
% 141.59/21.04 | | | | | | | | | | | | | are inconsistent by sub-proof #472.
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | (113) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 141.59/21.04 | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | BETA: splitting (113) gives:
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | Case 1:
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | (114) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | ALPHA: (114) implies:
% 141.59/21.04 | | | | | | | | | | | | | (115) all_57_14 = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | REF_CLOSE: (2), (22), (115) are inconsistent by sub-proof
% 141.59/21.04 | | | | | | | | | | | | | #1067.
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | (116) all_57_15 = e3 & op(e0, e0) = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | ALPHA: (116) implies:
% 141.59/21.04 | | | | | | | | | | | | | (117) op(e0, e0) = e3
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | | REF_CLOSE: (2), (5), (10), (11), (12), (15), (16), (19),
% 141.59/21.04 | | | | | | | | | | | | | (20), (21), (22), (24), (29), (34), (35), (36),
% 141.59/21.04 | | | | | | | | | | | | | (40), (42), (43), (47), (48), (50), (53), (56),
% 141.59/21.04 | | | | | | | | | | | | | (59), (107), (108), (117) are inconsistent by
% 141.59/21.04 | | | | | | | | | | | | | sub-proof #511.
% 141.59/21.04 | | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | Case 2:
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | (118) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | | REF_CLOSE: (2), (5), (7), (10), (12), (13), (21), (22), (23),
% 141.59/21.04 | | | | | | | | | | | (34), (35), (36), (40), (43), (44), (48), (50),
% 141.59/21.04 | | | | | | | | | | | (51), (53), (56), (58), (62), (67), (93), (118)
% 141.59/21.04 | | | | | | | | | | | are inconsistent by sub-proof #472.
% 141.59/21.04 | | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | | |
% 141.59/21.04 | | | | | | | | | End of split
% 141.59/21.04 | | | | | | | | |
% 141.59/21.04 | | | | | | | | End of split
% 141.59/21.04 | | | | | | | |
% 141.59/21.04 | | | | | | | End of split
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | End of split
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | End of split
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | End of split
% 141.59/21.04 | | | |
% 141.59/21.04 | | | Case 2:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | (119) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0)
% 141.59/21.04 | | | | = e2)
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | BETA: splitting (119) gives:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | Case 1:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | (120) all_57_4 = e2 & op(e3, e1) = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | ALPHA: (120) implies:
% 141.59/21.04 | | | | | (121) all_57_4 = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | REF_CLOSE: (36), (62), (121) are inconsistent by sub-proof #821.
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | Case 2:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | (122) all_57_9 = e2 & op(e3, e0) = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | ALPHA: (122) implies:
% 141.59/21.04 | | | | | (123) all_57_9 = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (9), (10), (12), (13), (14), (17),
% 141.59/21.04 | | | | | (18), (19), (20), (22), (23), (24), (27), (29), (30), (31),
% 141.59/21.04 | | | | | (32), (34), (35), (36), (39), (40), (41), (42), (43), (44),
% 141.59/21.04 | | | | | (46), (47), (48), (49), (50), (51), (52), (53), (54), (56),
% 141.59/21.04 | | | | | (123) are inconsistent by sub-proof #478.
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | End of split
% 141.59/21.04 | | | |
% 141.59/21.04 | | | End of split
% 141.59/21.04 | | |
% 141.59/21.04 | | Case 2:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (124) all_57_5 = e3 & op(e2, e1) = e3
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (36), (44), (124) are inconsistent by sub-proof #489.
% 141.59/21.04 | | |
% 141.59/21.04 | | End of split
% 141.59/21.04 | |
% 141.59/21.04 | Case 2:
% 141.59/21.04 | |
% 141.59/21.04 | | (125) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 141.59/21.04 | | e3)
% 141.59/21.04 | |
% 141.59/21.04 | | BETA: splitting (125) gives:
% 141.59/21.04 | |
% 141.59/21.04 | | Case 1:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (126) all_57_8 = e3 & op(e1, e1) = e3
% 141.59/21.04 | | |
% 141.59/21.04 | | | ALPHA: (126) implies:
% 141.59/21.04 | | | (127) op(e1, e1) = e3
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (23), (43), (48), (127) are inconsistent by sub-proof #1096.
% 141.59/21.04 | | |
% 141.59/21.04 | | Case 2:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (128) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (2), (22), (128) are inconsistent by sub-proof #777.
% 141.59/21.04 | | |
% 141.59/21.04 | | End of split
% 141.59/21.04 | |
% 141.59/21.04 | End of split
% 141.59/21.04 |
% 141.59/21.04 End of proof
% 141.59/21.04
% 141.59/21.04 Sub-proof #472 shows that the following formulas are inconsistent:
% 141.59/21.04 ----------------------------------------------------------------
% 141.59/21.04 (1) all_57_14 = e0
% 141.59/21.04 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.04 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.04 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.04 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.04 (4) all_57_11 = e0
% 141.59/21.04 (5) ~ (e2 = e1)
% 141.59/21.04 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.04 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.04 (7) all_57_4 = e3
% 141.59/21.04 (8) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.04 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.04 (9) ~ (e3 = e0)
% 141.59/21.04 (10) op(e1, e1) = e1
% 141.59/21.04 (11) ~ (e1 = e0)
% 141.59/21.04 (12) all_57_13 = e1
% 141.59/21.04 (13) ~ (e2 = e0)
% 141.59/21.04 (14) ~ (e3 = e2)
% 141.59/21.04 (15) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.04 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.04 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.04 (17) all_57_5 = e2
% 141.59/21.04 (18) ~ (e3 = e1)
% 141.59/21.04 (19) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.04 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.04 (20) all_57_1 = e2
% 141.59/21.04 (21) op(e2, e2) = e0
% 141.59/21.04 (22) all_57_0 = e0
% 141.59/21.04 (23) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.04 (24) all_57_3 = e0
% 141.59/21.04 (25) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.04 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.04
% 141.59/21.04 Begin of proof
% 141.59/21.04 |
% 141.59/21.04 | ALPHA: (23) implies:
% 141.59/21.04 | (26) all_57_13 = e3
% 141.59/21.04 |
% 141.59/21.04 | COMBINE_EQS: (12), (26) imply:
% 141.59/21.04 | (27) e3 = e1
% 141.59/21.04 |
% 141.59/21.04 | SIMP: (27) implies:
% 141.59/21.04 | (28) e3 = e1
% 141.59/21.04 |
% 141.59/21.04 | COMBINE_EQS: (7), (28) imply:
% 141.59/21.04 | (29) all_57_4 = e1
% 141.59/21.04 |
% 141.59/21.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 141.59/21.04 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (24), (25),
% 141.59/21.04 | (29) are inconsistent by sub-proof #476.
% 141.59/21.04 |
% 141.59/21.04 End of proof
% 141.59/21.04
% 141.59/21.04 Sub-proof #473 shows that the following formulas are inconsistent:
% 141.59/21.04 ----------------------------------------------------------------
% 141.59/21.04 (1) op(e1, e3) = all_52_2
% 141.59/21.04 (2) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.04 (3) all_57_11 = e0
% 141.59/21.04 (4) ~ (e2 = e1)
% 141.59/21.04 (5) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) = all_16_1
% 141.59/21.04 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0) =
% 141.59/21.04 all_16_1 & $i(all_16_1))
% 141.59/21.04 (6) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) = all_18_1
% 141.59/21.04 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0) =
% 141.59/21.04 all_18_1 & $i(all_18_1))
% 141.59/21.04 (7) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 141.59/21.04 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 141.59/21.04 all_14_1 & $i(all_14_1))
% 141.59/21.04 (8) op(e1, e3) = e2
% 141.59/21.04 (9) all_28_2 = e0
% 141.59/21.04 (10) ~ (e1 = e0)
% 141.59/21.04 (11) op(e3, e0) = all_52_12
% 141.59/21.04 (12) op(e0, e0) = e2
% 141.59/21.04 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.04 (14) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 141.59/21.04 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 141.59/21.04 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 141.59/21.04 (15) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.04 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.04
% 141.59/21.04 Begin of proof
% 141.59/21.04 |
% 141.59/21.04 | ALPHA: (2) implies:
% 141.59/21.04 | (16) op(e1, e2) = e3
% 141.59/21.04 |
% 141.59/21.04 | BETA: splitting (15) gives:
% 141.59/21.04 |
% 141.59/21.04 | Case 1:
% 141.59/21.04 | |
% 141.59/21.04 | | (17) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 141.59/21.04 | | e1)
% 141.59/21.04 | |
% 141.59/21.04 | | BETA: splitting (17) gives:
% 141.59/21.04 | |
% 141.59/21.04 | | Case 1:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (18) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.04 | | |
% 141.59/21.04 | | | ALPHA: (18) implies:
% 141.59/21.04 | | | (19) op(e3, e0) = e1
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (1), (7), (8), (9), (11), (13), (14), (19) are inconsistent by
% 141.59/21.04 | | | sub-proof #654.
% 141.59/21.04 | | |
% 141.59/21.04 | | Case 2:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (20) all_57_10 = e1 & op(e2, e0) = e1
% 141.59/21.04 | | |
% 141.59/21.04 | | | ALPHA: (20) implies:
% 141.59/21.04 | | | (21) op(e2, e0) = e1
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (5), (6), (13), (16), (21) are inconsistent by sub-proof #1020.
% 141.59/21.04 | | |
% 141.59/21.04 | | End of split
% 141.59/21.04 | |
% 141.59/21.04 | Case 2:
% 141.59/21.04 | |
% 141.59/21.04 | | (22) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.59/21.04 | | e1)
% 141.59/21.04 | |
% 141.59/21.04 | | REF_CLOSE: (3), (4), (10), (12), (13), (22) are inconsistent by sub-proof
% 141.59/21.04 | | #498.
% 141.59/21.04 | |
% 141.59/21.04 | End of split
% 141.59/21.04 |
% 141.59/21.04 End of proof
% 141.59/21.04
% 141.59/21.04 Sub-proof #474 shows that the following formulas are inconsistent:
% 141.59/21.04 ----------------------------------------------------------------
% 141.59/21.04 (1) all_57_14 = e0
% 141.59/21.04 (2) ~ (e2 = e1)
% 141.59/21.04 (3) all_57_4 = e3
% 141.59/21.04 (4) ~ (e2 = e0)
% 141.59/21.04 (5) ~ (e3 = e2)
% 141.59/21.04 (6) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.04 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.04 (7) all_57_1 = e1 & op(e3, e2) = e1
% 141.59/21.04 (8) all_57_5 = e2
% 141.59/21.04 (9) all_57_1 = e2
% 141.59/21.04 (10) all_57_8 = e1
% 141.59/21.04
% 141.59/21.04 Begin of proof
% 141.59/21.04 |
% 141.59/21.04 | ALPHA: (7) implies:
% 141.59/21.04 | (11) all_57_1 = e1
% 141.59/21.04 |
% 141.59/21.04 | COMBINE_EQS: (9), (11) imply:
% 141.59/21.04 | (12) e2 = e1
% 141.59/21.04 |
% 141.59/21.04 | COMBINE_EQS: (8), (12) imply:
% 141.59/21.04 | (13) all_57_5 = e1
% 141.59/21.04 |
% 141.59/21.04 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (10), (13) are inconsistent by
% 141.59/21.04 | sub-proof #870.
% 141.59/21.04 |
% 141.59/21.04 End of proof
% 141.59/21.04
% 141.59/21.04 Sub-proof #475 shows that the following formulas are inconsistent:
% 141.59/21.04 ----------------------------------------------------------------
% 141.59/21.04 (1) all_57_14 = e0
% 141.59/21.04 (2) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 141.59/21.04 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 141.59/21.04 (3) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.04 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.59/21.04 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.04 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.04 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.04 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.04 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.04 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.04 (7) op(e1, e3) = all_52_2
% 141.59/21.04 (8) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.04 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.59/21.04 (9) all_57_11 = e0
% 141.59/21.04 (10) ~ (e2 = e1)
% 141.59/21.04 (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.04 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.04 (12) ~ (all_52_7 = e0)
% 141.59/21.04 (13) op(e0, e3) = all_52_3
% 141.59/21.04 (14) op(e0, e1) = e0
% 141.59/21.04 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.04 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.59/21.04 e1)
% 141.59/21.04 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.59/21.04 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.04 (17) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.04 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.04 (18) ~ (e3 = e0)
% 141.59/21.04 (19) op(e1, e1) = e1
% 141.59/21.04 (20) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.04 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.59/21.04 e2)
% 141.59/21.04 (21) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 141.59/21.04 (all_57_11 = e0 & op(e1, e0) = e0)
% 141.59/21.04 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.59/21.04 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.59/21.04 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.59/21.04 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.59/21.04 (24) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.59/21.04 all_56_15 & $i(all_56_15))
% 141.59/21.04 (25) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.59/21.04 | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.04 (26) ~ (e1 = e0)
% 141.59/21.04 (27) ~ (e2 = e0)
% 141.59/21.04 (28) ~ (e3 = e2)
% 141.59/21.04 (29) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.59/21.04 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.59/21.04 (30) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.59/21.04 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.04 (31) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.04 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.04 (32) op(e0, e0) = e2
% 141.59/21.04 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.04 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.04 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.04 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.04 (35) ~ (all_52_3 = e0)
% 141.59/21.04 (36) all_57_4 = e1
% 141.59/21.04 (37) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.04 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.04 (38) ~ (e3 = e1)
% 141.59/21.04 (39) op(e0, e2) = all_52_7
% 141.59/21.04 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.04 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.04 (41) op(e2, e2) = e0
% 141.59/21.04 (42) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.59/21.04 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.59/21.04 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.59/21.04 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.59/21.04 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.59/21.04 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.59/21.04 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.59/21.04 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.59/21.04 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.59/21.04 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.59/21.04 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.59/21.04 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.59/21.04 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.59/21.04 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.59/21.04 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.59/21.04 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.59/21.04 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.59/21.04 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.59/21.04 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.59/21.04 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.59/21.04 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.59/21.04 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.59/21.04 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.59/21.04 $i(all_56_14))))
% 141.59/21.04 (43) all_57_0 = e0
% 141.59/21.04 (44) op(e3, e3) = e0
% 141.59/21.04 (45) all_57_3 = e0
% 141.59/21.04 (46) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.59/21.04 all_56_13 & $i(all_56_13))
% 141.59/21.04 (47) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.04 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.04
% 141.59/21.04 Begin of proof
% 141.59/21.04 |
% 141.59/21.04 | BETA: splitting (2) gives:
% 141.59/21.04 |
% 141.59/21.04 | Case 1:
% 141.59/21.04 | |
% 141.59/21.04 | | (48) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 141.59/21.04 | | e2)
% 141.59/21.04 | |
% 141.59/21.04 | | BETA: splitting (48) gives:
% 141.59/21.04 | |
% 141.59/21.04 | | Case 1:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (49) all_57_0 = e2 & op(e3, e3) = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | ALPHA: (49) implies:
% 141.59/21.04 | | | (50) op(e3, e3) = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (27), (34), (44), (50) are inconsistent by sub-proof #880.
% 141.59/21.04 | | |
% 141.59/21.04 | | Case 2:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (51) all_57_1 = e2 & op(e3, e2) = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | ALPHA: (51) implies:
% 141.59/21.04 | | | (52) all_57_1 = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | BETA: splitting (33) gives:
% 141.59/21.04 | | |
% 141.59/21.04 | | | Case 1:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | (53) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 141.59/21.04 | | | | = e2)
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | BETA: splitting (53) gives:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | Case 1:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | (54) all_57_4 = e2 & op(e3, e1) = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | ALPHA: (54) implies:
% 141.59/21.04 | | | | | (55) all_57_4 = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | REF_CLOSE: (10), (36), (55) are inconsistent by sub-proof #1088.
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | Case 2:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | (56) all_57_5 = e2 & op(e2, e1) = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | ALPHA: (56) implies:
% 141.59/21.04 | | | | | (57) all_57_5 = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | BETA: splitting (4) gives:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | Case 1:
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | | (58) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2,
% 141.59/21.04 | | | | | | e2) = e1)
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | | BETA: splitting (58) gives:
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | | Case 1:
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | (59) all_57_1 = e1 & op(e3, e2) = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | ALPHA: (59) implies:
% 141.59/21.04 | | | | | | | (60) all_57_1 = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | COMBINE_EQS: (52), (60) imply:
% 141.59/21.04 | | | | | | | (61) e2 = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | COMBINE_EQS: (57), (61) imply:
% 141.59/21.04 | | | | | | | (62) all_57_5 = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12),
% 141.59/21.04 | | | | | | | (13), (14), (15), (16), (18), (19), (20), (21), (22),
% 141.59/21.04 | | | | | | | (23), (24), (25), (26), (27), (28), (30), (31), (32),
% 141.59/21.04 | | | | | | | (33), (34), (35), (37), (38), (39), (40), (41), (42),
% 141.59/21.04 | | | | | | | (43), (44), (45), (62) are inconsistent by sub-proof
% 141.59/21.04 | | | | | | | #490.
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | Case 2:
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | (63) all_57_3 = e1 & op(e2, e2) = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | ALPHA: (63) implies:
% 141.59/21.04 | | | | | | | (64) op(e2, e2) = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | REF_CLOSE: (26), (34), (41), (64) are inconsistent by sub-proof
% 141.59/21.04 | | | | | | | #1117.
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | End of split
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | Case 2:
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | | (65) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0,
% 141.59/21.04 | | | | | | e2) = e1)
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | | BETA: splitting (65) gives:
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | | Case 1:
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | (66) all_57_7 = e1 & op(e1, e2) = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | ALPHA: (66) implies:
% 141.59/21.04 | | | | | | | (67) all_57_7 = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 141.59/21.04 | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 141.59/21.04 | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28), (29),
% 141.59/21.04 | | | | | | | (30), (31), (32), (33), (34), (35), (36), (37), (38),
% 141.59/21.04 | | | | | | | (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 141.59/21.04 | | | | | | | (52), (57), (67) are inconsistent by sub-proof #477.
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | Case 2:
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | (68) all_57_13 = e1 & op(e0, e2) = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | ALPHA: (68) implies:
% 141.59/21.04 | | | | | | | (69) all_57_13 = e1
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | | REF_CLOSE: (1), (4), (6), (9), (10), (11), (17), (18), (19), (26),
% 141.59/21.04 | | | | | | | (27), (28), (31), (34), (36), (38), (40), (41), (43),
% 141.59/21.04 | | | | | | | (45), (47), (52), (57), (69) are inconsistent by
% 141.59/21.04 | | | | | | | sub-proof #476.
% 141.59/21.04 | | | | | | |
% 141.59/21.04 | | | | | | End of split
% 141.59/21.04 | | | | | |
% 141.59/21.04 | | | | | End of split
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | End of split
% 141.59/21.04 | | | |
% 141.59/21.04 | | | Case 2:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | (70) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 141.59/21.04 | | | | = e2)
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | REF_CLOSE: (10), (12), (13), (19), (25), (27), (34), (35), (39), (70)
% 141.59/21.04 | | | | are inconsistent by sub-proof #496.
% 141.59/21.04 | | | |
% 141.59/21.04 | | | End of split
% 141.59/21.04 | | |
% 141.59/21.04 | | End of split
% 141.59/21.04 | |
% 141.59/21.04 | Case 2:
% 141.59/21.04 | |
% 141.59/21.04 | | (71) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 141.59/21.04 | | e2)
% 141.59/21.04 | |
% 141.59/21.04 | | BETA: splitting (71) gives:
% 141.59/21.04 | |
% 141.59/21.04 | | Case 1:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (72) all_57_4 = e2 & op(e3, e1) = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | REF_CLOSE: (10), (36), (72) are inconsistent by sub-proof #1109.
% 141.59/21.04 | | |
% 141.59/21.04 | | Case 2:
% 141.59/21.04 | | |
% 141.59/21.04 | | | (73) all_57_9 = e2 & op(e3, e0) = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | ALPHA: (73) implies:
% 141.59/21.04 | | | (74) all_57_9 = e2
% 141.59/21.04 | | |
% 141.59/21.04 | | | BETA: splitting (33) gives:
% 141.59/21.04 | | |
% 141.59/21.04 | | | Case 1:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | (75) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 141.59/21.04 | | | | = e2)
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | BETA: splitting (75) gives:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | Case 1:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | (76) all_57_4 = e2 & op(e3, e1) = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | REF_CLOSE: (10), (36), (76) are inconsistent by sub-proof #1109.
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | Case 2:
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | (77) all_57_5 = e2 & op(e2, e1) = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | ALPHA: (77) implies:
% 141.59/21.04 | | | | | (78) all_57_5 = e2
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 141.59/21.04 | | | | | (14), (15), (16), (18), (19), (20), (21), (22), (23), (24),
% 141.59/21.04 | | | | | (25), (26), (27), (28), (30), (31), (32), (33), (34), (35),
% 141.59/21.04 | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45), (74),
% 141.59/21.04 | | | | | (78) are inconsistent by sub-proof #478.
% 141.59/21.04 | | | | |
% 141.59/21.04 | | | | End of split
% 141.59/21.04 | | | |
% 141.59/21.04 | | | Case 2:
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | (79) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1)
% 141.59/21.04 | | | | = e2)
% 141.59/21.04 | | | |
% 141.59/21.04 | | | | REF_CLOSE: (10), (12), (13), (19), (25), (27), (34), (35), (39), (79)
% 141.59/21.04 | | | | are inconsistent by sub-proof #496.
% 141.59/21.04 | | | |
% 141.59/21.04 | | | End of split
% 141.59/21.04 | | |
% 141.59/21.04 | | End of split
% 141.59/21.04 | |
% 141.59/21.04 | End of split
% 141.59/21.04 |
% 141.59/21.04 End of proof
% 141.59/21.04
% 141.59/21.04 Sub-proof #476 shows that the following formulas are inconsistent:
% 141.59/21.04 ----------------------------------------------------------------
% 141.59/21.04 (1) all_57_14 = e0
% 141.59/21.04 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.04 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.04 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.04 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.04 (4) all_57_11 = e0
% 141.59/21.05 (5) ~ (e2 = e1)
% 141.59/21.05 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.05 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.05 (7) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.05 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.05 (8) ~ (e3 = e0)
% 141.59/21.05 (9) op(e1, e1) = e1
% 141.59/21.05 (10) ~ (e1 = e0)
% 141.59/21.05 (11) all_57_13 = e1
% 141.59/21.05 (12) ~ (e2 = e0)
% 141.59/21.05 (13) ~ (e3 = e2)
% 141.59/21.05 (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.05 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.05 (16) all_57_5 = e2
% 141.59/21.05 (17) all_57_4 = e1
% 141.59/21.05 (18) ~ (e3 = e1)
% 141.59/21.05 (19) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.05 (20) all_57_1 = e2
% 141.59/21.05 (21) op(e2, e2) = e0
% 141.59/21.05 (22) all_57_0 = e0
% 141.59/21.05 (23) all_57_3 = e0
% 141.59/21.05 (24) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.05 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.05
% 141.59/21.05 Begin of proof
% 141.59/21.05 |
% 141.59/21.05 | BETA: splitting (3) gives:
% 141.59/21.05 |
% 141.59/21.05 | Case 1:
% 141.59/21.05 | |
% 141.59/21.05 | | (25) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 141.59/21.05 | | e3)
% 141.59/21.05 | |
% 141.59/21.05 | | REF_CLOSE: (13), (16), (17), (18), (25) are inconsistent by sub-proof #488.
% 141.59/21.05 | |
% 141.59/21.05 | Case 2:
% 141.59/21.05 | |
% 141.59/21.05 | | (26) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 141.59/21.05 | | e3)
% 141.59/21.05 | |
% 141.59/21.05 | | BETA: splitting (26) gives:
% 141.59/21.05 | |
% 141.59/21.05 | | Case 1:
% 141.59/21.05 | | |
% 141.59/21.05 | | | (27) all_57_8 = e3 & op(e1, e1) = e3
% 141.59/21.05 | | |
% 141.59/21.05 | | | ALPHA: (27) implies:
% 141.59/21.05 | | | (28) all_57_8 = e3
% 141.59/21.05 | | |
% 141.59/21.05 | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.59/21.05 | | | (14), (15), (17), (18), (19), (20), (21), (22), (23), (24),
% 141.59/21.05 | | | (28) are inconsistent by sub-proof #482.
% 141.59/21.05 | | |
% 141.59/21.05 | | Case 2:
% 141.59/21.05 | | |
% 141.59/21.05 | | | (29) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.05 | | |
% 141.59/21.05 | | | ALPHA: (29) implies:
% 141.59/21.05 | | | (30) all_57_14 = e3
% 141.59/21.05 | | |
% 141.59/21.05 | | | REF_CLOSE: (1), (8), (30) are inconsistent by sub-proof #1067.
% 141.59/21.05 | | |
% 141.59/21.05 | | End of split
% 141.59/21.05 | |
% 141.59/21.05 | End of split
% 141.59/21.05 |
% 141.59/21.05 End of proof
% 141.59/21.05
% 141.59/21.05 Sub-proof #477 shows that the following formulas are inconsistent:
% 141.59/21.05 ----------------------------------------------------------------
% 141.59/21.05 (1) all_57_14 = e0
% 141.59/21.05 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.05 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.59/21.05 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.05 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.05 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.05 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.05 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.05 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.05 (6) op(e1, e3) = all_52_2
% 141.59/21.05 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.05 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.59/21.05 (8) all_57_11 = e0
% 141.59/21.05 (9) ~ (e2 = e1)
% 141.59/21.05 (10) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.05 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.05 (11) ~ (all_52_7 = e0)
% 141.59/21.05 (12) op(e0, e3) = all_52_3
% 141.59/21.05 (13) all_57_7 = e1
% 141.59/21.05 (14) op(e0, e1) = e0
% 141.59/21.05 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.05 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.59/21.05 e1)
% 141.59/21.05 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.59/21.05 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.05 (17) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.05 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.05 (18) ~ (e3 = e0)
% 141.59/21.05 (19) op(e1, e1) = e1
% 141.59/21.05 (20) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.05 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.59/21.05 e2)
% 141.59/21.05 (21) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 141.59/21.05 (all_57_11 = e0 & op(e1, e0) = e0)
% 141.59/21.05 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.59/21.05 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.59/21.05 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.59/21.05 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.59/21.05 (24) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.59/21.05 all_56_15 & $i(all_56_15))
% 141.59/21.05 (25) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.59/21.05 | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.05 (26) ~ (e1 = e0)
% 141.59/21.05 (27) ~ (e2 = e0)
% 141.59/21.05 (28) ~ (e3 = e2)
% 141.59/21.05 (29) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 141.59/21.05 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 141.59/21.05 (30) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.59/21.05 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.05 (31) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.05 (32) op(e0, e0) = e2
% 141.59/21.05 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.05 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.05 (35) all_57_5 = e2
% 141.59/21.05 (36) ~ (all_52_3 = e0)
% 141.59/21.05 (37) all_57_4 = e1
% 141.59/21.05 (38) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.05 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.05 (39) ~ (e3 = e1)
% 141.59/21.05 (40) op(e0, e2) = all_52_7
% 141.59/21.05 (41) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.05 (42) all_57_1 = e2
% 141.59/21.05 (43) op(e2, e2) = e0
% 141.59/21.05 (44) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.59/21.05 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.59/21.05 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.59/21.05 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.59/21.05 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.59/21.05 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.59/21.05 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.59/21.05 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.59/21.05 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.59/21.05 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.59/21.05 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.59/21.05 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.59/21.05 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.59/21.05 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.59/21.05 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.59/21.05 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.59/21.05 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.59/21.05 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.59/21.05 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.59/21.05 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.59/21.05 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.59/21.05 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.59/21.05 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.59/21.05 $i(all_56_14))))
% 141.59/21.05 (45) all_57_0 = e0
% 141.59/21.05 (46) op(e3, e3) = e0
% 141.59/21.05 (47) all_57_3 = e0
% 141.59/21.05 (48) (all_56_6 = e1 & op(e1, e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 141.59/21.05 all_56_13 & $i(all_56_13))
% 141.59/21.05 (49) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.05 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.05
% 141.59/21.05 Begin of proof
% 141.59/21.05 |
% 141.59/21.05 | BETA: splitting (31) gives:
% 141.59/21.05 |
% 141.59/21.05 | Case 1:
% 141.59/21.05 | |
% 141.59/21.05 | | (50) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 141.59/21.05 | | e2)
% 141.59/21.05 | |
% 141.59/21.05 | | BETA: splitting (50) gives:
% 141.59/21.05 | |
% 141.59/21.05 | | Case 1:
% 141.59/21.05 | | |
% 141.59/21.05 | | | (51) all_57_6 = e2 & op(e1, e3) = e2
% 141.59/21.05 | | |
% 141.59/21.05 | | | ALPHA: (51) implies:
% 141.59/21.05 | | | (52) all_57_6 = e2
% 141.59/21.05 | | | (53) op(e1, e3) = e2
% 141.59/21.05 | | |
% 141.59/21.05 | | | BETA: splitting (5) gives:
% 141.59/21.05 | | |
% 141.59/21.05 | | | Case 1:
% 141.59/21.05 | | | |
% 141.59/21.05 | | | | (54) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1)
% 141.59/21.05 | | | | = e3)
% 141.59/21.05 | | | |
% 141.59/21.05 | | | | REF_CLOSE: (28), (35), (37), (39), (54) are inconsistent by sub-proof
% 141.59/21.05 | | | | #488.
% 141.59/21.05 | | | |
% 141.59/21.05 | | | Case 2:
% 141.59/21.05 | | | |
% 141.59/21.05 | | | | (55) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1)
% 141.59/21.05 | | | | = e3)
% 141.59/21.05 | | | |
% 141.59/21.05 | | | | BETA: splitting (55) gives:
% 141.59/21.05 | | | |
% 141.59/21.05 | | | | Case 1:
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | (56) all_57_8 = e3 & op(e1, e1) = e3
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | ALPHA: (56) implies:
% 141.59/21.05 | | | | | (57) all_57_8 = e3
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | BETA: splitting (48) gives:
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | Case 1:
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | (58) all_56_6 = e1 & op(e1, e3) = e1
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | ALPHA: (58) implies:
% 141.59/21.05 | | | | | | (59) op(e1, e3) = e1
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | BETA: splitting (49) gives:
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | Case 1:
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | (60) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 141.59/21.05 | | | | | | | op(e2, e2) = e3)
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | REF_CLOSE: (18), (28), (34), (42), (43), (60) are inconsistent by
% 141.59/21.05 | | | | | | | sub-proof #841.
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | Case 2:
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | (61) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 141.59/21.05 | | | | | | | op(e0, e2) = e3)
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | BETA: splitting (61) gives:
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | (62) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | REF_CLOSE: (3), (8), (9), (10), (17), (18), (19), (26), (27),
% 141.59/21.05 | | | | | | | | (28), (31), (34), (37), (39), (41), (45), (47), (57),
% 141.59/21.05 | | | | | | | | (62) are inconsistent by sub-proof #484.
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | (63) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | ALPHA: (63) implies:
% 141.59/21.05 | | | | | | | | (64) all_57_13 = e3
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | BETA: splitting (41) gives:
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | (65) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 141.59/21.05 | | | | | | | | | op(e3, e2) = e3)
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | REF_CLOSE: (1), (4), (9), (15), (18), (26), (28), (32), (34),
% 141.59/21.05 | | | | | | | | | (39), (42), (45), (64), (65) are inconsistent by
% 141.59/21.05 | | | | | | | | | sub-proof #483.
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | (66) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 141.59/21.05 | | | | | | | | | op(e3, e0) = e3)
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | BETA: splitting (66) gives:
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | (67) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | REF_CLOSE: (3), (8), (9), (10), (17), (18), (19), (26), (27),
% 141.59/21.05 | | | | | | | | | | (28), (31), (34), (37), (39), (41), (42), (43),
% 141.59/21.05 | | | | | | | | | | (45), (47), (49), (57), (64), (67) are
% 141.59/21.05 | | | | | | | | | | inconsistent by sub-proof #481.
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | (68) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | ALPHA: (68) implies:
% 141.59/21.05 | | | | | | | | | | (69) all_57_9 = e3
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | BETA: splitting (10) gives:
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | (70) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 141.59/21.05 | | | | | | | | | | | & op(e1, e2) = e1)
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | BETA: splitting (70) gives:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | (71) all_57_6 = e1 & op(e1, e3) = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | ALPHA: (71) implies:
% 141.59/21.05 | | | | | | | | | | | | (72) all_57_6 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (8), (9), (13), (19), (27), (31), (34), (72) are
% 141.59/21.05 | | | | | | | | | | | | inconsistent by sub-proof #499.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_52_2, e1, e3, e1,
% 141.59/21.05 | | | | | | | | | | | | simplifying with (6), (59) gives:
% 141.59/21.05 | | | | | | | | | | | | (73) all_52_2 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | GROUND_INST: instantiating (34) with all_52_2, e2, e3, e1,
% 141.59/21.05 | | | | | | | | | | | | simplifying with (6), (53) gives:
% 141.59/21.05 | | | | | | | | | | | | (74) all_52_2 = e2
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | COMBINE_EQS: (73), (74) imply:
% 141.59/21.05 | | | | | | | | | | | | (75) e2 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | SIMP: (75) implies:
% 141.59/21.05 | | | | | | | | | | | | (76) e2 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | COMBINE_EQS: (35), (76) imply:
% 141.59/21.05 | | | | | | | | | | | | (77) all_57_5 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10),
% 141.59/21.05 | | | | | | | | | | | | (11), (12), (14), (15), (16), (18), (19), (20),
% 141.59/21.05 | | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 141.59/21.05 | | | | | | | | | | | | (30), (31), (32), (33), (34), (36), (38), (39),
% 141.59/21.05 | | | | | | | | | | | | (40), (41), (43), (44), (45), (46), (47), (77) are
% 141.59/21.05 | | | | | | | | | | | | inconsistent by sub-proof #490.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | (78) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 141.59/21.05 | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | BETA: splitting (78) gives:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | (79) all_57_8 = e1 & op(e1, e1) = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | ALPHA: (79) implies:
% 141.59/21.05 | | | | | | | | | | | | (80) all_57_8 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | COMBINE_EQS: (57), (80) imply:
% 141.59/21.05 | | | | | | | | | | | | (81) e3 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (8), (9), (10), (15), (17), (18),
% 141.59/21.05 | | | | | | | | | | | | (19), (26), (27), (28), (31), (32), (34), (37),
% 141.59/21.05 | | | | | | | | | | | | (39), (41), (42), (43), (45), (47), (49), (57),
% 141.59/21.05 | | | | | | | | | | | | (64), (69), (81) are inconsistent by sub-proof
% 141.59/21.05 | | | | | | | | | | | | #480.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | (82) all_57_11 = e1 & op(e1, e0) = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (8), (26), (82) are inconsistent by sub-proof
% 141.59/21.05 | | | | | | | | | | | | #596.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | End of split
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | End of split
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | End of split
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | Case 2:
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | (83) ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13)
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | ALPHA: (83) implies:
% 141.59/21.05 | | | | | | (84) op(e1, e1) = all_56_13
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | BETA: splitting (49) gives:
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | | Case 1:
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | (85) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 141.59/21.05 | | | | | | | op(e2, e2) = e3)
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | REF_CLOSE: (18), (28), (34), (42), (43), (85) are inconsistent by
% 141.59/21.05 | | | | | | | sub-proof #841.
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | Case 2:
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | (86) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 141.59/21.05 | | | | | | | op(e0, e2) = e3)
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | BETA: splitting (86) gives:
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | (87) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | REF_CLOSE: (3), (8), (9), (10), (17), (18), (19), (26), (27),
% 141.59/21.05 | | | | | | | | (28), (31), (34), (37), (39), (41), (45), (47), (57),
% 141.59/21.05 | | | | | | | | (87) are inconsistent by sub-proof #484.
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | (88) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | ALPHA: (88) implies:
% 141.59/21.05 | | | | | | | | (89) all_57_13 = e3
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | BETA: splitting (41) gives:
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | (90) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 141.59/21.05 | | | | | | | | | op(e3, e2) = e3)
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | REF_CLOSE: (1), (4), (9), (15), (18), (26), (28), (32), (34),
% 141.59/21.05 | | | | | | | | | (39), (42), (45), (89), (90) are inconsistent by
% 141.59/21.05 | | | | | | | | | sub-proof #483.
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | (91) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 141.59/21.05 | | | | | | | | | op(e3, e0) = e3)
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | BETA: splitting (91) gives:
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | (92) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | REF_CLOSE: (3), (8), (9), (10), (17), (18), (19), (26), (27),
% 141.59/21.05 | | | | | | | | | | (28), (31), (34), (37), (39), (41), (42), (43),
% 141.59/21.05 | | | | | | | | | | (45), (47), (49), (57), (89), (92) are
% 141.59/21.05 | | | | | | | | | | inconsistent by sub-proof #481.
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | (93) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | ALPHA: (93) implies:
% 141.59/21.05 | | | | | | | | | | (94) all_57_9 = e3
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | BETA: splitting (29) gives:
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | (95) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 141.59/21.05 | | | | | | | | | | | & op(e1, e2) = e3)
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | BETA: splitting (95) gives:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | (96) all_57_6 = e3 & op(e1, e3) = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | ALPHA: (96) implies:
% 141.59/21.05 | | | | | | | | | | | | (97) all_57_6 = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | COMBINE_EQS: (52), (97) imply:
% 141.59/21.05 | | | | | | | | | | | | (98) e3 = e2
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | COMBINE_EQS: (94), (98) imply:
% 141.59/21.05 | | | | | | | | | | | | (99) all_57_9 = e2
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10),
% 141.59/21.05 | | | | | | | | | | | | (11), (12), (14), (15), (16), (18), (19), (20),
% 141.59/21.05 | | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 141.59/21.05 | | | | | | | | | | | | (30), (31), (32), (33), (34), (35), (36), (38),
% 141.59/21.05 | | | | | | | | | | | | (39), (40), (41), (43), (44), (45), (46), (47),
% 141.59/21.05 | | | | | | | | | | | | (99) are inconsistent by sub-proof #478.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | (100) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | ALPHA: (100) implies:
% 141.59/21.05 | | | | | | | | | | | | (101) all_57_7 = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (3), (8), (9), (10), (17), (18), (19), (26), (27),
% 141.59/21.05 | | | | | | | | | | | | (28), (31), (34), (37), (39), (41), (45), (47),
% 141.59/21.05 | | | | | | | | | | | | (57), (94), (101) are inconsistent by sub-proof
% 141.59/21.05 | | | | | | | | | | | | #485.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | (102) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 141.59/21.05 | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | BETA: splitting (102) gives:
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 1:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | ALPHA: (56) implies:
% 141.59/21.05 | | | | | | | | | | | | (103) op(e1, e1) = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | GROUND_INST: instantiating (34) with e3, all_56_13, e1, e1,
% 141.59/21.05 | | | | | | | | | | | | simplifying with (84), (103) gives:
% 141.59/21.05 | | | | | | | | | | | | (104) all_56_13 = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | GROUND_INST: instantiating (34) with e1, all_56_13, e1, e1,
% 141.59/21.05 | | | | | | | | | | | | simplifying with (19), (84) gives:
% 141.59/21.05 | | | | | | | | | | | | (105) all_56_13 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | COMBINE_EQS: (104), (105) imply:
% 141.59/21.05 | | | | | | | | | | | | (106) e3 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | SIMP: (106) implies:
% 141.59/21.05 | | | | | | | | | | | | (107) e3 = e1
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (8), (9), (10), (15), (17), (18),
% 141.59/21.05 | | | | | | | | | | | | (19), (26), (27), (28), (31), (32), (34), (37),
% 141.59/21.05 | | | | | | | | | | | | (39), (41), (42), (43), (45), (47), (49), (57),
% 141.59/21.05 | | | | | | | | | | | | (89), (94), (107) are inconsistent by sub-proof
% 141.59/21.05 | | | | | | | | | | | | #480.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | Case 2:
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | (108) all_57_11 = e3 & op(e1, e0) = e3
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | | REF_CLOSE: (8), (18), (108) are inconsistent by sub-proof
% 141.59/21.05 | | | | | | | | | | | | #957.
% 141.59/21.05 | | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | | |
% 141.59/21.05 | | | | | | | | | End of split
% 141.59/21.05 | | | | | | | | |
% 141.59/21.05 | | | | | | | | End of split
% 141.59/21.05 | | | | | | | |
% 141.59/21.05 | | | | | | | End of split
% 141.59/21.05 | | | | | | |
% 141.59/21.05 | | | | | | End of split
% 141.59/21.05 | | | | | |
% 141.59/21.05 | | | | | End of split
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | Case 2:
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | (109) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | ALPHA: (109) implies:
% 141.59/21.05 | | | | | (110) all_57_14 = e3
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | | REF_CLOSE: (1), (18), (110) are inconsistent by sub-proof #1067.
% 141.59/21.05 | | | | |
% 141.59/21.05 | | | | End of split
% 141.59/21.05 | | | |
% 141.59/21.05 | | | End of split
% 141.59/21.05 | | |
% 141.59/21.05 | | Case 2:
% 141.59/21.05 | | |
% 141.59/21.05 | | | (111) all_57_7 = e2 & op(e1, e2) = e2
% 141.59/21.05 | | |
% 141.59/21.05 | | | ALPHA: (111) implies:
% 141.59/21.05 | | | (112) all_57_7 = e2
% 141.59/21.05 | | |
% 141.59/21.05 | | | COMBINE_EQS: (13), (112) imply:
% 141.59/21.05 | | | (113) e2 = e1
% 141.59/21.05 | | |
% 141.59/21.05 | | | COMBINE_EQS: (35), (113) imply:
% 141.59/21.05 | | | (114) all_57_5 = e1
% 141.59/21.05 | | |
% 141.59/21.05 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (14),
% 141.59/21.05 | | | (15), (16), (18), (19), (20), (21), (22), (23), (24), (25),
% 141.59/21.05 | | | (26), (27), (28), (30), (31), (32), (33), (34), (36), (38),
% 141.59/21.05 | | | (39), (40), (41), (43), (44), (45), (46), (47), (114) are
% 141.59/21.05 | | | inconsistent by sub-proof #490.
% 141.59/21.05 | | |
% 141.59/21.05 | | End of split
% 141.59/21.05 | |
% 141.59/21.05 | Case 2:
% 141.59/21.05 | |
% 141.59/21.05 | | (115) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 141.59/21.05 | | e2)
% 141.59/21.05 | |
% 141.59/21.05 | | REF_CLOSE: (8), (9), (19), (27), (34), (115) are inconsistent by sub-proof
% 141.59/21.05 | | #1082.
% 141.59/21.05 | |
% 141.59/21.05 | End of split
% 141.59/21.05 |
% 141.59/21.05 End of proof
% 141.59/21.05
% 141.59/21.05 Sub-proof #478 shows that the following formulas are inconsistent:
% 141.59/21.05 ----------------------------------------------------------------
% 141.59/21.05 (1) all_57_14 = e0
% 141.59/21.05 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.05 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.59/21.05 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.05 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.05 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.05 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.05 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.05 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.05 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.05 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.59/21.05 (7) all_57_11 = e0
% 141.59/21.05 (8) ~ (e2 = e1)
% 141.59/21.05 (9) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.05 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.05 (10) ~ (all_52_7 = e0)
% 141.59/21.05 (11) op(e0, e3) = all_52_3
% 141.59/21.05 (12) op(e0, e1) = e0
% 141.59/21.05 (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.05 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.59/21.05 e1)
% 141.59/21.05 (14) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.59/21.05 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.05 (15) ~ (e3 = e0)
% 141.59/21.05 (16) op(e1, e1) = e1
% 141.59/21.05 (17) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.05 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.59/21.05 e2)
% 141.59/21.05 (18) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 141.59/21.05 (all_57_11 = e0 & op(e1, e0) = e0)
% 141.59/21.05 (19) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.59/21.05 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.59/21.05 (20) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.59/21.05 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.59/21.05 (21) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.59/21.05 all_56_15 & $i(all_56_15))
% 141.59/21.05 (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.59/21.05 | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.05 (23) ~ (e1 = e0)
% 141.59/21.05 (24) all_57_9 = e2
% 141.59/21.05 (25) ~ (e2 = e0)
% 141.59/21.05 (26) ~ (e3 = e2)
% 141.59/21.05 (27) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.59/21.05 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.05 (28) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.05 (29) op(e0, e0) = e2
% 141.59/21.05 (30) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.05 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.05 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.05 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.05 (32) all_57_5 = e2
% 141.59/21.05 (33) ~ (all_52_3 = e0)
% 141.59/21.05 (34) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.05 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.05 (35) ~ (e3 = e1)
% 141.59/21.05 (36) op(e0, e2) = all_52_7
% 141.59/21.05 (37) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.05 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.05 (38) op(e2, e2) = e0
% 141.59/21.06 (39) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.59/21.06 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.59/21.06 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.59/21.06 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.59/21.06 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.59/21.06 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.59/21.06 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.59/21.06 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.59/21.06 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.59/21.06 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.59/21.06 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.59/21.06 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.59/21.06 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.59/21.06 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.59/21.06 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.59/21.06 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.59/21.06 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.59/21.06 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.59/21.06 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.59/21.06 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.59/21.06 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.59/21.06 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.59/21.06 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.59/21.06 $i(all_56_14))))
% 141.59/21.06 (40) all_57_0 = e0
% 141.59/21.06 (41) op(e3, e3) = e0
% 141.59/21.06 (42) all_57_3 = e0
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (27) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (43) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (43) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (44) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (24), (26), (44) are inconsistent by sub-proof #479.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (45) all_57_10 = e3 & op(e2, e0) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (45) implies:
% 141.59/21.06 | | | (46) all_57_10 = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | BETA: splitting (34) gives:
% 141.59/21.06 | | |
% 141.59/21.06 | | | Case 1:
% 141.59/21.06 | | | |
% 141.59/21.06 | | | | (47) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 141.59/21.06 | | | | = e1)
% 141.59/21.06 | | | |
% 141.59/21.06 | | | | BETA: splitting (47) gives:
% 141.59/21.06 | | | |
% 141.59/21.06 | | | | Case 1:
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | (48) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | ALPHA: (48) implies:
% 141.59/21.06 | | | | | (49) all_57_9 = e1
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | COMBINE_EQS: (24), (49) imply:
% 141.59/21.06 | | | | | (50) e2 = e1
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | COMBINE_EQS: (32), (50) imply:
% 141.59/21.06 | | | | | (51) all_57_5 = e1
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 141.59/21.06 | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20), (21),
% 141.59/21.06 | | | | | (22), (23), (25), (26), (27), (28), (29), (30), (31), (33),
% 141.59/21.06 | | | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (51)
% 141.59/21.06 | | | | | are inconsistent by sub-proof #490.
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | Case 2:
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | (52) all_57_10 = e1 & op(e2, e0) = e1
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | ALPHA: (52) implies:
% 141.59/21.06 | | | | | (53) all_57_10 = e1
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | | REF_CLOSE: (35), (46), (53) are inconsistent by sub-proof #877.
% 141.59/21.06 | | | | |
% 141.59/21.06 | | | | End of split
% 141.59/21.06 | | | |
% 141.59/21.06 | | | Case 2:
% 141.59/21.06 | | | |
% 141.59/21.06 | | | | (54) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 141.59/21.06 | | | | e0) = e1)
% 141.59/21.06 | | | |
% 141.59/21.06 | | | | REF_CLOSE: (7), (8), (23), (29), (31), (54) are inconsistent by
% 141.59/21.06 | | | | sub-proof #495.
% 141.59/21.06 | | | |
% 141.59/21.06 | | | End of split
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (55) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (7), (8), (11), (12), (15), (16), (21), (23), (25), (26), (31),
% 141.59/21.06 | | (33), (39), (41), (55) are inconsistent by sub-proof #491.
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #479 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.06 (2) all_57_9 = e2
% 141.59/21.06 (3) ~ (e3 = e2)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | ALPHA: (1) implies:
% 141.59/21.06 | (4) all_57_9 = e3
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (2), (4) imply:
% 141.59/21.06 | (5) e3 = e2
% 141.59/21.06 |
% 141.59/21.06 | REDUCE: (3), (5) imply:
% 141.59/21.06 | (6) $false
% 141.59/21.06 |
% 141.59/21.06 | CLOSE: (6) is inconsistent.
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #480 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) all_57_14 = e0
% 141.59/21.06 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.06 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.06 (4) all_57_11 = e0
% 141.59/21.06 (5) ~ (e2 = e1)
% 141.59/21.06 (6) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.06 (7) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.59/21.06 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.06 (8) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.06 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.06 (9) ~ (e3 = e0)
% 141.59/21.06 (10) op(e1, e1) = e1
% 141.59/21.06 (11) ~ (e1 = e0)
% 141.59/21.06 (12) ~ (e2 = e0)
% 141.59/21.06 (13) ~ (e3 = e2)
% 141.59/21.06 (14) all_57_9 = e3
% 141.59/21.06 (15) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.06 (16) op(e0, e0) = e2
% 141.59/21.06 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.06 (18) all_57_4 = e1
% 141.59/21.06 (19) ~ (e3 = e1)
% 141.59/21.06 (20) e3 = e1
% 141.59/21.06 (21) all_57_13 = e3
% 141.59/21.06 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.06 (23) all_57_1 = e2
% 141.59/21.06 (24) op(e2, e2) = e0
% 141.59/21.06 (25) all_57_0 = e0
% 141.59/21.06 (26) all_57_8 = e3
% 141.59/21.06 (27) all_57_3 = e0
% 141.59/21.06 (28) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.06 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (14), (20) imply:
% 141.59/21.06 | (29) all_57_9 = e1
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (22) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (30) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (1), (3), (5), (7), (9), (11), (13), (16), (17), (19), (21),
% 141.59/21.06 | | (23), (25), (30) are inconsistent by sub-proof #483.
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (31) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (31) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (32) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 141.59/21.06 | | | (17), (18), (19), (21), (22), (23), (24), (25), (26), (27),
% 141.59/21.06 | | | (28), (32) are inconsistent by sub-proof #481.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (33) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | COMBINE_EQS: (14), (29) imply:
% 141.59/21.06 | | | (34) e3 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | COMBINE_EQS: (20), (21) imply:
% 141.59/21.06 | | | (35) all_57_13 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 141.59/21.06 | | | (17), (18), (19), (22), (23), (24), (25), (26), (27), (28),
% 141.59/21.06 | | | (35) are inconsistent by sub-proof #482.
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #481 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (2) all_57_11 = e0
% 141.59/21.06 (3) ~ (e2 = e1)
% 141.59/21.06 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.06 (5) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.06 (6) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.06 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.06 (7) ~ (e3 = e0)
% 141.59/21.06 (8) op(e1, e1) = e1
% 141.59/21.06 (9) ~ (e1 = e0)
% 141.59/21.06 (10) ~ (e2 = e0)
% 141.59/21.06 (11) ~ (e3 = e2)
% 141.59/21.06 (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.06 (14) all_57_4 = e1
% 141.59/21.06 (15) ~ (e3 = e1)
% 141.59/21.06 (16) all_57_13 = e3
% 141.59/21.06 (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.06 (18) all_57_1 = e2
% 141.59/21.06 (19) op(e2, e2) = e0
% 141.59/21.06 (20) all_57_0 = e0
% 141.59/21.06 (21) all_57_8 = e3
% 141.59/21.06 (22) all_57_3 = e0
% 141.59/21.06 (23) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.06 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | ALPHA: (5) implies:
% 141.59/21.06 | (24) all_57_4 = e3
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (14), (24) imply:
% 141.59/21.06 | (25) e3 = e1
% 141.59/21.06 |
% 141.59/21.06 | SIMP: (25) implies:
% 141.59/21.06 | (26) e3 = e1
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (16), (26) imply:
% 141.59/21.06 | (27) all_57_13 = e1
% 141.59/21.06 |
% 141.59/21.06 | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.59/21.06 | (14), (15), (17), (18), (19), (20), (21), (22), (23), (27) are
% 141.59/21.06 | inconsistent by sub-proof #482.
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #482 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (2) all_57_11 = e0
% 141.59/21.06 (3) ~ (e2 = e1)
% 141.59/21.06 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.06 (5) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.06 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.06 (6) ~ (e3 = e0)
% 141.59/21.06 (7) op(e1, e1) = e1
% 141.59/21.06 (8) ~ (e1 = e0)
% 141.59/21.06 (9) all_57_13 = e1
% 141.59/21.06 (10) ~ (e2 = e0)
% 141.59/21.06 (11) ~ (e3 = e2)
% 141.59/21.06 (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.06 (14) all_57_4 = e1
% 141.59/21.06 (15) ~ (e3 = e1)
% 141.59/21.06 (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.06 (17) all_57_1 = e2
% 141.59/21.06 (18) op(e2, e2) = e0
% 141.59/21.06 (19) all_57_0 = e0
% 141.59/21.06 (20) all_57_8 = e3
% 141.59/21.06 (21) all_57_3 = e0
% 141.59/21.06 (22) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.06 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (22) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (23) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (6), (11), (13), (17), (18), (23) are inconsistent by sub-proof
% 141.59/21.06 | | #841.
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (24) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (24) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (25) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 141.59/21.06 | | | (14), (15), (16), (19), (20), (21), (25) are inconsistent by
% 141.59/21.06 | | | sub-proof #484.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (26) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (26) implies:
% 141.59/21.06 | | | (27) all_57_13 = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (9), (15), (27) are inconsistent by sub-proof #1001.
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #483 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) all_57_14 = e0
% 141.59/21.06 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.06 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.06 (3) ~ (e2 = e1)
% 141.59/21.06 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 141.59/21.06 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.06 (5) ~ (e3 = e0)
% 141.59/21.06 (6) ~ (e1 = e0)
% 141.59/21.06 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 141.59/21.06 (8) ~ (e3 = e2)
% 141.59/21.06 (9) op(e0, e0) = e2
% 141.59/21.06 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.06 (11) ~ (e3 = e1)
% 141.59/21.06 (12) all_57_13 = e3
% 141.59/21.06 (13) all_57_1 = e2
% 141.59/21.06 (14) all_57_0 = e0
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (7) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (15) all_57_0 = e3 & op(e3, e3) = e3
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (5), (14), (15) are inconsistent by sub-proof #1108.
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (16) all_57_1 = e3 & op(e3, e2) = e3
% 141.59/21.06 | |
% 141.59/21.06 | | ALPHA: (16) implies:
% 141.59/21.06 | | (17) all_57_1 = e3
% 141.59/21.06 | |
% 141.59/21.06 | | COMBINE_EQS: (13), (17) imply:
% 141.59/21.06 | | (18) e3 = e2
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (18)
% 141.59/21.06 | | are inconsistent by sub-proof #925.
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #484 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (2) all_57_7 = e3 & op(e1, e2) = e3
% 141.59/21.06 (3) all_57_11 = e0
% 141.59/21.06 (4) ~ (e2 = e1)
% 141.59/21.06 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.06 (6) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.06 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.06 (7) ~ (e3 = e0)
% 141.59/21.06 (8) op(e1, e1) = e1
% 141.59/21.06 (9) ~ (e1 = e0)
% 141.59/21.06 (10) ~ (e2 = e0)
% 141.59/21.06 (11) ~ (e3 = e2)
% 141.59/21.06 (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.06 (14) all_57_4 = e1
% 141.59/21.06 (15) ~ (e3 = e1)
% 141.59/21.06 (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.06 (17) all_57_0 = e0
% 141.59/21.06 (18) all_57_8 = e3
% 141.59/21.06 (19) all_57_3 = e0
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | ALPHA: (2) implies:
% 141.59/21.06 | (20) all_57_7 = e3
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (16) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (1), (4), (6), (7), (9), (10), (11), (15), (17), (19), (20), (21)
% 141.59/21.06 | | are inconsistent by sub-proof #514.
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (22) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (22) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (23) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (23) implies:
% 141.59/21.06 | | | (24) all_57_4 = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (14), (15), (24) are inconsistent by sub-proof #631.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (25) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (25) implies:
% 141.59/21.06 | | | (26) all_57_9 = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 141.59/21.06 | | | (14), (15), (16), (17), (18), (19), (20), (26) are inconsistent
% 141.59/21.06 | | | by sub-proof #485.
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #485 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (2) all_57_11 = e0
% 141.59/21.06 (3) ~ (e2 = e1)
% 141.59/21.06 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.06 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.06 (5) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.06 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.06 (6) ~ (e3 = e0)
% 141.59/21.06 (7) op(e1, e1) = e1
% 141.59/21.06 (8) ~ (e1 = e0)
% 141.59/21.06 (9) ~ (e2 = e0)
% 141.59/21.06 (10) ~ (e3 = e2)
% 141.59/21.06 (11) all_57_9 = e3
% 141.59/21.06 (12) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.06 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.06 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.06 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.06 (14) all_57_4 = e1
% 141.59/21.06 (15) ~ (e3 = e1)
% 141.59/21.06 (16) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.06 (17) all_57_0 = e0
% 141.59/21.06 (18) all_57_8 = e3
% 141.59/21.06 (19) all_57_7 = e3
% 141.59/21.06 (20) all_57_3 = e0
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (4) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (21) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.59/21.06 | | e1)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (21) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (22) all_57_6 = e1 & op(e1, e3) = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (22) implies:
% 141.59/21.06 | | | (23) all_57_6 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (2), (3), (7), (9), (10), (12), (13), (19), (23) are
% 141.59/21.06 | | | inconsistent by sub-proof #1081.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (24) all_57_7 = e1 & op(e1, e2) = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (24) implies:
% 141.59/21.06 | | | (25) all_57_7 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | COMBINE_EQS: (19), (25) imply:
% 141.59/21.06 | | | (26) e3 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (14), (15), (16),
% 141.59/21.06 | | | (17), (19), (20), (26) are inconsistent by sub-proof #486.
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (27) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.59/21.06 | | e1)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (27) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (28) all_57_8 = e1 & op(e1, e1) = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (28) implies:
% 141.59/21.06 | | | (29) all_57_8 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | COMBINE_EQS: (18), (29) imply:
% 141.59/21.06 | | | (30) e3 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (10), (11), (14), (15), (16),
% 141.59/21.06 | | | (17), (19), (20), (30) are inconsistent by sub-proof #486.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (31) all_57_11 = e1 & op(e1, e0) = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (31) implies:
% 141.59/21.06 | | | (32) all_57_11 = e1
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (2), (8), (32) are inconsistent by sub-proof #690.
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #486 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (2) ~ (e2 = e1)
% 141.59/21.06 (3) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.06 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.06 (4) ~ (e3 = e0)
% 141.59/21.06 (5) ~ (e1 = e0)
% 141.59/21.06 (6) ~ (e2 = e0)
% 141.59/21.06 (7) ~ (e3 = e2)
% 141.59/21.06 (8) all_57_9 = e3
% 141.59/21.06 (9) all_57_4 = e1
% 141.59/21.06 (10) ~ (e3 = e1)
% 141.59/21.06 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.06 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.06 (12) all_57_0 = e0
% 141.59/21.06 (13) all_57_7 = e3
% 141.59/21.06 (14) e3 = e1
% 141.59/21.06 (15) all_57_3 = e0
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | SIMP: (14) implies:
% 141.59/21.06 | (16) e3 = e1
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (8), (16) imply:
% 141.59/21.06 | (17) all_57_9 = e1
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (11) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (18) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (10), (12), (13), (15), (18)
% 141.59/21.06 | | are inconsistent by sub-proof #514.
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (19) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 141.59/21.06 | | e3)
% 141.59/21.06 | |
% 141.59/21.06 | | BETA: splitting (19) gives:
% 141.59/21.06 | |
% 141.59/21.06 | | Case 1:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (20) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | ALPHA: (20) implies:
% 141.59/21.06 | | | (21) all_57_4 = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (9), (10), (21) are inconsistent by sub-proof #631.
% 141.59/21.06 | | |
% 141.59/21.06 | | Case 2:
% 141.59/21.06 | | |
% 141.59/21.06 | | | (22) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.06 | | |
% 141.59/21.06 | | | REF_CLOSE: (10), (17), (22) are inconsistent by sub-proof #487.
% 141.59/21.06 | | |
% 141.59/21.06 | | End of split
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #487 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.06 (2) all_57_9 = e1
% 141.59/21.06 (3) ~ (e3 = e1)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | ALPHA: (1) implies:
% 141.59/21.06 | (4) all_57_9 = e3
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (2), (4) imply:
% 141.59/21.06 | (5) e3 = e1
% 141.59/21.06 |
% 141.59/21.06 | SIMP: (5) implies:
% 141.59/21.06 | (6) e3 = e1
% 141.59/21.06 |
% 141.59/21.06 | REDUCE: (3), (6) imply:
% 141.59/21.06 | (7) $false
% 141.59/21.06 |
% 141.59/21.06 | CLOSE: (7) is inconsistent.
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #488 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 141.59/21.06 (2) ~ (e3 = e2)
% 141.59/21.06 (3) all_57_5 = e2
% 141.59/21.06 (4) all_57_4 = e1
% 141.59/21.06 (5) ~ (e3 = e1)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | BETA: splitting (1) gives:
% 141.59/21.06 |
% 141.59/21.06 | Case 1:
% 141.59/21.06 | |
% 141.59/21.06 | | (6) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.06 | |
% 141.59/21.06 | | ALPHA: (6) implies:
% 141.59/21.06 | | (7) all_57_4 = e3
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (4), (5), (7) are inconsistent by sub-proof #631.
% 141.59/21.06 | |
% 141.59/21.06 | Case 2:
% 141.59/21.06 | |
% 141.59/21.06 | | (8) all_57_5 = e3 & op(e2, e1) = e3
% 141.59/21.06 | |
% 141.59/21.06 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #489.
% 141.59/21.06 | |
% 141.59/21.06 | End of split
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #489 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) all_57_5 = e3 & op(e2, e1) = e3
% 141.59/21.06 (2) all_57_5 = e2
% 141.59/21.06 (3) ~ (e3 = e2)
% 141.59/21.06
% 141.59/21.06 Begin of proof
% 141.59/21.06 |
% 141.59/21.06 | ALPHA: (1) implies:
% 141.59/21.06 | (4) all_57_5 = e3
% 141.59/21.06 |
% 141.59/21.06 | COMBINE_EQS: (2), (4) imply:
% 141.59/21.06 | (5) e3 = e2
% 141.59/21.06 |
% 141.59/21.06 | REDUCE: (3), (5) imply:
% 141.59/21.06 | (6) $false
% 141.59/21.06 |
% 141.59/21.06 | CLOSE: (6) is inconsistent.
% 141.59/21.06 |
% 141.59/21.06 End of proof
% 141.59/21.06
% 141.59/21.06 Sub-proof #490 shows that the following formulas are inconsistent:
% 141.59/21.06 ----------------------------------------------------------------
% 141.59/21.06 (1) all_57_14 = e0
% 141.59/21.06 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 141.59/21.06 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 141.59/21.06 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 141.59/21.06 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.06 (4) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 141.59/21.06 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.06 (5) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.07 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.07 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 141.59/21.07 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 141.59/21.07 (7) all_57_11 = e0
% 141.59/21.07 (8) ~ (e2 = e1)
% 141.59/21.07 (9) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.07 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.07 (10) all_57_5 = e1
% 141.59/21.07 (11) ~ (all_52_7 = e0)
% 141.59/21.07 (12) op(e0, e3) = all_52_3
% 141.59/21.07 (13) op(e0, e1) = e0
% 141.59/21.07 (14) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 141.59/21.07 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 141.59/21.07 e1)
% 141.59/21.07 (15) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 141.59/21.07 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 141.59/21.07 (16) ~ (e3 = e0)
% 141.59/21.07 (17) op(e1, e1) = e1
% 141.59/21.07 (18) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 141.59/21.07 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 141.59/21.07 e2)
% 141.59/21.07 (19) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 141.59/21.07 (all_57_11 = e0 & op(e1, e0) = e0)
% 141.59/21.07 (20) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 141.59/21.07 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 141.59/21.07 (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 141.59/21.07 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 141.59/21.07 (22) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.59/21.07 all_56_15 & $i(all_56_15))
% 141.59/21.07 (23) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 141.59/21.07 | (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.07 (24) ~ (e1 = e0)
% 141.59/21.07 (25) ~ (e2 = e0)
% 141.59/21.07 (26) ~ (e3 = e2)
% 141.59/21.07 (27) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 141.59/21.07 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.07 (28) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.07 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.07 (29) op(e0, e0) = e2
% 141.59/21.07 (30) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.07 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.07 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.07 (32) ~ (all_52_3 = e0)
% 141.59/21.07 (33) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.07 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.07 (34) ~ (e3 = e1)
% 141.59/21.07 (35) op(e0, e2) = all_52_7
% 141.59/21.07 (36) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 141.59/21.07 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 141.59/21.07 (37) op(e2, e2) = e0
% 141.59/21.07 (38) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.59/21.07 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.59/21.07 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.59/21.07 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.59/21.07 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.59/21.07 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.59/21.07 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.59/21.07 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.59/21.07 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.59/21.07 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.59/21.07 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.59/21.07 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.59/21.07 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.59/21.07 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.59/21.07 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.59/21.07 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.59/21.07 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.59/21.07 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.59/21.07 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.59/21.07 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.59/21.07 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.59/21.07 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.59/21.07 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.59/21.07 $i(all_56_14))))
% 141.59/21.07 (39) all_57_0 = e0
% 141.59/21.07 (40) op(e3, e3) = e0
% 141.59/21.07 (41) all_57_3 = e0
% 141.59/21.07
% 141.59/21.07 Begin of proof
% 141.59/21.07 |
% 141.59/21.07 | BETA: splitting (6) gives:
% 141.59/21.07 |
% 141.59/21.07 | Case 1:
% 141.59/21.07 | |
% 141.59/21.07 | | (42) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 141.59/21.07 | | e2)
% 141.59/21.07 | |
% 141.59/21.07 | | BETA: splitting (42) gives:
% 141.59/21.07 | |
% 141.59/21.07 | | Case 1:
% 141.59/21.07 | | |
% 141.59/21.07 | | | (43) all_57_2 = e2 & op(e2, e3) = e2
% 141.59/21.07 | | |
% 141.59/21.07 | | | ALPHA: (43) implies:
% 141.59/21.07 | | | (44) all_57_2 = e2
% 141.59/21.07 | | |
% 141.59/21.07 | | | BETA: splitting (30) gives:
% 141.59/21.07 | | |
% 141.59/21.07 | | | Case 1:
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | (45) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1)
% 141.59/21.07 | | | | = e2)
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | BETA: splitting (45) gives:
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | Case 1:
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | (46) all_57_4 = e2 & op(e3, e1) = e2
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | ALPHA: (46) implies:
% 141.59/21.07 | | | | | (47) all_57_4 = e2
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | BETA: splitting (2) gives:
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | Case 1:
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | (48) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 141.59/21.07 | | | | | | e2) = e3)
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | REF_CLOSE: (16), (26), (31), (37), (44), (48) are inconsistent by
% 141.59/21.07 | | | | | | sub-proof #822.
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | Case 2:
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | (49) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 141.59/21.07 | | | | | | e0) = e3)
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | BETA: splitting (49) gives:
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | Case 1:
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | (50) all_57_5 = e3 & op(e2, e1) = e3
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | REF_CLOSE: (10), (34), (50) are inconsistent by sub-proof #504.
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | Case 2:
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | (51) all_57_10 = e3 & op(e2, e0) = e3
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | ALPHA: (51) implies:
% 141.59/21.07 | | | | | | | (52) all_57_10 = e3
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | BETA: splitting (5) gives:
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | | (53) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 141.59/21.07 | | | | | | | | op(e2, e1) = e3)
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | | REF_CLOSE: (10), (26), (34), (47), (53) are inconsistent by
% 141.59/21.07 | | | | | | | | sub-proof #503.
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | | (54) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 &
% 141.59/21.07 | | | | | | | | op(e0, e1) = e3)
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | | BETA: splitting (54) gives:
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | (55) all_57_8 = e3 & op(e1, e1) = e3
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | ALPHA: (55) implies:
% 141.59/21.07 | | | | | | | | | (56) all_57_8 = e3
% 141.59/21.07 | | | | | | | | | (57) op(e1, e1) = e3
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | BETA: splitting (21) gives:
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | (58) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 141.59/21.07 | | | | | | | | | | op(e2, e3) = e1)
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | BETA: splitting (58) gives:
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | (59) all_57_0 = e1 & op(e3, e3) = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | ALPHA: (59) implies:
% 141.59/21.07 | | | | | | | | | | | (60) op(e3, e3) = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | REF_CLOSE: (24), (31), (40), (60) are inconsistent by
% 141.59/21.07 | | | | | | | | | | | sub-proof #840.
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | (61) all_57_2 = e1 & op(e2, e3) = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | ALPHA: (61) implies:
% 141.59/21.07 | | | | | | | | | | | (62) all_57_2 = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | COMBINE_EQS: (44), (62) imply:
% 141.59/21.07 | | | | | | | | | | | (63) e2 = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | REDUCE: (8), (63) imply:
% 141.59/21.07 | | | | | | | | | | | (64) $false
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | CLOSE: (64) is inconsistent.
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | (65) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 141.59/21.07 | | | | | | | | | | & op(e0, e3) = e1)
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | BETA: splitting (65) gives:
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | (66) all_57_6 = e1 & op(e1, e3) = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | ALPHA: (66) implies:
% 141.59/21.07 | | | | | | | | | | | (67) all_57_6 = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | BETA: splitting (33) gives:
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | (68) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 =
% 141.59/21.07 | | | | | | | | | | | | e1 & op(e2, e0) = e1)
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | BETA: splitting (68) gives:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | (69) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | ALPHA: (69) implies:
% 141.59/21.07 | | | | | | | | | | | | | (70) all_57_9 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | BETA: splitting (20) gives:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | (71) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 141.59/21.07 | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | BETA: splitting (71) gives:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | (72) all_57_0 = e3 & op(e3, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (72) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | #1108.
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | (73) all_57_2 = e3 & op(e2, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | REF_CLOSE: (26), (44), (73) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | #823.
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | (74) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 141.59/21.07 | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | BETA: splitting (74) gives:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | (75) all_57_6 = e3 & op(e1, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | REF_CLOSE: (34), (67), (75) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | #1093.
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | (76) all_57_12 = e3 & op(e0, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | ALPHA: (76) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | (77) all_57_12 = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | BETA: splitting (36) gives:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | (78) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | & op(e3, e2) = e3)
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | BETA: splitting (78) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | (79) all_57_0 = e3 & op(e3, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (79) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | #1108.
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | (80) all_57_1 = e3 & op(e3, e2) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | ALPHA: (80) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (81) all_57_1 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | BETA: splitting (3) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | (82) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e1)
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | BETA: splitting (82) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (83) all_57_1 = e1 & op(e3, e2) = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | ALPHA: (83) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (84) all_57_1 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (81), (84) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (85) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (85) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (86) all_57_12 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (15), (16), (19), (20), (24),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (25), (26), (29), (31), (33), (34), (39), (44),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (52), (67), (86) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | #500.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (87) all_57_3 = e1 & op(e2, e2) = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | ALPHA: (87) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (88) op(e2, e2) = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (24), (31), (37), (88) are inconsistent by
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | sub-proof #1117.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | (89) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 =
% 141.59/21.07 | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | BETA: splitting (89) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (90) all_57_7 = e1 & op(e1, e2) = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | ALPHA: (90) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (91) all_57_7 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (17), (25), (28), (31), (67), (91) are
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #499.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (92) all_57_13 = e1 & op(e0, e2) = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | ALPHA: (92) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (93) all_57_13 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | BETA: splitting (4) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | (94) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (94) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | GROUND_INST: instantiating (31) with e1, e3, e1, e1,
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | simplifying with (17), (57) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (95) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (95) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (96) all_57_12 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (15), (16), (19), (20), (24),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (25), (26), (29), (31), (33), (34), (39), (44),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (52), (67), (96) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | #500.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (97) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | ALPHA: (97) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (98) all_57_13 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (93), (98) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (99) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (99) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (100) all_57_12 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (16), (20), (24), (26), (29),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (31), (34), (39), (44), (67), (98), (100) are
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #502.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | (101) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | BETA: splitting (101) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (102) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (16), (102) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | #777.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (103) all_57_15 = e3 & op(e0, e0) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | ALPHA: (103) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (104) op(e0, e0) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (18), (25), (26), (31), (77), (93),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | | (104) are inconsistent by sub-proof #658.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | (105) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | & op(e3, e0) = e3)
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | BETA: splitting (105) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | (106) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | ALPHA: (106) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (107) all_57_4 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (26), (47), (107) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | #821.
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | (108) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | ALPHA: (108) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (109) all_57_9 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (70), (109) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (110) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | SIMP: (110) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (111) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | COMBINE_EQS: (77), (111) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (112) all_57_12 = e1
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (15), (16), (19), (20), (24),
% 141.59/21.07 | | | | | | | | | | | | | | | | | (25), (26), (29), (31), (33), (34), (39), (44),
% 141.59/21.07 | | | | | | | | | | | | | | | | | (52), (67), (112) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | #500.
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | (113) all_57_10 = e1 & op(e2, e0) = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | REF_CLOSE: (34), (52), (113) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | #929.
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | (114) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 =
% 141.59/21.07 | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | REF_CLOSE: (7), (8), (24), (29), (31), (114) are inconsistent
% 141.59/21.07 | | | | | | | | | | | | by sub-proof #498.
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | (115) all_57_12 = e1 & op(e0, e3) = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | ALPHA: (115) implies:
% 141.59/21.07 | | | | | | | | | | | (116) all_57_12 = e1
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | BETA: splitting (9) gives:
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | (117) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1
% 141.59/21.07 | | | | | | | | | | | | & op(e1, e2) = e1)
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | BETA: splitting (117) gives:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | (118) all_57_6 = e1 & op(e1, e3) = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | ALPHA: (118) implies:
% 141.59/21.07 | | | | | | | | | | | | | (119) all_57_6 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (15), (16), (19), (20), (24),
% 141.59/21.07 | | | | | | | | | | | | | (25), (26), (29), (31), (33), (34), (39), (44),
% 141.59/21.07 | | | | | | | | | | | | | (52), (116), (119) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | #500.
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | (120) all_57_7 = e1 & op(e1, e2) = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | ALPHA: (120) implies:
% 141.59/21.07 | | | | | | | | | | | | | (121) all_57_7 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | BETA: splitting (4) gives:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | (122) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 =
% 141.59/21.07 | | | | | | | | | | | | | | e3 & op(e0, e2) = e3)
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | BETA: splitting (122) gives:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | (123) all_57_12 = e3 & op(e0, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | REF_CLOSE: (34), (116), (123) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | #798.
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | (124) all_57_13 = e3 & op(e0, e2) = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | ALPHA: (124) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | (125) all_57_13 = e3
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | (126) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | BETA: splitting (126) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | (127) all_57_6 = e2 & op(e1, e3) = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | ALPHA: (127) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | (128) all_57_6 = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | (129) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | BETA: splitting (129) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (130) all_57_0 = e3 & op(e3, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (16), (39), (130) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | #1108.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (131) all_57_2 = e3 & op(e2, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | ALPHA: (131) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (132) all_57_2 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (44), (132) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (133) e3 = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (133) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (134) all_57_13 = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (16), (24), (26), (29), (31),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (34), (134) are inconsistent by sub-proof #1064.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | (135) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 141.59/21.07 | | | | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | BETA: splitting (135) gives:
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (136) all_57_6 = e3 & op(e1, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | ALPHA: (136) implies:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (137) all_57_6 = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (128), (137) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (138) e3 = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (125), (138) imply:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (139) all_57_13 = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (8), (14), (16), (24), (26), (29), (31),
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (34), (139) are inconsistent by sub-proof #1064.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | (140) all_57_12 = e3 & op(e0, e3) = e3
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (116), (140) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | | | #798.
% 141.59/21.07 | | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | (141) all_57_7 = e2 & op(e1, e2) = e2
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | | REF_CLOSE: (8), (121), (141) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | | | | | #997.
% 141.59/21.07 | | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | (142) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 141.59/21.07 | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | | REF_CLOSE: (7), (8), (17), (25), (31), (142) are inconsistent
% 141.59/21.07 | | | | | | | | | | | | | | | | by sub-proof #497.
% 141.59/21.07 | | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | (143) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 =
% 141.59/21.07 | | | | | | | | | | | | | | e3 & op(e0, e0) = e3)
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | | REF_CLOSE: (1), (8), (15), (16), (19), (24), (25), (26),
% 141.59/21.07 | | | | | | | | | | | | | | (31), (33), (34), (52), (143) are inconsistent by
% 141.59/21.07 | | | | | | | | | | | | | | sub-proof #501.
% 141.59/21.07 | | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | (144) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 =
% 141.59/21.07 | | | | | | | | | | | | e1 & op(e1, e0) = e1)
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | BETA: splitting (144) gives:
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | Case 1:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | (145) all_57_8 = e1 & op(e1, e1) = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | ALPHA: (145) implies:
% 141.59/21.07 | | | | | | | | | | | | | (146) all_57_8 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | COMBINE_EQS: (56), (146) imply:
% 141.59/21.07 | | | | | | | | | | | | | (147) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | SIMP: (147) implies:
% 141.59/21.07 | | | | | | | | | | | | | (148) e3 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | REDUCE: (34), (148) imply:
% 141.59/21.07 | | | | | | | | | | | | | (149) $false
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | CLOSE: (149) is inconsistent.
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | (150) all_57_11 = e1 & op(e1, e0) = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | ALPHA: (150) implies:
% 141.59/21.07 | | | | | | | | | | | | | (151) all_57_11 = e1
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | | REF_CLOSE: (7), (24), (151) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | | | | | #690.
% 141.59/21.07 | | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | | |
% 141.59/21.07 | | | | | | | | | End of split
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | Case 2:
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | (152) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | ALPHA: (152) implies:
% 141.59/21.07 | | | | | | | | | (153) all_57_14 = e3
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | | REF_CLOSE: (1), (16), (153) are inconsistent by sub-proof
% 141.59/21.07 | | | | | | | | | #1067.
% 141.59/21.07 | | | | | | | | |
% 141.59/21.07 | | | | | | | | End of split
% 141.59/21.07 | | | | | | | |
% 141.59/21.07 | | | | | | | End of split
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | End of split
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | End of split
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | Case 2:
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | (154) all_57_5 = e2 & op(e2, e1) = e2
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | ALPHA: (154) implies:
% 141.59/21.07 | | | | | (155) all_57_5 = e2
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | REF_CLOSE: (8), (10), (155) are inconsistent by sub-proof #1031.
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | End of split
% 141.59/21.07 | | | |
% 141.59/21.07 | | | Case 2:
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | (156) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0,
% 141.59/21.07 | | | | e1) = e2)
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | REF_CLOSE: (8), (11), (12), (17), (23), (25), (31), (32), (35), (156)
% 141.59/21.07 | | | | are inconsistent by sub-proof #496.
% 141.59/21.07 | | | |
% 141.59/21.07 | | | End of split
% 141.59/21.07 | | |
% 141.59/21.07 | | Case 2:
% 141.59/21.07 | | |
% 141.59/21.07 | | | (157) all_57_3 = e2 & op(e2, e2) = e2
% 141.59/21.07 | | |
% 141.59/21.07 | | | REF_CLOSE: (25), (41), (157) are inconsistent by sub-proof #516.
% 141.59/21.07 | | |
% 141.59/21.07 | | End of split
% 141.59/21.07 | |
% 141.59/21.07 | Case 2:
% 141.59/21.07 | |
% 141.59/21.07 | | (158) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 141.59/21.07 | | e2)
% 141.59/21.07 | |
% 141.59/21.07 | | BETA: splitting (158) gives:
% 141.59/21.07 | |
% 141.59/21.07 | | Case 1:
% 141.59/21.07 | | |
% 141.59/21.07 | | | (159) all_57_5 = e2 & op(e2, e1) = e2
% 141.59/21.07 | | |
% 141.59/21.07 | | | REF_CLOSE: (8), (10), (159) are inconsistent by sub-proof #1012.
% 141.59/21.07 | | |
% 141.59/21.07 | | Case 2:
% 141.59/21.07 | | |
% 141.59/21.07 | | | (160) all_57_10 = e2 & op(e2, e0) = e2
% 141.59/21.07 | | |
% 141.59/21.07 | | | ALPHA: (160) implies:
% 141.59/21.07 | | | (161) all_57_10 = e2
% 141.59/21.07 | | |
% 141.59/21.07 | | | BETA: splitting (27) gives:
% 141.59/21.07 | | |
% 141.59/21.07 | | | Case 1:
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | (162) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2,
% 141.59/21.07 | | | | e0) = e3)
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | BETA: splitting (162) gives:
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | Case 1:
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | (163) all_57_9 = e3 & op(e3, e0) = e3
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | ALPHA: (163) implies:
% 141.59/21.07 | | | | | (164) all_57_9 = e3
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | BETA: splitting (30) gives:
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | Case 1:
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | (165) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2,
% 141.59/21.07 | | | | | | e1) = e2)
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | BETA: splitting (165) gives:
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | Case 1:
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | (166) all_57_4 = e2 & op(e3, e1) = e2
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | ALPHA: (166) implies:
% 141.59/21.07 | | | | | | | (167) all_57_4 = e2
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (16), (17), (24), (25),
% 141.59/21.07 | | | | | | | (26), (28), (29), (30), (31), (33), (34), (161), (164),
% 141.59/21.07 | | | | | | | (167) are inconsistent by sub-proof #493.
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | Case 2:
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | (168) all_57_5 = e2 & op(e2, e1) = e2
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | | REF_CLOSE: (8), (10), (168) are inconsistent by sub-proof #1012.
% 141.59/21.07 | | | | | | |
% 141.59/21.07 | | | | | | End of split
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | Case 2:
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | (169) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 141.59/21.07 | | | | | | op(e0, e1) = e2)
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | | REF_CLOSE: (8), (11), (12), (17), (23), (25), (31), (32), (35),
% 141.59/21.07 | | | | | | (169) are inconsistent by sub-proof #496.
% 141.59/21.07 | | | | | |
% 141.59/21.07 | | | | | End of split
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | Case 2:
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | (170) all_57_10 = e3 & op(e2, e0) = e3
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | ALPHA: (170) implies:
% 141.59/21.07 | | | | | (171) all_57_10 = e3
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | | REF_CLOSE: (26), (161), (171) are inconsistent by sub-proof #492.
% 141.59/21.07 | | | | |
% 141.59/21.07 | | | | End of split
% 141.59/21.07 | | | |
% 141.59/21.07 | | | Case 2:
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | (172) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0,
% 141.59/21.07 | | | | e0) = e3)
% 141.59/21.07 | | | |
% 141.59/21.07 | | | | REF_CLOSE: (7), (8), (12), (13), (16), (17), (22), (24), (25), (26),
% 141.59/21.07 | | | | (31), (32), (38), (40), (172) are inconsistent by sub-proof
% 141.59/21.07 | | | | #491.
% 141.59/21.07 | | | |
% 141.59/21.07 | | | End of split
% 141.59/21.07 | | |
% 141.59/21.07 | | End of split
% 141.59/21.07 | |
% 141.59/21.07 | End of split
% 141.59/21.07 |
% 141.59/21.07 End of proof
% 141.59/21.07
% 141.59/21.07 Sub-proof #491 shows that the following formulas are inconsistent:
% 141.59/21.07 ----------------------------------------------------------------
% 141.59/21.07 (1) all_57_11 = e0
% 141.59/21.07 (2) ~ (e2 = e1)
% 141.59/21.07 (3) op(e0, e3) = all_52_3
% 141.59/21.07 (4) op(e0, e1) = e0
% 141.59/21.07 (5) ~ (e3 = e0)
% 141.59/21.07 (6) op(e1, e1) = e1
% 141.59/21.07 (7) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 141.59/21.07 all_56_15 & $i(all_56_15))
% 141.59/21.07 (8) ~ (e1 = e0)
% 141.59/21.07 (9) ~ (e2 = e0)
% 141.59/21.07 (10) ~ (e3 = e2)
% 141.59/21.07 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.07 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.07 (12) ~ (all_52_3 = e0)
% 141.59/21.08 (13) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 141.59/21.08 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 141.59/21.08 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 141.59/21.08 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 141.59/21.08 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 141.59/21.08 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 141.59/21.08 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 141.59/21.08 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 141.59/21.08 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 141.59/21.08 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 141.59/21.08 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 141.59/21.08 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 141.59/21.08 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 141.59/21.08 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 141.59/21.08 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 141.59/21.08 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 141.59/21.08 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 141.59/21.08 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 141.59/21.08 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 141.59/21.08 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 141.59/21.08 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 141.59/21.08 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 141.59/21.08 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 141.59/21.08 $i(all_56_14))))
% 141.59/21.08 (14) op(e3, e3) = e0
% 141.59/21.08 (15) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (15) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (16) all_57_11 = e3 & op(e1, e0) = e3
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (1), (5), (16) are inconsistent by sub-proof #957.
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (17) all_57_15 = e3 & op(e0, e0) = e3
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (17) implies:
% 141.59/21.08 | | (18) op(e0, e0) = e3
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 141.59/21.08 | | (18) are inconsistent by sub-proof #672.
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #492 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_10 = e3
% 141.59/21.08 (2) all_57_10 = e2
% 141.59/21.08 (3) ~ (e3 = e2)
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | COMBINE_EQS: (1), (2) imply:
% 141.59/21.08 | (4) e3 = e2
% 141.59/21.08 |
% 141.59/21.08 | SIMP: (4) implies:
% 141.59/21.08 | (5) e3 = e2
% 141.59/21.08 |
% 141.59/21.08 | REDUCE: (3), (5) imply:
% 141.59/21.08 | (6) $false
% 141.59/21.08 |
% 141.59/21.08 | CLOSE: (6) is inconsistent.
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #493 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_14 = e0
% 141.59/21.08 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.08 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.08 (3) all_57_10 = e2
% 141.59/21.08 (4) all_57_4 = e2
% 141.59/21.08 (5) all_57_11 = e0
% 141.59/21.08 (6) ~ (e2 = e1)
% 141.59/21.08 (7) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 141.59/21.08 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 141.59/21.08 (8) all_57_5 = e1
% 141.59/21.08 (9) ~ (e3 = e0)
% 141.59/21.08 (10) op(e1, e1) = e1
% 141.59/21.08 (11) ~ (e1 = e0)
% 141.59/21.08 (12) ~ (e2 = e0)
% 141.59/21.08 (13) ~ (e3 = e2)
% 141.59/21.08 (14) all_57_9 = e3
% 141.59/21.08 (15) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 141.59/21.08 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.08 (16) op(e0, e0) = e2
% 141.59/21.08 (17) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.08 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.08 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.08 (19) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 141.59/21.08 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.08 (20) ~ (e3 = e1)
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (7) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (21) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) =
% 141.59/21.08 | | e1)
% 141.59/21.08 | |
% 141.59/21.08 | | BETA: splitting (21) gives:
% 141.59/21.08 | |
% 141.59/21.08 | | Case 1:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (22) all_57_6 = e1 & op(e1, e3) = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | ALPHA: (22) implies:
% 141.59/21.08 | | | (23) all_57_6 = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | BETA: splitting (15) gives:
% 141.59/21.08 | | |
% 141.59/21.08 | | | Case 1:
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | (24) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 141.59/21.08 | | | | = e2)
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | BETA: splitting (24) gives:
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | Case 1:
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | (25) all_57_6 = e2 & op(e1, e3) = e2
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | REF_CLOSE: (6), (23), (25) are inconsistent by sub-proof #1110.
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | Case 2:
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | (26) all_57_7 = e2 & op(e1, e2) = e2
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | ALPHA: (26) implies:
% 141.59/21.08 | | | | | (27) all_57_7 = e2
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | BETA: splitting (19) gives:
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | Case 1:
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | (28) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 141.59/21.08 | | | | | | e0) = e1)
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | BETA: splitting (28) gives:
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | Case 1:
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | (29) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | REF_CLOSE: (14), (20), (29) are inconsistent by sub-proof #599.
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | Case 2:
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | (30) all_57_10 = e1 & op(e2, e0) = e1
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | ALPHA: (30) implies:
% 141.59/21.08 | | | | | | | (31) all_57_10 = e1
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | COMBINE_EQS: (3), (31) imply:
% 141.59/21.08 | | | | | | | (32) e2 = e1
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | COMBINE_EQS: (27), (32) imply:
% 141.59/21.08 | | | | | | | (33) all_57_7 = e1
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | REF_CLOSE: (5), (6), (10), (12), (15), (18), (23), (33) are
% 141.59/21.08 | | | | | | | inconsistent by sub-proof #499.
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | End of split
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | Case 2:
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | (34) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 141.59/21.08 | | | | | | op(e0, e0) = e1)
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | REF_CLOSE: (5), (6), (11), (16), (18), (34) are inconsistent by
% 141.59/21.08 | | | | | | sub-proof #495.
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | End of split
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | End of split
% 141.59/21.08 | | | |
% 141.59/21.08 | | | Case 2:
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | (35) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 141.59/21.08 | | | | = e2)
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | REF_CLOSE: (5), (6), (10), (12), (18), (35) are inconsistent by
% 141.59/21.08 | | | | sub-proof #497.
% 141.59/21.08 | | | |
% 141.59/21.08 | | | End of split
% 141.59/21.08 | | |
% 141.59/21.08 | | Case 2:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (36) all_57_7 = e1 & op(e1, e2) = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | ALPHA: (36) implies:
% 141.59/21.08 | | | (37) all_57_7 = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | BETA: splitting (15) gives:
% 141.59/21.08 | | |
% 141.59/21.08 | | | Case 1:
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | (38) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 141.59/21.08 | | | | = e2)
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | BETA: splitting (38) gives:
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | Case 1:
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | (39) all_57_6 = e2 & op(e1, e3) = e2
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | ALPHA: (39) implies:
% 141.59/21.08 | | | | | (40) all_57_6 = e2
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | BETA: splitting (2) gives:
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | Case 1:
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | (41) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 141.59/21.08 | | | | | | e1) = e3)
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | REF_CLOSE: (4), (8), (13), (20), (41) are inconsistent by sub-proof
% 141.59/21.08 | | | | | | #503.
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | Case 2:
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | (42) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 141.59/21.08 | | | | | | e1) = e3)
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | BETA: splitting (42) gives:
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | | Case 1:
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | (43) all_57_8 = e3 & op(e1, e1) = e3
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | ALPHA: (43) implies:
% 141.59/21.08 | | | | | | | (44) all_57_8 = e3
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | BETA: splitting (19) gives:
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | Case 1:
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | | (45) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 &
% 141.59/21.08 | | | | | | | | op(e2, e0) = e1)
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | | BETA: splitting (45) gives:
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | | Case 1:
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | (46) all_57_9 = e1 & op(e3, e0) = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | ALPHA: (46) implies:
% 141.59/21.08 | | | | | | | | | (47) all_57_9 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | COMBINE_EQS: (14), (47) imply:
% 141.59/21.08 | | | | | | | | | (48) e3 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | COMBINE_EQS: (44), (48) imply:
% 141.59/21.08 | | | | | | | | | (49) all_57_8 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | REF_CLOSE: (1), (2), (6), (8), (9), (12), (13), (17), (20),
% 141.59/21.08 | | | | | | | | | (49) are inconsistent by sub-proof #494.
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | Case 2:
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | (50) all_57_10 = e1 & op(e2, e0) = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | ALPHA: (50) implies:
% 141.59/21.08 | | | | | | | | | (51) all_57_10 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | COMBINE_EQS: (3), (51) imply:
% 141.59/21.08 | | | | | | | | | (52) e2 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | SIMP: (52) implies:
% 141.59/21.08 | | | | | | | | | (53) e2 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | COMBINE_EQS: (40), (53) imply:
% 141.59/21.08 | | | | | | | | | (54) all_57_6 = e1
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | | REF_CLOSE: (5), (6), (10), (12), (15), (18), (37), (54) are
% 141.59/21.08 | | | | | | | | | inconsistent by sub-proof #499.
% 141.59/21.08 | | | | | | | | |
% 141.59/21.08 | | | | | | | | End of split
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | Case 2:
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | | (55) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 &
% 141.59/21.08 | | | | | | | | op(e0, e0) = e1)
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | | REF_CLOSE: (5), (6), (11), (16), (18), (55) are inconsistent by
% 141.59/21.08 | | | | | | | | sub-proof #495.
% 141.59/21.08 | | | | | | | |
% 141.59/21.08 | | | | | | | End of split
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | Case 2:
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | (56) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | | REF_CLOSE: (1), (9), (56) are inconsistent by sub-proof #777.
% 141.59/21.08 | | | | | | |
% 141.59/21.08 | | | | | | End of split
% 141.59/21.08 | | | | | |
% 141.59/21.08 | | | | | End of split
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | Case 2:
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | (57) all_57_7 = e2 & op(e1, e2) = e2
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | | REF_CLOSE: (6), (37), (57) are inconsistent by sub-proof #997.
% 141.59/21.08 | | | | |
% 141.59/21.08 | | | | End of split
% 141.59/21.08 | | | |
% 141.59/21.08 | | | Case 2:
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | (58) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 141.59/21.08 | | | | = e2)
% 141.59/21.08 | | | |
% 141.59/21.08 | | | | REF_CLOSE: (5), (6), (10), (12), (18), (58) are inconsistent by
% 141.59/21.08 | | | | sub-proof #497.
% 141.59/21.08 | | | |
% 141.59/21.08 | | | End of split
% 141.59/21.08 | | |
% 141.59/21.08 | | End of split
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (59) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) =
% 141.59/21.08 | | e1)
% 141.59/21.08 | |
% 141.59/21.08 | | BETA: splitting (59) gives:
% 141.59/21.08 | |
% 141.59/21.08 | | Case 1:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (60) all_57_8 = e1 & op(e1, e1) = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | ALPHA: (60) implies:
% 141.59/21.08 | | | (61) all_57_8 = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | REF_CLOSE: (1), (2), (6), (8), (9), (12), (13), (17), (20), (61) are
% 141.59/21.08 | | | inconsistent by sub-proof #494.
% 141.59/21.08 | | |
% 141.59/21.08 | | Case 2:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (62) all_57_11 = e1 & op(e1, e0) = e1
% 141.59/21.08 | | |
% 141.59/21.08 | | | REF_CLOSE: (5), (11), (62) are inconsistent by sub-proof #596.
% 141.59/21.08 | | |
% 141.59/21.08 | | End of split
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #494 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_14 = e0
% 141.59/21.08 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 141.59/21.08 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 141.59/21.08 (3) ~ (e2 = e1)
% 141.59/21.08 (4) all_57_5 = e1
% 141.59/21.08 (5) ~ (e3 = e0)
% 141.59/21.08 (6) ~ (e2 = e0)
% 141.59/21.08 (7) ~ (e3 = e2)
% 141.59/21.08 (8) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 141.59/21.08 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.08 (9) ~ (e3 = e1)
% 141.59/21.08 (10) all_57_8 = e1
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (2) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (11) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 141.59/21.08 | | e3)
% 141.59/21.08 | |
% 141.59/21.08 | | BETA: splitting (11) gives:
% 141.59/21.08 | |
% 141.59/21.08 | | Case 1:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (12) all_57_4 = e3 & op(e3, e1) = e3
% 141.59/21.08 | | |
% 141.59/21.08 | | | ALPHA: (12) implies:
% 141.59/21.08 | | | (13) all_57_4 = e3
% 141.59/21.08 | | |
% 141.59/21.08 | | | REF_CLOSE: (1), (3), (4), (6), (7), (8), (10), (13) are inconsistent by
% 141.59/21.08 | | | sub-proof #870.
% 141.59/21.08 | | |
% 141.59/21.08 | | Case 2:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (14) all_57_5 = e3 & op(e2, e1) = e3
% 141.59/21.08 | | |
% 141.59/21.08 | | | REF_CLOSE: (4), (9), (14) are inconsistent by sub-proof #504.
% 141.59/21.08 | | |
% 141.59/21.08 | | End of split
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (15) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 141.59/21.08 | | e3)
% 141.59/21.08 | |
% 141.59/21.08 | | BETA: splitting (15) gives:
% 141.59/21.08 | |
% 141.59/21.08 | | Case 1:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (16) all_57_8 = e3 & op(e1, e1) = e3
% 141.59/21.08 | | |
% 141.59/21.08 | | | REF_CLOSE: (9), (10), (16) are inconsistent by sub-proof #506.
% 141.59/21.08 | | |
% 141.59/21.08 | | Case 2:
% 141.59/21.08 | | |
% 141.59/21.08 | | | (17) all_57_14 = e3 & op(e0, e1) = e3
% 141.59/21.08 | | |
% 141.59/21.08 | | | REF_CLOSE: (1), (5), (17) are inconsistent by sub-proof #777.
% 141.59/21.08 | | |
% 141.59/21.08 | | End of split
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #495 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_11 = e0
% 141.59/21.08 (2) ~ (e2 = e1)
% 141.59/21.08 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.08 (4) ~ (e1 = e0)
% 141.59/21.08 (5) op(e0, e0) = e2
% 141.59/21.08 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (3) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #596.
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (8) implies:
% 141.59/21.08 | | (9) op(e0, e0) = e1
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #1070.
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #496 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 141.59/21.08 (2) ~ (e2 = e1)
% 141.59/21.08 (3) ~ (all_52_7 = e0)
% 141.59/21.08 (4) op(e0, e3) = all_52_3
% 141.59/21.08 (5) op(e1, e1) = e1
% 141.59/21.08 (6) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 141.59/21.08 (all_57_14 = e0 & op(e0, e1) = e0)
% 141.59/21.08 (7) ~ (e2 = e0)
% 141.59/21.08 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.08 (9) ~ (all_52_3 = e0)
% 141.59/21.08 (10) op(e0, e2) = all_52_7
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (1) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (11) all_57_8 = e2 & op(e1, e1) = e2
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (11) implies:
% 141.59/21.08 | | (12) op(e1, e1) = e2
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (2), (5), (8), (12) are inconsistent by sub-proof #1085.
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (13) all_57_14 = e2 & op(e0, e1) = e2
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (3), (4), (6), (7), (8), (9), (10), (13) are inconsistent by
% 141.59/21.08 | | sub-proof #652.
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #497 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_11 = e0
% 141.59/21.08 (2) ~ (e2 = e1)
% 141.59/21.08 (3) op(e1, e1) = e1
% 141.59/21.08 (4) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 141.59/21.08 (5) ~ (e2 = e0)
% 141.59/21.08 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (4) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (7) implies:
% 141.59/21.08 | | (8) op(e1, e1) = e2
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1085.
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (9) all_57_11 = e2 & op(e1, e0) = e2
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (9) implies:
% 141.59/21.08 | | (10) all_57_11 = e2
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #996.
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #498 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_11 = e0
% 141.59/21.08 (2) ~ (e2 = e1)
% 141.59/21.08 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 141.59/21.08 (4) ~ (e1 = e0)
% 141.59/21.08 (5) op(e0, e0) = e2
% 141.59/21.08 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 141.59/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 141.59/21.08
% 141.59/21.08 Begin of proof
% 141.59/21.08 |
% 141.59/21.08 | BETA: splitting (3) gives:
% 141.59/21.08 |
% 141.59/21.08 | Case 1:
% 141.59/21.08 | |
% 141.59/21.08 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (7) implies:
% 141.59/21.08 | | (8) all_57_11 = e1
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #690.
% 141.59/21.08 | |
% 141.59/21.08 | Case 2:
% 141.59/21.08 | |
% 141.59/21.08 | | (9) all_57_15 = e1 & op(e0, e0) = e1
% 141.59/21.08 | |
% 141.59/21.08 | | ALPHA: (9) implies:
% 141.59/21.08 | | (10) op(e0, e0) = e1
% 141.59/21.08 | |
% 141.59/21.08 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1070.
% 141.59/21.08 | |
% 141.59/21.08 | End of split
% 141.59/21.08 |
% 141.59/21.08 End of proof
% 141.59/21.08
% 141.59/21.08 Sub-proof #499 shows that the following formulas are inconsistent:
% 141.59/21.08 ----------------------------------------------------------------
% 141.59/21.08 (1) all_57_11 = e0
% 141.59/21.08 (2) ~ (e2 = e1)
% 141.59/21.08 (3) all_57_7 = e1
% 141.59/21.08 (4) op(e1, e1) = e1
% 141.59/21.08 (5) ~ (e2 = e0)
% 142.00/21.08 (6) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.00/21.08 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.00/21.08 (7) all_57_6 = e1
% 142.00/21.08 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.08
% 142.00/21.08 Begin of proof
% 142.00/21.08 |
% 142.00/21.08 | BETA: splitting (6) gives:
% 142.00/21.08 |
% 142.00/21.08 | Case 1:
% 142.00/21.08 | |
% 142.00/21.08 | | (9) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 142.00/21.08 | |
% 142.00/21.08 | | BETA: splitting (9) gives:
% 142.00/21.08 | |
% 142.00/21.08 | | Case 1:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (10) all_57_6 = e2 & op(e1, e3) = e2
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #1110.
% 142.00/21.08 | | |
% 142.00/21.08 | | Case 2:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (11) all_57_7 = e2 & op(e1, e2) = e2
% 142.00/21.08 | | |
% 142.00/21.08 | | | ALPHA: (11) implies:
% 142.00/21.08 | | | (12) all_57_7 = e2
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (2), (3), (12) are inconsistent by sub-proof #872.
% 142.00/21.08 | | |
% 142.00/21.08 | | End of split
% 142.00/21.08 | |
% 142.00/21.08 | Case 2:
% 142.00/21.08 | |
% 142.00/21.08 | | (13) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 142.00/21.08 | | e2)
% 142.00/21.08 | |
% 142.00/21.08 | | REF_CLOSE: (1), (2), (4), (5), (8), (13) are inconsistent by sub-proof
% 142.00/21.08 | | #1082.
% 142.00/21.08 | |
% 142.00/21.08 | End of split
% 142.00/21.08 |
% 142.00/21.08 End of proof
% 142.00/21.08
% 142.00/21.08 Sub-proof #500 shows that the following formulas are inconsistent:
% 142.00/21.08 ----------------------------------------------------------------
% 142.00/21.08 (1) all_57_14 = e0
% 142.00/21.08 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.00/21.08 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.00/21.08 (3) ~ (e2 = e1)
% 142.00/21.08 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.08 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.08 (5) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.00/21.08 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.08 (6) ~ (e3 = e0)
% 142.00/21.08 (7) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.00/21.08 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.00/21.08 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.00/21.08 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.08 (9) ~ (e1 = e0)
% 142.00/21.08 (10) ~ (e2 = e0)
% 142.00/21.08 (11) ~ (e3 = e2)
% 142.00/21.08 (12) all_57_10 = e3
% 142.00/21.08 (13) op(e0, e0) = e2
% 142.00/21.08 (14) all_57_6 = e1
% 142.00/21.08 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.08 (16) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.00/21.08 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.08 (17) ~ (e3 = e1)
% 142.00/21.08 (18) all_57_0 = e0
% 142.00/21.08 (19) all_57_2 = e2
% 142.00/21.08 (20) all_57_12 = e1
% 142.00/21.08
% 142.00/21.08 Begin of proof
% 142.00/21.08 |
% 142.00/21.08 | BETA: splitting (2) gives:
% 142.00/21.08 |
% 142.00/21.08 | Case 1:
% 142.00/21.08 | |
% 142.00/21.08 | | (21) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 142.00/21.08 | | e3)
% 142.00/21.08 | |
% 142.00/21.08 | | BETA: splitting (21) gives:
% 142.00/21.08 | |
% 142.00/21.08 | | Case 1:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (22) all_57_12 = e3 & op(e0, e3) = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (17), (20), (22) are inconsistent by sub-proof #798.
% 142.00/21.08 | | |
% 142.00/21.08 | | Case 2:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (23) all_57_13 = e3 & op(e0, e2) = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | ALPHA: (23) implies:
% 142.00/21.08 | | | (24) all_57_13 = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (11), (13), (14), (15),
% 142.00/21.08 | | | (17), (18), (19), (20), (24) are inconsistent by sub-proof
% 142.00/21.08 | | | #502.
% 142.00/21.08 | | |
% 142.00/21.08 | | End of split
% 142.00/21.08 | |
% 142.00/21.08 | Case 2:
% 142.00/21.08 | |
% 142.00/21.08 | | (25) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 142.00/21.08 | | e3)
% 142.00/21.08 | |
% 142.00/21.08 | | REF_CLOSE: (1), (3), (5), (6), (7), (9), (10), (11), (12), (15), (16), (17),
% 142.00/21.08 | | (25) are inconsistent by sub-proof #501.
% 142.00/21.08 | |
% 142.00/21.08 | End of split
% 142.00/21.08 |
% 142.00/21.08 End of proof
% 142.00/21.08
% 142.00/21.08 Sub-proof #501 shows that the following formulas are inconsistent:
% 142.00/21.08 ----------------------------------------------------------------
% 142.00/21.08 (1) all_57_14 = e0
% 142.00/21.08 (2) ~ (e2 = e1)
% 142.00/21.08 (3) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.00/21.08 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.08 (4) ~ (e3 = e0)
% 142.00/21.08 (5) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.00/21.08 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.00/21.08 (6) ~ (e1 = e0)
% 142.00/21.08 (7) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.00/21.08 (8) ~ (e2 = e0)
% 142.00/21.08 (9) ~ (e3 = e2)
% 142.00/21.08 (10) all_57_10 = e3
% 142.00/21.08 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.08 (12) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.00/21.08 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.08 (13) ~ (e3 = e1)
% 142.00/21.08
% 142.00/21.08 Begin of proof
% 142.00/21.08 |
% 142.00/21.08 | BETA: splitting (7) gives:
% 142.00/21.08 |
% 142.00/21.08 | Case 1:
% 142.00/21.08 | |
% 142.00/21.08 | | (14) all_57_14 = e3 & op(e0, e1) = e3
% 142.00/21.08 | |
% 142.00/21.08 | | REF_CLOSE: (1), (4), (14) are inconsistent by sub-proof #777.
% 142.00/21.08 | |
% 142.00/21.08 | Case 2:
% 142.00/21.08 | |
% 142.00/21.08 | | (15) all_57_15 = e3 & op(e0, e0) = e3
% 142.00/21.08 | |
% 142.00/21.08 | | ALPHA: (15) implies:
% 142.00/21.08 | | (16) op(e0, e0) = e3
% 142.00/21.08 | |
% 142.00/21.08 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13), (16)
% 142.00/21.08 | | are inconsistent by sub-proof #687.
% 142.00/21.08 | |
% 142.00/21.08 | End of split
% 142.00/21.08 |
% 142.00/21.08 End of proof
% 142.00/21.08
% 142.00/21.08 Sub-proof #502 shows that the following formulas are inconsistent:
% 142.00/21.08 ----------------------------------------------------------------
% 142.00/21.08 (1) all_57_14 = e0
% 142.00/21.08 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.00/21.08 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.00/21.08 (3) ~ (e2 = e1)
% 142.00/21.08 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.08 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.08 (5) ~ (e3 = e0)
% 142.00/21.08 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.00/21.08 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.08 (7) ~ (e1 = e0)
% 142.00/21.08 (8) ~ (e3 = e2)
% 142.00/21.08 (9) op(e0, e0) = e2
% 142.00/21.08 (10) all_57_6 = e1
% 142.00/21.08 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.08 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.08 (12) ~ (e3 = e1)
% 142.00/21.08 (13) all_57_13 = e3
% 142.00/21.08 (14) all_57_0 = e0
% 142.00/21.08 (15) all_57_2 = e2
% 142.00/21.08 (16) all_57_12 = e1
% 142.00/21.08
% 142.00/21.08 Begin of proof
% 142.00/21.08 |
% 142.00/21.08 | BETA: splitting (6) gives:
% 142.00/21.08 |
% 142.00/21.08 | Case 1:
% 142.00/21.08 | |
% 142.00/21.08 | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 142.00/21.08 | | e3)
% 142.00/21.08 | |
% 142.00/21.08 | | BETA: splitting (17) gives:
% 142.00/21.08 | |
% 142.00/21.08 | | Case 1:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (18) all_57_0 = e3 & op(e3, e3) = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (5), (14), (18) are inconsistent by sub-proof #1108.
% 142.00/21.08 | | |
% 142.00/21.08 | | Case 2:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (19) all_57_2 = e3 & op(e2, e3) = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | ALPHA: (19) implies:
% 142.00/21.08 | | | (20) all_57_2 = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | COMBINE_EQS: (15), (20) imply:
% 142.00/21.08 | | | (21) e3 = e2
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (21)
% 142.00/21.08 | | | are inconsistent by sub-proof #925.
% 142.00/21.08 | | |
% 142.00/21.08 | | End of split
% 142.00/21.08 | |
% 142.00/21.08 | Case 2:
% 142.00/21.08 | |
% 142.00/21.08 | | (22) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.00/21.08 | | e3)
% 142.00/21.08 | |
% 142.00/21.08 | | BETA: splitting (22) gives:
% 142.00/21.08 | |
% 142.00/21.08 | | Case 1:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (23) all_57_6 = e3 & op(e1, e3) = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (10), (12), (23) are inconsistent by sub-proof #1093.
% 142.00/21.08 | | |
% 142.00/21.08 | | Case 2:
% 142.00/21.08 | | |
% 142.00/21.08 | | | (24) all_57_12 = e3 & op(e0, e3) = e3
% 142.00/21.08 | | |
% 142.00/21.08 | | | REF_CLOSE: (12), (16), (24) are inconsistent by sub-proof #798.
% 142.00/21.08 | | |
% 142.00/21.08 | | End of split
% 142.00/21.08 | |
% 142.00/21.08 | End of split
% 142.00/21.08 |
% 142.00/21.08 End of proof
% 142.00/21.08
% 142.00/21.08 Sub-proof #503 shows that the following formulas are inconsistent:
% 142.00/21.08 ----------------------------------------------------------------
% 142.00/21.08 (1) all_57_4 = e2
% 142.00/21.08 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 142.00/21.08 (3) all_57_5 = e1
% 142.00/21.08 (4) ~ (e3 = e2)
% 142.00/21.08 (5) ~ (e3 = e1)
% 142.00/21.08
% 142.00/21.08 Begin of proof
% 142.00/21.08 |
% 142.00/21.08 | BETA: splitting (2) gives:
% 142.00/21.08 |
% 142.00/21.08 | Case 1:
% 142.00/21.08 | |
% 142.00/21.08 | | (6) all_57_4 = e3 & op(e3, e1) = e3
% 142.00/21.08 | |
% 142.00/21.08 | | ALPHA: (6) implies:
% 142.00/21.08 | | (7) all_57_4 = e3
% 142.00/21.08 | |
% 142.00/21.08 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #821.
% 142.00/21.08 | |
% 142.00/21.08 | Case 2:
% 142.00/21.08 | |
% 142.00/21.08 | | (8) all_57_5 = e3 & op(e2, e1) = e3
% 142.00/21.08 | |
% 142.00/21.08 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #504.
% 142.00/21.08 | |
% 142.00/21.08 | End of split
% 142.00/21.08 |
% 142.00/21.08 End of proof
% 142.00/21.08
% 142.00/21.08 Sub-proof #504 shows that the following formulas are inconsistent:
% 142.00/21.08 ----------------------------------------------------------------
% 142.00/21.08 (1) all_57_5 = e3 & op(e2, e1) = e3
% 142.00/21.08 (2) all_57_5 = e1
% 142.00/21.08 (3) ~ (e3 = e1)
% 142.00/21.08
% 142.00/21.08 Begin of proof
% 142.00/21.08 |
% 142.00/21.08 | ALPHA: (1) implies:
% 142.00/21.09 | (4) all_57_5 = e3
% 142.00/21.09 |
% 142.00/21.09 | COMBINE_EQS: (2), (4) imply:
% 142.00/21.09 | (5) e3 = e1
% 142.00/21.09 |
% 142.00/21.09 | REDUCE: (3), (5) imply:
% 142.00/21.09 | (6) $false
% 142.00/21.09 |
% 142.00/21.09 | CLOSE: (6) is inconsistent.
% 142.00/21.09 |
% 142.00/21.09 End of proof
% 142.00/21.09
% 142.00/21.09 Sub-proof #505 shows that the following formulas are inconsistent:
% 142.00/21.09 ----------------------------------------------------------------
% 142.00/21.09 (1) all_57_14 = e0
% 142.00/21.09 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.09 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.00/21.09 (3) all_57_11 = e0
% 142.00/21.09 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.09 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.00/21.09 (5) op(e0, e0) = e3
% 142.00/21.09 (6) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) = all_16_1
% 142.00/21.09 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0) =
% 142.00/21.09 all_16_1 & $i(all_16_1))
% 142.00/21.09 (7) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) = all_18_1
% 142.00/21.09 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0) =
% 142.00/21.09 all_18_1 & $i(all_18_1))
% 142.00/21.09 (8) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.09 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.09 (9) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.00/21.09 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.09 (10) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.00/21.09 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.09 (11) ~ (e3 = e0)
% 142.00/21.09 (12) op(e1, e1) = e1
% 142.00/21.09 (13) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.09 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.00/21.09 e2)
% 142.00/21.09 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.00/21.09 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.09 (15) ~ (all_56_15 = e2)
% 142.00/21.09 (16) ~ (e1 = e0)
% 142.00/21.09 (17) op(e3, e2) = all_52_4
% 142.00/21.09 (18) ~ (all_56_13 = e2)
% 142.00/21.09 (19) op(e3, e2) = all_56_0
% 142.00/21.09 (20) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.00/21.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.00/21.09 (21) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.00/21.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.00/21.09 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.09 (23) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.00/21.09 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.09 (24) ~ (e3 = e1)
% 142.00/21.09 (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.00/21.09 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.00/21.09 (26) op(e0, e0) = all_56_15
% 142.00/21.09 (27) all_57_0 = e0
% 142.00/21.09 (28) op(e3, e3) = e0
% 142.00/21.09 (29) ~ (all_56_0 = e3)
% 142.00/21.09 (30) op(e1, e1) = all_56_13
% 142.00/21.09 (31) all_57_3 = e0
% 142.00/21.09 (32) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 142.00/21.09 all_56_9 & $i(all_56_9))
% 142.00/21.09 (33) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.00/21.09 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.00/21.09 (34) all_57_8 = e1
% 142.00/21.09
% 142.00/21.09 Begin of proof
% 142.00/21.09 |
% 142.00/21.09 | BETA: splitting (32) gives:
% 142.00/21.09 |
% 142.00/21.09 | Case 1:
% 142.00/21.09 | |
% 142.00/21.09 | | (35) all_56_0 = e3 & op(e3, e2) = e3
% 142.00/21.09 | |
% 142.00/21.09 | | ALPHA: (35) implies:
% 142.00/21.09 | | (36) all_56_0 = e3
% 142.00/21.09 | |
% 142.00/21.09 | | REDUCE: (29), (36) imply:
% 142.00/21.09 | | (37) $false
% 142.00/21.09 | |
% 142.00/21.09 | | CLOSE: (37) is inconsistent.
% 142.00/21.09 | |
% 142.00/21.09 | Case 2:
% 142.00/21.09 | |
% 142.00/21.09 | | (38) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 142.00/21.09 | |
% 142.00/21.09 | | ALPHA: (38) implies:
% 142.00/21.09 | | (39) ~ (all_56_9 = e2)
% 142.00/21.09 | | (40) op(e3, e3) = all_56_9
% 142.00/21.09 | |
% 142.00/21.09 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.00/21.09 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.00/21.09 | | (24), (25), (26), (27), (28), (29), (30), (31), (33), (34), (39),
% 142.00/21.09 | | (40) are inconsistent by sub-proof #510.
% 142.00/21.09 | |
% 142.00/21.09 | End of split
% 142.00/21.09 |
% 142.00/21.09 End of proof
% 142.00/21.09
% 142.00/21.09 Sub-proof #506 shows that the following formulas are inconsistent:
% 142.00/21.09 ----------------------------------------------------------------
% 142.00/21.09 (1) all_57_8 = e3 & op(e1, e1) = e3
% 142.00/21.09 (2) all_57_8 = e1
% 142.00/21.09 (3) ~ (e3 = e1)
% 142.00/21.09
% 142.00/21.09 Begin of proof
% 142.00/21.09 |
% 142.00/21.09 | ALPHA: (1) implies:
% 142.00/21.09 | (4) all_57_8 = e3
% 142.00/21.09 |
% 142.00/21.09 | COMBINE_EQS: (2), (4) imply:
% 142.00/21.09 | (5) e3 = e1
% 142.00/21.09 |
% 142.00/21.09 | REDUCE: (3), (5) imply:
% 142.00/21.09 | (6) $false
% 142.00/21.09 |
% 142.00/21.09 | CLOSE: (6) is inconsistent.
% 142.00/21.09 |
% 142.00/21.09 End of proof
% 142.00/21.09
% 142.00/21.09 Sub-proof #507 shows that the following formulas are inconsistent:
% 142.00/21.09 ----------------------------------------------------------------
% 142.00/21.09 (1) all_57_14 = e0
% 142.00/21.09 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.09 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.00/21.09 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.00/21.09 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.00/21.09 (4) all_57_11 = e0
% 142.00/21.09 (5) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.09 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.00/21.09 (6) ~ (e2 = e1)
% 142.00/21.09 (7) op(e0, e0) = e3
% 142.00/21.09 (8) all_57_5 = e1
% 142.00/21.09 (9) ~ (all_52_7 = e0)
% 142.00/21.09 (10) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 142.00/21.09 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 142.00/21.09 e0) = all_16_1 & $i(all_16_1))
% 142.00/21.09 (11) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 142.00/21.09 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2,
% 142.00/21.09 e0) = all_18_1 & $i(all_18_1))
% 142.00/21.09 (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.00/21.09 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.00/21.09 e1)
% 142.00/21.09 (13) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 142.00/21.09 all_56_0 & $i(all_56_0))
% 142.00/21.09 (14) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.00/21.09 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.09 (15) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.00/21.09 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.09 (16) ~ (e3 = e0)
% 142.00/21.09 (17) op(e1, e1) = e1
% 142.00/21.09 (18) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.09 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.00/21.09 e2)
% 142.00/21.09 (19) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.00/21.09 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.00/21.09 (20) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 142.00/21.09 all_56_15 & $i(all_56_15))
% 142.00/21.09 (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.00/21.09 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.09 (22) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.00/21.09 | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.00/21.09 (23) ~ (e1 = e0)
% 142.00/21.09 (24) op(e3, e2) = all_52_4
% 142.00/21.09 (25) ~ (e2 = e0)
% 142.00/21.09 (26) ~ (e3 = e2)
% 142.00/21.09 (27) ~ (all_56_7 = e1)
% 142.00/21.09 (28) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.00/21.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.00/21.09 (29) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.00/21.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.00/21.09 (30) (all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 142.00/21.09 all_56_13 & $i(all_56_13))
% 142.00/21.09 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.09 (32) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.00/21.09 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.09 (33) ~ (e3 = e1)
% 142.00/21.09 (34) op(e0, e2) = all_52_7
% 142.00/21.09 (35) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.00/21.09 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.00/21.09 (36) all_57_0 = e0
% 142.00/21.09 (37) op(e3, e3) = e0
% 142.00/21.09 (38) all_57_3 = e0
% 142.00/21.09 (39) (all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 142.00/21.09 all_56_9 & $i(all_56_9))
% 142.00/21.09 (40) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.00/21.09 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.00/21.09
% 142.00/21.09 Begin of proof
% 142.00/21.09 |
% 142.00/21.09 | BETA: splitting (29) gives:
% 142.00/21.09 |
% 142.00/21.09 | Case 1:
% 142.00/21.09 | |
% 142.00/21.09 | | (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 142.00/21.09 | | e2)
% 142.00/21.09 | |
% 142.00/21.09 | | BETA: splitting (41) gives:
% 142.00/21.09 | |
% 142.00/21.09 | | Case 1:
% 142.00/21.09 | | |
% 142.00/21.09 | | | (42) all_57_4 = e2 & op(e3, e1) = e2
% 142.00/21.09 | | |
% 142.00/21.09 | | | ALPHA: (42) implies:
% 142.00/21.09 | | | (43) all_57_4 = e2
% 142.00/21.09 | | |
% 142.00/21.09 | | | BETA: splitting (20) gives:
% 142.00/21.09 | | |
% 142.00/21.09 | | | Case 1:
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | (44) all_56_12 = e0 & op(e0, e2) = e0
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | ALPHA: (44) implies:
% 142.00/21.09 | | | | (45) op(e0, e2) = e0
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | REF_CLOSE: (9), (31), (34), (45) are inconsistent by sub-proof #977.
% 142.00/21.09 | | | |
% 142.00/21.09 | | | Case 2:
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | (46) ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | ALPHA: (46) implies:
% 142.00/21.09 | | | | (47) ~ (all_56_15 = e2)
% 142.00/21.09 | | | | (48) op(e0, e0) = all_56_15
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | BETA: splitting (3) gives:
% 142.00/21.09 | | | |
% 142.00/21.09 | | | | Case 1:
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | | (49) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2,
% 142.00/21.09 | | | | | e1) = e3)
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | | REF_CLOSE: (8), (26), (33), (43), (49) are inconsistent by sub-proof
% 142.00/21.09 | | | | | #820.
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | Case 2:
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | | (50) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0,
% 142.00/21.09 | | | | | e1) = e3)
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | | BETA: splitting (50) gives:
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | | Case 1:
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | (51) all_57_8 = e3 & op(e1, e1) = e3
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | ALPHA: (51) implies:
% 142.00/21.09 | | | | | | (52) all_57_8 = e3
% 142.00/21.09 | | | | | | (53) op(e1, e1) = e3
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | BETA: splitting (30) gives:
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | Case 1:
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | (54) all_56_7 = e1 & op(e1, e2) = e1
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | ALPHA: (54) implies:
% 142.00/21.09 | | | | | | | (55) all_56_7 = e1
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | REDUCE: (27), (55) imply:
% 142.00/21.09 | | | | | | | (56) $false
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | CLOSE: (56) is inconsistent.
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | Case 2:
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | (57) ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.00/21.09 | | | | | | | $i(all_56_13)
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | ALPHA: (57) implies:
% 142.00/21.09 | | | | | | | (58) ~ (all_56_13 = e2)
% 142.00/21.09 | | | | | | | (59) op(e1, e1) = all_56_13
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | BETA: splitting (13) gives:
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | (60) all_56_9 = e2 & op(e3, e3) = e2
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | ALPHA: (60) implies:
% 142.00/21.09 | | | | | | | | (61) op(e3, e3) = e2
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | REF_CLOSE: (25), (31), (37), (61) are inconsistent by sub-proof
% 142.00/21.09 | | | | | | | | #880.
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | (62) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.00/21.09 | | | | | | | | $i(all_56_0)
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | ALPHA: (62) implies:
% 142.00/21.09 | | | | | | | | (63) ~ (all_56_0 = e3)
% 142.00/21.09 | | | | | | | | (64) op(e3, e2) = all_56_0
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | BETA: splitting (39) gives:
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | (65) all_56_0 = e3 & op(e3, e2) = e3
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | ALPHA: (65) implies:
% 142.00/21.09 | | | | | | | | | (66) all_56_0 = e3
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | REDUCE: (63), (66) imply:
% 142.00/21.09 | | | | | | | | | (67) $false
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | CLOSE: (67) is inconsistent.
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | (68) ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 142.00/21.09 | | | | | | | | | $i(all_56_9)
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | ALPHA: (68) implies:
% 142.00/21.09 | | | | | | | | | (69) ~ (all_56_9 = e2)
% 142.00/21.09 | | | | | | | | | (70) op(e3, e3) = all_56_9
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | BETA: splitting (35) gives:
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | (71) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 142.00/21.09 | | | | | | | | | | op(e3, e2) = e3)
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | BETA: splitting (71) gives:
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | (72) all_57_0 = e3 & op(e3, e3) = e3
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | REF_CLOSE: (16), (36), (72) are inconsistent by sub-proof
% 142.00/21.09 | | | | | | | | | | | #1108.
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | (73) all_57_1 = e3 & op(e3, e2) = e3
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | ALPHA: (73) implies:
% 142.00/21.09 | | | | | | | | | | | (74) all_57_1 = e3
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | BETA: splitting (19) gives:
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | (75) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.00/21.09 | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | BETA: splitting (75) gives:
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | (76) all_57_0 = e1 & op(e3, e3) = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | ALPHA: (76) implies:
% 142.00/21.09 | | | | | | | | | | | | | (77) all_57_0 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | COMBINE_EQS: (36), (77) imply:
% 142.00/21.09 | | | | | | | | | | | | | (78) e1 = e0
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | SIMP: (78) implies:
% 142.00/21.09 | | | | | | | | | | | | | (79) e1 = e0
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | REDUCE: (23), (79) imply:
% 142.00/21.09 | | | | | | | | | | | | | (80) $false
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | CLOSE: (80) is inconsistent.
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | (81) all_57_1 = e1 & op(e3, e2) = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | ALPHA: (81) implies:
% 142.00/21.09 | | | | | | | | | | | | | (82) all_57_1 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | COMBINE_EQS: (74), (82) imply:
% 142.00/21.09 | | | | | | | | | | | | | (83) e3 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | COMBINE_EQS: (52), (83) imply:
% 142.00/21.09 | | | | | | | | | | | | | (84) all_57_8 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (10), (11), (12), (14),
% 142.00/21.09 | | | | | | | | | | | | | (15), (16), (17), (18), (21), (23), (24), (28),
% 142.00/21.09 | | | | | | | | | | | | | (29), (31), (32), (33), (35), (36), (37), (38),
% 142.00/21.09 | | | | | | | | | | | | | (40), (47), (48), (58), (59), (63), (64), (69),
% 142.00/21.09 | | | | | | | | | | | | | (70), (84) are inconsistent by sub-proof #510.
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | End of split
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | (85) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.00/21.09 | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | BETA: splitting (85) gives:
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | (86) all_57_4 = e1 & op(e3, e1) = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | ALPHA: (86) implies:
% 142.00/21.09 | | | | | | | | | | | | | (87) all_57_4 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | REF_CLOSE: (6), (43), (87) are inconsistent by sub-proof
% 142.00/21.09 | | | | | | | | | | | | | #1088.
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | GROUND_INST: instantiating (31) with e3, all_56_13, e1, e1,
% 142.00/21.09 | | | | | | | | | | | | | simplifying with (53), (59) gives:
% 142.00/21.09 | | | | | | | | | | | | | (88) all_56_13 = e3
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | GROUND_INST: instantiating (31) with e1, all_56_13, e1, e1,
% 142.00/21.09 | | | | | | | | | | | | | simplifying with (17), (59) gives:
% 142.00/21.09 | | | | | | | | | | | | | (89) all_56_13 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | COMBINE_EQS: (88), (89) imply:
% 142.00/21.09 | | | | | | | | | | | | | (90) e3 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | COMBINE_EQS: (52), (90) imply:
% 142.00/21.09 | | | | | | | | | | | | | (91) all_57_8 = e1
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (7), (10), (11), (12), (14),
% 142.00/21.09 | | | | | | | | | | | | | (15), (16), (17), (18), (21), (23), (24), (28),
% 142.00/21.09 | | | | | | | | | | | | | (29), (31), (32), (33), (35), (36), (37), (38),
% 142.00/21.09 | | | | | | | | | | | | | (40), (47), (48), (58), (59), (63), (64), (69),
% 142.00/21.09 | | | | | | | | | | | | | (70), (91) are inconsistent by sub-proof #510.
% 142.00/21.09 | | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | | End of split
% 142.00/21.09 | | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | End of split
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | End of split
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | (92) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 142.00/21.09 | | | | | | | | | | op(e3, e0) = e3)
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | BETA: splitting (92) gives:
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | Case 1:
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | (93) all_57_4 = e3 & op(e3, e1) = e3
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | ALPHA: (93) implies:
% 142.00/21.09 | | | | | | | | | | | (94) all_57_4 = e3
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | REF_CLOSE: (26), (43), (94) are inconsistent by sub-proof
% 142.00/21.09 | | | | | | | | | | | #821.
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | Case 2:
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | (95) all_57_9 = e3 & op(e3, e0) = e3
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | | REF_CLOSE: (4), (6), (7), (14), (23), (25), (26), (31), (32),
% 142.00/21.09 | | | | | | | | | | | (33), (95) are inconsistent by sub-proof #595.
% 142.00/21.09 | | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | | End of split
% 142.00/21.09 | | | | | | | | | |
% 142.00/21.09 | | | | | | | | | End of split
% 142.00/21.09 | | | | | | | | |
% 142.00/21.09 | | | | | | | | End of split
% 142.00/21.09 | | | | | | | |
% 142.00/21.09 | | | | | | | End of split
% 142.00/21.09 | | | | | | |
% 142.00/21.09 | | | | | | End of split
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | Case 2:
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | (96) all_57_14 = e3 & op(e0, e1) = e3
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | ALPHA: (96) implies:
% 142.00/21.09 | | | | | | (97) all_57_14 = e3
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | | REF_CLOSE: (6), (7), (9), (12), (16), (18), (22), (23), (25), (26),
% 142.00/21.09 | | | | | | (31), (33), (34), (97) are inconsistent by sub-proof
% 142.00/21.09 | | | | | | #509.
% 142.00/21.09 | | | | | |
% 142.00/21.09 | | | | | End of split
% 142.00/21.09 | | | | |
% 142.00/21.09 | | | | End of split
% 142.00/21.09 | | | |
% 142.00/21.09 | | | End of split
% 142.00/21.09 | | |
% 142.00/21.09 | | Case 2:
% 142.00/21.09 | | |
% 142.00/21.09 | | | (98) all_57_5 = e2 & op(e2, e1) = e2
% 142.00/21.09 | | |
% 142.00/21.09 | | | ALPHA: (98) implies:
% 142.00/21.09 | | | (99) all_57_5 = e2
% 142.00/21.09 | | |
% 142.00/21.09 | | | REF_CLOSE: (6), (8), (99) are inconsistent by sub-proof #1031.
% 142.00/21.09 | | |
% 142.00/21.09 | | End of split
% 142.00/21.09 | |
% 142.00/21.09 | Case 2:
% 142.00/21.09 | |
% 142.00/21.09 | | (100) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.00/21.09 | | e2)
% 142.00/21.09 | |
% 142.00/21.09 | | REF_CLOSE: (1), (6), (17), (25), (31), (100) are inconsistent by sub-proof
% 142.00/21.09 | | #508.
% 142.00/21.09 | |
% 142.00/21.09 | End of split
% 142.00/21.09 |
% 142.00/21.09 End of proof
% 142.00/21.09
% 142.00/21.09 Sub-proof #508 shows that the following formulas are inconsistent:
% 142.00/21.09 ----------------------------------------------------------------
% 142.00/21.09 (1) all_57_14 = e0
% 142.00/21.09 (2) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.00/21.09 (3) ~ (e2 = e1)
% 142.00/21.09 (4) op(e1, e1) = e1
% 142.00/21.09 (5) ~ (e2 = e0)
% 142.00/21.09 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.09
% 142.00/21.09 Begin of proof
% 142.00/21.09 |
% 142.00/21.09 | BETA: splitting (2) gives:
% 142.00/21.09 |
% 142.00/21.09 | Case 1:
% 142.00/21.09 | |
% 142.00/21.09 | | (7) all_57_8 = e2 & op(e1, e1) = e2
% 142.00/21.09 | |
% 142.00/21.09 | | ALPHA: (7) implies:
% 142.00/21.09 | | (8) op(e1, e1) = e2
% 142.00/21.09 | |
% 142.00/21.09 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #1085.
% 142.00/21.09 | |
% 142.00/21.09 | Case 2:
% 142.00/21.09 | |
% 142.00/21.09 | | (9) all_57_14 = e2 & op(e0, e1) = e2
% 142.00/21.09 | |
% 142.00/21.09 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #968.
% 142.00/21.09 | |
% 142.00/21.09 | End of split
% 142.00/21.09 |
% 142.00/21.09 End of proof
% 142.00/21.09
% 142.00/21.09 Sub-proof #509 shows that the following formulas are inconsistent:
% 142.00/21.09 ----------------------------------------------------------------
% 142.00/21.09 (1) ~ (e2 = e1)
% 142.00/21.09 (2) op(e0, e0) = e3
% 142.00/21.09 (3) ~ (all_52_7 = e0)
% 142.00/21.09 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.09 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.09 (5) ~ (e3 = e0)
% 142.00/21.09 (6) all_57_14 = e3
% 142.00/21.09 (7) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.00/21.09 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.09 (8) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.00/21.09 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.00/21.09 (9) ~ (e1 = e0)
% 142.00/21.09 (10) ~ (e2 = e0)
% 142.00/21.09 (11) ~ (e3 = e2)
% 142.00/21.09 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.09 (13) ~ (e3 = e1)
% 142.00/21.09 (14) op(e0, e2) = all_52_7
% 142.00/21.09
% 142.00/21.09 Begin of proof
% 142.00/21.09 |
% 142.00/21.09 | BETA: splitting (8) gives:
% 142.00/21.09 |
% 142.00/21.09 | Case 1:
% 142.00/21.09 | |
% 142.00/21.09 | | (15) all_57_12 = e0 & op(e0, e3) = e0
% 142.00/21.09 | |
% 142.00/21.09 | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (11), (12), (13), (15) are
% 142.00/21.09 | | inconsistent by sub-proof #702.
% 142.00/21.09 | |
% 142.00/21.09 | Case 2:
% 142.00/21.09 | |
% 142.00/21.09 | | (16) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.00/21.09 | | e0)
% 142.00/21.09 | |
% 142.00/21.09 | | BETA: splitting (16) gives:
% 142.00/21.09 | |
% 142.00/21.09 | | Case 1:
% 142.00/21.09 | | |
% 142.00/21.09 | | | (17) all_57_13 = e0 & op(e0, e2) = e0
% 142.00/21.09 | | |
% 142.00/21.09 | | | ALPHA: (17) implies:
% 142.00/21.09 | | | (18) op(e0, e2) = e0
% 142.00/21.09 | | |
% 142.00/21.09 | | | REF_CLOSE: (3), (12), (14), (18) are inconsistent by sub-proof #977.
% 142.00/21.09 | | |
% 142.00/21.09 | | Case 2:
% 142.00/21.09 | | |
% 142.00/21.09 | | | (19) all_57_14 = e0 & op(e0, e1) = e0
% 142.00/21.09 | | |
% 142.00/21.09 | | | ALPHA: (19) implies:
% 142.00/21.09 | | | (20) all_57_14 = e0
% 142.00/21.09 | | |
% 142.00/21.09 | | | REF_CLOSE: (5), (6), (20) are inconsistent by sub-proof #1067.
% 142.00/21.09 | | |
% 142.00/21.09 | | End of split
% 142.00/21.09 | |
% 142.00/21.09 | End of split
% 142.00/21.09 |
% 142.00/21.09 End of proof
% 142.00/21.09
% 142.00/21.09 Sub-proof #510 shows that the following formulas are inconsistent:
% 142.00/21.09 ----------------------------------------------------------------
% 142.00/21.09 (1) all_57_14 = e0
% 142.00/21.09 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.09 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.00/21.09 (3) all_57_11 = e0
% 142.00/21.09 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.09 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.00/21.09 (5) op(e0, e0) = e3
% 142.00/21.09 (6) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) = all_16_1
% 142.00/21.09 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0) =
% 142.00/21.09 all_16_1 & $i(all_16_1))
% 142.00/21.09 (7) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) = all_18_1
% 142.00/21.09 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0) =
% 142.00/21.09 all_18_1 & $i(all_18_1))
% 142.00/21.09 (8) ~ (all_56_9 = e2)
% 142.00/21.09 (9) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.09 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.09 (10) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.00/21.09 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.09 (11) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.00/21.09 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.09 (12) ~ (e3 = e0)
% 142.00/21.09 (13) op(e1, e1) = e1
% 142.00/21.09 (14) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.09 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.00/21.09 e2)
% 142.00/21.09 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.00/21.09 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.09 (16) ~ (all_56_15 = e2)
% 142.00/21.09 (17) ~ (e1 = e0)
% 142.00/21.09 (18) op(e3, e2) = all_52_4
% 142.00/21.09 (19) ~ (all_56_13 = e2)
% 142.00/21.09 (20) op(e3, e2) = all_56_0
% 142.00/21.09 (21) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.00/21.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.00/21.09 (22) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.00/21.09 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.00/21.09 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.09 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.09 (24) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.00/21.09 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.09 (25) ~ (e3 = e1)
% 142.00/21.09 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.00/21.09 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.00/21.09 (27) op(e0, e0) = all_56_15
% 142.00/21.09 (28) all_57_0 = e0
% 142.00/21.09 (29) op(e3, e3) = e0
% 142.00/21.09 (30) ~ (all_56_0 = e3)
% 142.00/21.09 (31) op(e1, e1) = all_56_13
% 142.00/21.09 (32) all_57_3 = e0
% 142.00/21.09 (33) op(e3, e3) = all_56_9
% 142.00/21.10 (34) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.00/21.10 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.00/21.10 (35) all_57_8 = e1
% 142.00/21.10
% 142.00/21.10 Begin of proof
% 142.00/21.10 |
% 142.00/21.10 | GROUND_INST: instantiating (23) with e3, all_56_15, e0, e0, simplifying with
% 142.00/21.10 | (5), (27) gives:
% 142.00/21.10 | (36) all_56_15 = e3
% 142.00/21.10 |
% 142.00/21.10 | GROUND_INST: instantiating (23) with e1, all_56_13, e1, e1, simplifying with
% 142.00/21.10 | (13), (31) gives:
% 142.00/21.10 | (37) all_56_13 = e1
% 142.00/21.10 |
% 142.00/21.10 | GROUND_INST: instantiating (23) with all_52_4, all_56_0, e2, e3, simplifying
% 142.00/21.10 | with (18), (20) gives:
% 142.00/21.10 | (38) all_56_0 = all_52_4
% 142.00/21.10 |
% 142.00/21.10 | GROUND_INST: instantiating (23) with e0, all_56_9, e3, e3, simplifying with
% 142.00/21.10 | (29), (33) gives:
% 142.00/21.10 | (39) all_56_9 = e0
% 142.00/21.10 |
% 142.00/21.10 | REDUCE: (30), (38) imply:
% 142.00/21.10 | (40) ~ (all_52_4 = e3)
% 142.00/21.10 |
% 142.00/21.10 | REDUCE: (8), (39) imply:
% 142.00/21.10 | (41) ~ (e2 = e0)
% 142.00/21.10 |
% 142.00/21.10 | SIMP: (41) implies:
% 142.00/21.10 | (42) ~ (e2 = e0)
% 142.00/21.10 |
% 142.00/21.10 | REDUCE: (19), (37) imply:
% 142.00/21.10 | (43) ~ (e2 = e1)
% 142.00/21.10 |
% 142.00/21.10 | SIMP: (43) implies:
% 142.00/21.10 | (44) ~ (e2 = e1)
% 142.00/21.10 |
% 142.00/21.10 | REDUCE: (16), (36) imply:
% 142.00/21.10 | (45) ~ (e3 = e2)
% 142.00/21.10 |
% 142.00/21.10 | BETA: splitting (34) gives:
% 142.00/21.10 |
% 142.00/21.10 | Case 1:
% 142.00/21.10 | |
% 142.00/21.10 | | (46) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 142.00/21.10 | | e3)
% 142.00/21.10 | |
% 142.00/21.10 | | BETA: splitting (46) gives:
% 142.00/21.10 | |
% 142.00/21.10 | | Case 1:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (47) all_57_1 = e3 & op(e3, e2) = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | ALPHA: (47) implies:
% 142.00/21.10 | | | (48) op(e3, e2) = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (18), (23), (40), (48) are inconsistent by sub-proof #1107.
% 142.00/21.10 | | |
% 142.00/21.10 | | Case 2:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (49) all_57_3 = e3 & op(e2, e2) = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (12), (32), (49) are inconsistent by sub-proof #517.
% 142.00/21.10 | | |
% 142.00/21.10 | | End of split
% 142.00/21.10 | |
% 142.00/21.10 | Case 2:
% 142.00/21.10 | |
% 142.00/21.10 | | (50) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 142.00/21.10 | | e3)
% 142.00/21.10 | |
% 142.00/21.10 | | BETA: splitting (50) gives:
% 142.00/21.10 | |
% 142.00/21.10 | | Case 1:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (51) all_57_7 = e3 & op(e1, e2) = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | ALPHA: (51) implies:
% 142.00/21.10 | | | (52) all_57_7 = e3
% 142.00/21.10 | | | (53) op(e1, e2) = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14),
% 142.00/21.10 | | | (15), (17), (21), (22), (23), (24), (25), (26), (28), (32),
% 142.00/21.10 | | | (35), (42), (44), (45), (52), (53) are inconsistent by
% 142.00/21.10 | | | sub-proof #511.
% 142.00/21.10 | | |
% 142.00/21.10 | | Case 2:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (54) all_57_13 = e3 & op(e0, e2) = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | ALPHA: (54) implies:
% 142.00/21.10 | | | (55) all_57_13 = e3
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (1), (5), (9), (14), (17), (23), (25), (42), (44), (45), (55)
% 142.00/21.10 | | | are inconsistent by sub-proof #666.
% 142.00/21.10 | | |
% 142.00/21.10 | | End of split
% 142.00/21.10 | |
% 142.00/21.10 | End of split
% 142.00/21.10 |
% 142.00/21.10 End of proof
% 142.00/21.10
% 142.00/21.10 Sub-proof #511 shows that the following formulas are inconsistent:
% 142.00/21.10 ----------------------------------------------------------------
% 142.00/21.10 (1) all_57_14 = e0
% 142.00/21.10 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.10 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.00/21.10 (3) all_57_11 = e0
% 142.00/21.10 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.10 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.00/21.10 (5) ~ (e2 = e1)
% 142.00/21.10 (6) op(e0, e0) = e3
% 142.00/21.10 (7) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) = all_16_1
% 142.00/21.10 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2, e0) =
% 142.00/21.10 all_16_1 & $i(all_16_1))
% 142.00/21.10 (8) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) = all_18_1
% 142.00/21.10 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2, e0) =
% 142.00/21.10 all_18_1 & $i(all_18_1))
% 142.00/21.10 (9) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.10 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.10 (10) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.00/21.10 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.10 (11) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.00/21.10 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.10 (12) ~ (e3 = e0)
% 142.00/21.10 (13) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.10 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.00/21.10 e2)
% 142.00/21.10 (14) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.00/21.10 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.10 (15) ~ (e1 = e0)
% 142.00/21.10 (16) ~ (e2 = e0)
% 142.00/21.10 (17) ~ (e3 = e2)
% 142.00/21.10 (18) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.00/21.10 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.00/21.10 (19) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.00/21.10 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.00/21.10 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.10 (21) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.00/21.10 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.10 (22) ~ (e3 = e1)
% 142.00/21.10 (23) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.00/21.10 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.00/21.10 (24) op(e1, e2) = e3
% 142.00/21.10 (25) all_57_0 = e0
% 142.00/21.10 (26) all_57_7 = e3
% 142.00/21.10 (27) all_57_3 = e0
% 142.00/21.10 (28) all_57_8 = e1
% 142.00/21.10
% 142.00/21.10 Begin of proof
% 142.00/21.10 |
% 142.00/21.10 | BETA: splitting (18) gives:
% 142.00/21.10 |
% 142.00/21.10 | Case 1:
% 142.00/21.10 | |
% 142.00/21.10 | | (29) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) =
% 142.00/21.10 | | e2)
% 142.00/21.10 | |
% 142.00/21.10 | | BETA: splitting (29) gives:
% 142.00/21.10 | |
% 142.00/21.10 | | Case 1:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (30) all_57_6 = e2 & op(e1, e3) = e2
% 142.00/21.10 | | |
% 142.00/21.10 | | | ALPHA: (30) implies:
% 142.00/21.10 | | | (31) all_57_6 = e2
% 142.00/21.10 | | |
% 142.00/21.10 | | | BETA: splitting (14) gives:
% 142.00/21.10 | | |
% 142.00/21.10 | | | Case 1:
% 142.00/21.10 | | | |
% 142.00/21.10 | | | | (32) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 142.00/21.10 | | | | = e3)
% 142.00/21.10 | | | |
% 142.00/21.10 | | | | BETA: splitting (32) gives:
% 142.00/21.10 | | | |
% 142.00/21.10 | | | | Case 1:
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | | (33) all_57_0 = e3 & op(e3, e3) = e3
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | | REF_CLOSE: (12), (25), (33) are inconsistent by sub-proof #1108.
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | Case 2:
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | | (34) all_57_2 = e3 & op(e2, e3) = e3
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | | ALPHA: (34) implies:
% 142.00/21.10 | | | | | (35) all_57_2 = e3
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | | BETA: splitting (23) gives:
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | | Case 1:
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | | (36) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 142.00/21.10 | | | | | | e2) = e3)
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | | REF_CLOSE: (2), (5), (11), (12), (15), (16), (17), (22), (25), (26),
% 142.00/21.10 | | | | | | (27), (36) are inconsistent by sub-proof #514.
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | Case 2:
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | | (37) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 142.00/21.10 | | | | | | e0) = e3)
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | | BETA: splitting (37) gives:
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | | Case 1:
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | | (38) all_57_4 = e3 & op(e3, e1) = e3
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | | ALPHA: (38) implies:
% 142.00/21.10 | | | | | | | (39) all_57_4 = e3
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | | BETA: splitting (4) gives:
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | | Case 1:
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | | (40) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 &
% 142.00/21.10 | | | | | | | | op(e2, e2) = e1)
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | | BETA: splitting (40) gives:
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | | Case 1:
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | (41) all_57_2 = e1 & op(e2, e3) = e1
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | REF_CLOSE: (22), (35), (41) are inconsistent by sub-proof
% 142.00/21.10 | | | | | | | | | #939.
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | Case 2:
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | (42) all_57_3 = e1 & op(e2, e2) = e1
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | REF_CLOSE: (15), (27), (42) are inconsistent by sub-proof
% 142.00/21.10 | | | | | | | | | #513.
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | End of split
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | Case 2:
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | | (43) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 &
% 142.00/21.10 | | | | | | | | op(e2, e0) = e1)
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | | BETA: splitting (43) gives:
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | | Case 1:
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | (44) all_57_5 = e1 & op(e2, e1) = e1
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | ALPHA: (44) implies:
% 142.00/21.10 | | | | | | | | | (45) all_57_5 = e1
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | REF_CLOSE: (1), (5), (16), (17), (19), (28), (39), (45) are
% 142.00/21.10 | | | | | | | | | inconsistent by sub-proof #870.
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | Case 2:
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | (46) all_57_10 = e1 & op(e2, e0) = e1
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | ALPHA: (46) implies:
% 142.00/21.10 | | | | | | | | | (47) op(e2, e0) = e1
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | | REF_CLOSE: (7), (8), (20), (24), (47) are inconsistent by
% 142.00/21.10 | | | | | | | | | sub-proof #1020.
% 142.00/21.10 | | | | | | | | |
% 142.00/21.10 | | | | | | | | End of split
% 142.00/21.10 | | | | | | | |
% 142.00/21.10 | | | | | | | End of split
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | Case 2:
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | | (48) all_57_9 = e3 & op(e3, e0) = e3
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | | REF_CLOSE: (3), (5), (6), (10), (15), (16), (17), (20), (21),
% 142.00/21.10 | | | | | | | (22), (48) are inconsistent by sub-proof #595.
% 142.00/21.10 | | | | | | |
% 142.00/21.10 | | | | | | End of split
% 142.00/21.10 | | | | | |
% 142.00/21.10 | | | | | End of split
% 142.00/21.10 | | | | |
% 142.00/21.10 | | | | End of split
% 142.00/21.10 | | | |
% 142.00/21.10 | | | Case 2:
% 142.00/21.10 | | | |
% 142.00/21.10 | | | | (49) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 142.00/21.10 | | | | = e3)
% 142.00/21.10 | | | |
% 142.00/21.10 | | | | REF_CLOSE: (1), (5), (6), (9), (13), (15), (16), (17), (20), (22), (31),
% 142.00/21.10 | | | | (49) are inconsistent by sub-proof #512.
% 142.00/21.10 | | | |
% 142.00/21.10 | | | End of split
% 142.00/21.10 | | |
% 142.00/21.10 | | Case 2:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (50) all_57_7 = e2 & op(e1, e2) = e2
% 142.00/21.10 | | |
% 142.00/21.10 | | | ALPHA: (50) implies:
% 142.00/21.10 | | | (51) all_57_7 = e2
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (17), (26), (51) are inconsistent by sub-proof #1098.
% 142.00/21.10 | | |
% 142.00/21.10 | | End of split
% 142.00/21.10 | |
% 142.00/21.10 | Case 2:
% 142.00/21.10 | |
% 142.00/21.10 | | (52) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) =
% 142.00/21.10 | | e2)
% 142.00/21.10 | |
% 142.00/21.10 | | BETA: splitting (52) gives:
% 142.00/21.10 | |
% 142.00/21.10 | | Case 1:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (53) all_57_8 = e2 & op(e1, e1) = e2
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (5), (28), (53) are inconsistent by sub-proof #871.
% 142.00/21.10 | | |
% 142.00/21.10 | | Case 2:
% 142.00/21.10 | | |
% 142.00/21.10 | | | (54) all_57_11 = e2 & op(e1, e0) = e2
% 142.00/21.10 | | |
% 142.00/21.10 | | | REF_CLOSE: (3), (16), (54) are inconsistent by sub-proof #1083.
% 142.00/21.10 | | |
% 142.00/21.10 | | End of split
% 142.00/21.10 | |
% 142.00/21.10 | End of split
% 142.00/21.10 |
% 142.00/21.10 End of proof
% 142.00/21.10
% 142.00/21.10 Sub-proof #512 shows that the following formulas are inconsistent:
% 142.00/21.10 ----------------------------------------------------------------
% 142.00/21.10 (1) all_57_14 = e0
% 142.00/21.10 (2) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.00/21.10 (3) ~ (e2 = e1)
% 142.00/21.10 (4) op(e0, e0) = e3
% 142.00/21.10 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.00/21.10 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.00/21.10 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.00/21.10 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.00/21.10 (7) ~ (e1 = e0)
% 142.00/21.10 (8) ~ (e2 = e0)
% 142.00/21.10 (9) all_57_6 = e2
% 142.00/21.10 (10) ~ (e3 = e2)
% 142.00/21.10 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.00/21.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.00/21.10 (12) ~ (e3 = e1)
% 142.00/21.10
% 142.00/21.10 Begin of proof
% 142.00/21.10 |
% 142.00/21.10 | BETA: splitting (2) gives:
% 142.00/21.10 |
% 142.00/21.10 | Case 1:
% 142.00/21.10 | |
% 142.00/21.10 | | (13) all_57_6 = e3 & op(e1, e3) = e3
% 142.00/21.10 | |
% 142.00/21.10 | | REF_CLOSE: (9), (10), (13) are inconsistent by sub-proof #916.
% 142.00/21.10 | |
% 142.00/21.10 | Case 2:
% 142.00/21.10 | |
% 142.00/21.10 | | (14) all_57_12 = e3 & op(e0, e3) = e3
% 142.00/21.10 | |
% 142.00/21.10 | | ALPHA: (14) implies:
% 142.00/21.10 | | (15) all_57_12 = e3
% 142.00/21.10 | |
% 142.00/21.10 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (10), (11), (12), (15) are
% 142.00/21.10 | | inconsistent by sub-proof #657.
% 142.00/21.10 | |
% 142.00/21.10 | End of split
% 142.00/21.10 |
% 142.00/21.10 End of proof
% 142.00/21.10
% 142.00/21.10 Sub-proof #513 shows that the following formulas are inconsistent:
% 142.00/21.10 ----------------------------------------------------------------
% 142.00/21.10 (1) all_57_3 = e1 & op(e2, e2) = e1
% 142.00/21.10 (2) all_57_3 = e0
% 142.00/21.10 (3) ~ (e1 = e0)
% 142.00/21.10
% 142.00/21.10 Begin of proof
% 142.00/21.10 |
% 142.00/21.10 | ALPHA: (1) implies:
% 142.00/21.10 | (4) all_57_3 = e1
% 142.00/21.10 |
% 142.00/21.10 | COMBINE_EQS: (2), (4) imply:
% 142.00/21.10 | (5) e1 = e0
% 142.00/21.10 |
% 142.00/21.10 | REDUCE: (3), (5) imply:
% 142.00/21.10 | (6) $false
% 142.00/21.10 |
% 142.00/21.10 | CLOSE: (6) is inconsistent.
% 142.00/21.10 |
% 142.00/21.10 End of proof
% 142.00/21.10
% 142.00/21.10 Sub-proof #514 shows that the following formulas are inconsistent:
% 142.00/21.10 ----------------------------------------------------------------
% 142.00/21.10 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.00/21.10 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.00/21.10 (2) ~ (e2 = e1)
% 142.00/21.10 (3) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.00/21.10 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.00/21.10 (4) ~ (e3 = e0)
% 142.00/21.10 (5) ~ (e1 = e0)
% 142.00/21.10 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 142.00/21.10 (7) ~ (e2 = e0)
% 142.00/21.10 (8) ~ (e3 = e2)
% 142.00/21.10 (9) ~ (e3 = e1)
% 142.00/21.10 (10) all_57_0 = e0
% 142.00/21.10 (11) all_57_7 = e3
% 142.00/21.10 (12) all_57_3 = e0
% 142.00/21.10
% 142.00/21.10 Begin of proof
% 142.00/21.10 |
% 142.00/21.10 | BETA: splitting (6) gives:
% 142.00/21.10 |
% 142.00/21.10 | Case 1:
% 142.00/21.10 | |
% 142.06/21.10 | | (13) all_57_0 = e3 & op(e3, e3) = e3
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (4), (10), (13) are inconsistent by sub-proof #1108.
% 142.06/21.10 | |
% 142.06/21.10 | Case 2:
% 142.06/21.10 | |
% 142.06/21.10 | | (14) all_57_1 = e3 & op(e3, e2) = e3
% 142.06/21.10 | |
% 142.06/21.10 | | ALPHA: (14) implies:
% 142.06/21.10 | | (15) all_57_1 = e3
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (12), (15) are
% 142.06/21.10 | | inconsistent by sub-proof #515.
% 142.06/21.10 | |
% 142.06/21.10 | End of split
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #515 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.06/21.10 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.06/21.10 (2) ~ (e2 = e1)
% 142.06/21.10 (3) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.06/21.10 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.06/21.10 (4) ~ (e1 = e0)
% 142.06/21.10 (5) ~ (e2 = e0)
% 142.06/21.10 (6) ~ (e3 = e2)
% 142.06/21.10 (7) all_57_1 = e3
% 142.06/21.10 (8) ~ (e3 = e1)
% 142.06/21.10 (9) all_57_7 = e3
% 142.06/21.10 (10) all_57_3 = e0
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | BETA: splitting (3) gives:
% 142.06/21.10 |
% 142.06/21.10 | Case 1:
% 142.06/21.10 | |
% 142.06/21.10 | | (11) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 142.06/21.10 | | e2)
% 142.06/21.10 | |
% 142.06/21.10 | | BETA: splitting (11) gives:
% 142.06/21.10 | |
% 142.06/21.10 | | Case 1:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (12) all_57_1 = e2 & op(e3, e2) = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (6), (7), (12) are inconsistent by sub-proof #782.
% 142.06/21.10 | | |
% 142.06/21.10 | | Case 2:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (13) all_57_3 = e2 & op(e2, e2) = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (5), (10), (13) are inconsistent by sub-proof #516.
% 142.06/21.10 | | |
% 142.06/21.10 | | End of split
% 142.06/21.10 | |
% 142.06/21.10 | Case 2:
% 142.06/21.10 | |
% 142.06/21.10 | | (14) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.06/21.10 | | e2)
% 142.06/21.10 | |
% 142.06/21.10 | | BETA: splitting (14) gives:
% 142.06/21.10 | |
% 142.06/21.10 | | Case 1:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (15) all_57_7 = e2 & op(e1, e2) = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | ALPHA: (15) implies:
% 142.06/21.10 | | | (16) all_57_7 = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (6), (9), (16) are inconsistent by sub-proof #1098.
% 142.06/21.10 | | |
% 142.06/21.10 | | Case 2:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (17) all_57_13 = e2 & op(e0, e2) = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | ALPHA: (17) implies:
% 142.06/21.10 | | | (18) all_57_13 = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | BETA: splitting (1) gives:
% 142.06/21.10 | | |
% 142.06/21.10 | | | Case 1:
% 142.06/21.10 | | | |
% 142.06/21.10 | | | | (19) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 142.06/21.10 | | | | = e1)
% 142.06/21.10 | | | |
% 142.06/21.10 | | | | BETA: splitting (19) gives:
% 142.06/21.10 | | | |
% 142.06/21.10 | | | | Case 1:
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | (20) all_57_1 = e1 & op(e3, e2) = e1
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | ALPHA: (20) implies:
% 142.06/21.10 | | | | | (21) all_57_1 = e1
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | COMBINE_EQS: (7), (21) imply:
% 142.06/21.10 | | | | | (22) e3 = e1
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | REDUCE: (8), (22) imply:
% 142.06/21.10 | | | | | (23) $false
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | CLOSE: (23) is inconsistent.
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | Case 2:
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | (24) all_57_3 = e1 & op(e2, e2) = e1
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | ALPHA: (24) implies:
% 142.06/21.10 | | | | | (25) all_57_3 = e1
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | COMBINE_EQS: (10), (25) imply:
% 142.06/21.10 | | | | | (26) e1 = e0
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | SIMP: (26) implies:
% 142.06/21.10 | | | | | (27) e1 = e0
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | REDUCE: (4), (27) imply:
% 142.06/21.10 | | | | | (28) $false
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | | CLOSE: (28) is inconsistent.
% 142.06/21.10 | | | | |
% 142.06/21.10 | | | | End of split
% 142.06/21.10 | | | |
% 142.06/21.10 | | | Case 2:
% 142.06/21.10 | | | |
% 142.06/21.10 | | | | (29) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 142.06/21.10 | | | | = e1)
% 142.06/21.10 | | | |
% 142.06/21.10 | | | | REF_CLOSE: (2), (8), (9), (18), (29) are inconsistent by sub-proof
% 142.06/21.10 | | | | #1056.
% 142.06/21.10 | | | |
% 142.06/21.10 | | | End of split
% 142.06/21.10 | | |
% 142.06/21.10 | | End of split
% 142.06/21.10 | |
% 142.06/21.10 | End of split
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #516 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) all_57_3 = e2 & op(e2, e2) = e2
% 142.06/21.10 (2) all_57_3 = e0
% 142.06/21.10 (3) ~ (e2 = e0)
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | ALPHA: (1) implies:
% 142.06/21.10 | (4) all_57_3 = e2
% 142.06/21.10 |
% 142.06/21.10 | COMBINE_EQS: (2), (4) imply:
% 142.06/21.10 | (5) e2 = e0
% 142.06/21.10 |
% 142.06/21.10 | SIMP: (5) implies:
% 142.06/21.10 | (6) e2 = e0
% 142.06/21.10 |
% 142.06/21.10 | REDUCE: (3), (6) imply:
% 142.06/21.10 | (7) $false
% 142.06/21.10 |
% 142.06/21.10 | CLOSE: (7) is inconsistent.
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #517 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) all_57_3 = e3 & op(e2, e2) = e3
% 142.06/21.10 (2) all_57_3 = e0
% 142.06/21.10 (3) ~ (e3 = e0)
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | ALPHA: (1) implies:
% 142.06/21.10 | (4) all_57_3 = e3
% 142.06/21.10 |
% 142.06/21.10 | COMBINE_EQS: (2), (4) imply:
% 142.06/21.10 | (5) e3 = e0
% 142.06/21.10 |
% 142.06/21.10 | SIMP: (5) implies:
% 142.06/21.10 | (6) e3 = e0
% 142.06/21.10 |
% 142.06/21.10 | REDUCE: (3), (6) imply:
% 142.06/21.10 | (7) $false
% 142.06/21.10 |
% 142.06/21.10 | CLOSE: (7) is inconsistent.
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #518 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) op(e0, e0) = e0
% 142.06/21.10 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.06/21.10 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.06/21.10 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.06/21.10 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.06/21.10 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.06/21.10 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.06/21.10 e1) = all_56_14 & $i(all_56_14))
% 142.06/21.10 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.06/21.10 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.06/21.10 (4) op(e1, e1) = all_4_2
% 142.06/21.10 (5) op(e3, e1) = all_52_8
% 142.06/21.10 (6) ~ (all_4_2 = e3)
% 142.06/21.10 (7) ~ (e1 = e0)
% 142.06/21.10 (8) ~ (all_52_11 = e0)
% 142.06/21.10 (9) op(e0, e1) = all_52_11
% 142.06/21.10 (10) ~ (all_4_2 = e2)
% 142.06/21.10 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.06/21.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.06/21.10 (12) ~ (all_52_8 = e0)
% 142.06/21.10 (13) op(e0, e0) = all_56_15
% 142.06/21.10 (14) op(e2, e1) = all_52_9
% 142.06/21.10 (15) ~ (all_52_9 = e0)
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | BETA: splitting (3) gives:
% 142.06/21.10 |
% 142.06/21.10 | Case 1:
% 142.06/21.10 | |
% 142.06/21.10 | | (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 142.06/21.10 | | e0)
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (5), (11), (12), (14), (15), (16) are inconsistent by sub-proof
% 142.06/21.10 | | #980.
% 142.06/21.10 | |
% 142.06/21.10 | Case 2:
% 142.06/21.10 | |
% 142.06/21.10 | | (17) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.06/21.10 | | e0)
% 142.06/21.10 | |
% 142.06/21.10 | | BETA: splitting (17) gives:
% 142.06/21.10 | |
% 142.06/21.10 | | Case 1:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (18) all_57_8 = e0 & op(e1, e1) = e0
% 142.06/21.10 | | |
% 142.06/21.10 | | | ALPHA: (18) implies:
% 142.06/21.10 | | | (19) op(e1, e1) = e0
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (1), (2), (4), (6), (7), (10), (11), (13), (19) are
% 142.06/21.10 | | | inconsistent by sub-proof #745.
% 142.06/21.10 | | |
% 142.06/21.10 | | Case 2:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (20) all_57_14 = e0 & op(e0, e1) = e0
% 142.06/21.10 | | |
% 142.06/21.10 | | | ALPHA: (20) implies:
% 142.06/21.10 | | | (21) op(e0, e1) = e0
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (8), (9), (11), (21) are inconsistent by sub-proof #886.
% 142.06/21.10 | | |
% 142.06/21.10 | | End of split
% 142.06/21.10 | |
% 142.06/21.10 | End of split
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #519 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) all_57_13 = e0 & op(e0, e2) = e0
% 142.06/21.10 (2) all_57_13 = e1
% 142.06/21.10 (3) ~ (e1 = e0)
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | ALPHA: (1) implies:
% 142.06/21.10 | (4) all_57_13 = e0
% 142.06/21.10 |
% 142.06/21.10 | COMBINE_EQS: (2), (4) imply:
% 142.06/21.10 | (5) e1 = e0
% 142.06/21.10 |
% 142.06/21.10 | REDUCE: (3), (5) imply:
% 142.06/21.10 | (6) $false
% 142.06/21.10 |
% 142.06/21.10 | CLOSE: (6) is inconsistent.
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #520 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) ~ (e2 = e1)
% 142.06/21.10 (2) op(e2, e2) = e1
% 142.06/21.10 (3) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.06/21.10 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.06/21.10 (4) all_57_13 = e1
% 142.06/21.10 (5) ~ (e2 = e0)
% 142.06/21.10 (6) ~ (e3 = e2)
% 142.06/21.10 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.06/21.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.06/21.10 (8) all_57_1 = e3
% 142.06/21.10 (9) all_57_7 = e0
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | BETA: splitting (3) gives:
% 142.06/21.10 |
% 142.06/21.10 | Case 1:
% 142.06/21.10 | |
% 142.06/21.10 | | (10) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 142.06/21.10 | | e2)
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (1), (2), (6), (7), (8), (10) are inconsistent by sub-proof #522.
% 142.06/21.10 | |
% 142.06/21.10 | Case 2:
% 142.06/21.10 | |
% 142.06/21.10 | | (11) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.06/21.10 | | e2)
% 142.06/21.10 | |
% 142.06/21.10 | | BETA: splitting (11) gives:
% 142.06/21.10 | |
% 142.06/21.10 | | Case 1:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (12) all_57_7 = e2 & op(e1, e2) = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | ALPHA: (12) implies:
% 142.06/21.10 | | | (13) all_57_7 = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (5), (9), (13) are inconsistent by sub-proof #578.
% 142.06/21.10 | | |
% 142.06/21.10 | | Case 2:
% 142.06/21.10 | | |
% 142.06/21.10 | | | (14) all_57_13 = e2 & op(e0, e2) = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | ALPHA: (14) implies:
% 142.06/21.10 | | | (15) all_57_13 = e2
% 142.06/21.10 | | |
% 142.06/21.10 | | | REF_CLOSE: (1), (4), (15) are inconsistent by sub-proof #1057.
% 142.06/21.10 | | |
% 142.06/21.10 | | End of split
% 142.06/21.10 | |
% 142.06/21.10 | End of split
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #521 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) ~ (e2 = e1)
% 142.06/21.10 (2) all_57_7 = e1
% 142.06/21.10 (3) all_57_13 = e0
% 142.06/21.10 (4) ~ (e2 = e0)
% 142.06/21.10 (5) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | BETA: splitting (5) gives:
% 142.06/21.10 |
% 142.06/21.10 | Case 1:
% 142.06/21.10 | |
% 142.06/21.10 | | (6) all_57_7 = e2 & op(e1, e2) = e2
% 142.06/21.10 | |
% 142.06/21.10 | | ALPHA: (6) implies:
% 142.06/21.10 | | (7) all_57_7 = e2
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #872.
% 142.06/21.10 | |
% 142.06/21.10 | Case 2:
% 142.06/21.10 | |
% 142.06/21.10 | | (8) all_57_13 = e2 & op(e0, e2) = e2
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #588.
% 142.06/21.10 | |
% 142.06/21.10 | End of split
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #522 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) ~ (e2 = e1)
% 142.06/21.10 (2) op(e2, e2) = e1
% 142.06/21.10 (3) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 142.06/21.10 (4) ~ (e3 = e2)
% 142.06/21.10 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.06/21.10 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.06/21.10 (6) all_57_1 = e3
% 142.06/21.10
% 142.06/21.10 Begin of proof
% 142.06/21.10 |
% 142.06/21.10 | BETA: splitting (3) gives:
% 142.06/21.10 |
% 142.06/21.10 | Case 1:
% 142.06/21.10 | |
% 142.06/21.10 | | (7) all_57_1 = e2 & op(e3, e2) = e2
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (4), (6), (7) are inconsistent by sub-proof #782.
% 142.06/21.10 | |
% 142.06/21.10 | Case 2:
% 142.06/21.10 | |
% 142.06/21.10 | | (8) all_57_3 = e2 & op(e2, e2) = e2
% 142.06/21.10 | |
% 142.06/21.10 | | ALPHA: (8) implies:
% 142.06/21.10 | | (9) op(e2, e2) = e2
% 142.06/21.10 | |
% 142.06/21.10 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #749.
% 142.06/21.10 | |
% 142.06/21.10 | End of split
% 142.06/21.10 |
% 142.06/21.10 End of proof
% 142.06/21.10
% 142.06/21.10 Sub-proof #523 shows that the following formulas are inconsistent:
% 142.06/21.10 ----------------------------------------------------------------
% 142.06/21.10 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.06/21.10 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.06/21.10 (2) ~ (all_52_8 = all_52_11)
% 142.06/21.10 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.06/21.10 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.06/21.10 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.06/21.10 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.06/21.10 (5) ~ (all_52_11 = all_10_2)
% 142.06/21.10 (6) ~ (all_52_13 = all_10_2)
% 142.06/21.10 (7) ~ (all_52_6 = all_4_2)
% 142.06/21.10 (8) ~ (all_52_3 = all_52_7)
% 142.06/21.10 (9) op(e1, e3) = all_52_2
% 142.06/21.10 (10) ~ (all_52_8 = all_52_9)
% 142.06/21.10 (11) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.06/21.10 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.06/21.10 (12) op(e1, e2) = all_52_6
% 142.06/21.10 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.06/21.10 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.06/21.10 (14) ~ (all_52_4 = e0)
% 142.06/21.10 (15) all_54_11 = all_52_14
% 142.06/21.10 (16) all_46_2 = all_10_2
% 142.06/21.11 (17) all_54_10 = e3 | all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 142.06/21.11 (18) op(e0, e3) = all_52_3
% 142.06/21.11 (19) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.06/21.11 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.06/21.11 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.06/21.11 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.06/21.11 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.06/21.11 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.06/21.11 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.06/21.11 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.06/21.11 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.06/21.11 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.06/21.11 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.06/21.11 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.06/21.11 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.06/21.11 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.06/21.11 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.06/21.11 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.06/21.11 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.06/21.11 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.06/21.11 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.06/21.11 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.06/21.11 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.06/21.11 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.06/21.11 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.06/21.11 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.06/21.11 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.06/21.11 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.06/21.11 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.06/21.11 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.06/21.11 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.06/21.11 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.06/21.11 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.06/21.11 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.06/21.11 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.06/21.11 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.06/21.11 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.06/21.11 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.06/21.11 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.06/21.11 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.06/21.11 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.06/21.11 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.06/21.11 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.06/21.11 (20) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.06/21.11 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.06/21.11 (21) ~ (all_10_2 = e1)
% 142.06/21.11 (22) op(e2, e2) = e1
% 142.06/21.11 (23) ~ (all_52_8 = all_4_2)
% 142.06/21.11 (24) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 142.06/21.11 (25) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.06/21.11 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.06/21.11 e1)
% 142.06/21.11 (26) all_48_2 = all_4_2
% 142.06/21.11 (27) ~ (all_52_9 = all_52_11)
% 142.06/21.11 (28) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.06/21.11 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.06/21.11 (29) all_54_2 = all_52_8
% 142.06/21.11 (30) ~ (all_52_1 = e0)
% 142.06/21.11 (31) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.06/21.11 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.06/21.11 (32) ~ (e3 = e0)
% 142.06/21.11 (33) op(e1, e1) = all_4_2
% 142.06/21.11 (34) op(e3, e1) = all_52_8
% 142.06/21.11 (35) ~ (all_52_12 = all_52_14)
% 142.06/21.11 (36) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.06/21.11 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.06/21.11 (37) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.06/21.11 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.06/21.11 e2)
% 142.06/21.11 (38) op(e2, e3) = all_52_1
% 142.06/21.11 (39) ~ (all_52_12 = e0)
% 142.06/21.11 (40) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.06/21.11 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.06/21.11 e0) = all_14_1 & $i(all_14_1))
% 142.06/21.11 (41) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.06/21.11 (42) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.06/21.11 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.06/21.11 (43) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.06/21.11 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.06/21.11 (44) ~ (all_52_6 = all_52_14)
% 142.06/21.11 (45) ~ (all_52_13 = all_52_14)
% 142.06/21.11 (46) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.06/21.11 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.06/21.11 (47) op(e0, e0) = all_10_2
% 142.06/21.11 (48) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.06/21.11 (49) all_57_3 = e1
% 142.06/21.11 (50) ~ (all_4_2 = e3)
% 142.06/21.11 (51) all_28_2 = e0
% 142.06/21.11 (52) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.06/21.11 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.06/21.11 (53) ~ (e1 = e0)
% 142.06/21.11 (54) all_42_2 = all_10_2
% 142.06/21.11 (55) op(e3, e2) = all_52_4
% 142.06/21.11 (56) ~ (all_52_7 = all_52_11)
% 142.06/21.11 (57) ~ (e2 = e0)
% 142.06/21.11 (58) ~ (e3 = e2)
% 142.06/21.11 (59) ~ (all_46_2 = e3) | ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 &
% 142.06/21.11 op(e0, e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 =
% 142.06/21.11 e1) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 142.06/21.11 (60) op(e0, e1) = all_52_11
% 142.06/21.11 (61) op(e3, e0) = all_52_12
% 142.06/21.11 (62) ~ (all_42_2 = e3) | ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 &
% 142.06/21.11 op(e0, e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 142.06/21.11 e2) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 142.06/21.11 (63) all_54_15 = e3 | all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 142.06/21.11 (64) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.06/21.11 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.06/21.11 (65) ~ (all_52_9 = all_4_2)
% 142.06/21.11 (66) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.06/21.11 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.06/21.11 (67) ~ (all_4_2 = e2)
% 142.06/21.11 (68) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.06/21.11 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.06/21.11 (69) all_54_15 = all_10_2
% 142.06/21.11 (70) all_54_10 = all_4_2
% 142.06/21.11 (71) all_54_14 = all_52_11
% 142.06/21.11 (72) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.06/21.11 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.06/21.11 (73) ~ (all_52_14 = all_10_2)
% 142.06/21.11 (74) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.06/21.11 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.06/21.11 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.06/21.11 (75) ~ (all_52_3 = e0)
% 142.06/21.11 (76) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.06/21.11 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.06/21.11 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.06/21.11 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.06/21.11 (77) ~ (all_52_8 = e0)
% 142.06/21.11 (78) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.06/21.11 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.06/21.11 (79) op(e0, e2) = all_52_7
% 142.06/21.11 (80) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.06/21.11 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.06/21.11 (81) ~ (all_48_2 = e0) | ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 &
% 142.06/21.11 op(e1, e0) = all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 =
% 142.06/21.11 e2) & op(e1, e0) = all_48_1 & $i(all_48_1))
% 142.06/21.11 (82) ~ (all_52_9 = e1)
% 142.06/21.11 (83) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.06/21.11 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.06/21.11 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.06/21.11 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.06/21.11 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.06/21.11 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.06/21.11 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.06/21.11 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.06/21.11 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.06/21.11 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.06/21.11 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.06/21.11 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.06/21.11 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.06/21.11 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.06/21.11 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.06/21.11 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.06/21.11 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.06/21.11 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.06/21.11 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.06/21.11 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.06/21.11 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.06/21.11 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.06/21.11 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.06/21.11 $i(all_56_14))))
% 142.06/21.11 (84) all_57_0 = e0
% 142.06/21.11 (85) op(e3, e3) = e0
% 142.06/21.11 (86) op(e2, e1) = all_52_9
% 142.06/21.11 (87) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.06/21.11 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.06/21.11 (88) ~ (all_52_13 = e1)
% 142.06/21.11 (89) ~ (all_24_2 = e2) | ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 &
% 142.06/21.11 op(e0, e2) = all_24_1 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 =
% 142.06/21.11 e3) & op(e0, e2) = all_24_1 & $i(all_24_1))
% 142.06/21.11 (90) all_24_2 = all_10_2
% 142.06/21.11 (91) op(e2, e0) = all_52_13
% 142.06/21.11 (92) ~ (all_52_12 = all_10_2)
% 142.06/21.11 (93) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.06/21.11 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.06/21.11 (94) op(e1, e0) = all_52_14
% 142.06/21.11 (95) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.06/21.11 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.06/21.11
% 142.06/21.11 Begin of proof
% 142.06/21.11 |
% 142.06/21.11 | BETA: splitting (89) gives:
% 142.06/21.11 |
% 142.06/21.11 | Case 1:
% 142.06/21.11 | |
% 142.06/21.11 | | (96) ~ (all_24_2 = e2)
% 142.06/21.11 | |
% 142.06/21.11 | | REDUCE: (90), (96) imply:
% 142.06/21.11 | | (97) ~ (all_10_2 = e2)
% 142.06/21.11 | |
% 142.06/21.11 | | BETA: splitting (74) gives:
% 142.06/21.11 | |
% 142.06/21.11 | | Case 1:
% 142.06/21.11 | | |
% 142.06/21.11 | | | (98) ~ (all_28_2 = e0)
% 142.06/21.11 | | |
% 142.06/21.11 | | | REDUCE: (51), (98) imply:
% 142.06/21.11 | | | (99) $false
% 142.06/21.11 | | |
% 142.06/21.11 | | | CLOSE: (99) is inconsistent.
% 142.06/21.11 | | |
% 142.06/21.11 | | Case 2:
% 142.06/21.11 | | |
% 142.06/21.11 | | | (100) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.06/21.11 | | | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) &
% 142.06/21.11 | | | op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.06/21.11 | | |
% 142.06/21.11 | | | BETA: splitting (62) gives:
% 142.06/21.11 | | |
% 142.06/21.11 | | | Case 1:
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | (101) ~ (all_42_2 = e3)
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | REDUCE: (54), (101) imply:
% 142.06/21.11 | | | | (102) ~ (all_10_2 = e3)
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | BETA: splitting (63) gives:
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | Case 1:
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | (103) all_54_15 = e3
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | REF_CLOSE: (69), (102), (103) are inconsistent by sub-proof #755.
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | Case 2:
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | (104) ~ (all_54_15 = e3)
% 142.06/21.11 | | | | | (105) all_54_15 = e2 | all_54_15 = e1 | all_54_15 = e0
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | BETA: splitting (105) gives:
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | Case 1:
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | (106) all_54_15 = e2
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | REF_CLOSE: (69), (97), (106) are inconsistent by sub-proof #754.
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | Case 2:
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | (107) ~ (all_54_15 = e2)
% 142.06/21.11 | | | | | | (108) all_54_15 = e1 | all_54_15 = e0
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | BETA: splitting (108) gives:
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | Case 1:
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | (109) all_54_15 = e1
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REF_CLOSE: (21), (69), (109) are inconsistent by sub-proof #748.
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | Case 2:
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | (110) all_54_15 = e0
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | COMBINE_EQS: (69), (110) imply:
% 142.06/21.11 | | | | | | | (111) all_10_2 = e0
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | SIMP: (111) implies:
% 142.06/21.11 | | | | | | | (112) all_10_2 = e0
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REDUCE: (6), (112) imply:
% 142.06/21.11 | | | | | | | (113) ~ (all_52_13 = e0)
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REDUCE: (102), (112) imply:
% 142.06/21.11 | | | | | | | (114) ~ (e3 = e0)
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REDUCE: (97), (112) imply:
% 142.06/21.11 | | | | | | | (115) ~ (e2 = e0)
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REDUCE: (21), (112) imply:
% 142.06/21.11 | | | | | | | (116) ~ (e1 = e0)
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REDUCE: (47), (112) imply:
% 142.06/21.11 | | | | | | | (117) op(e0, e0) = e0
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REF_CLOSE: (22), (30), (32), (33), (38), (50), (53), (57), (67),
% 142.06/21.11 | | | | | | | (72), (82), (83), (85), (86), (91), (95), (113), (117)
% 142.06/21.11 | | | | | | | are inconsistent by sub-proof #639.
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | End of split
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | End of split
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | End of split
% 142.06/21.11 | | | |
% 142.06/21.11 | | | Case 2:
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | (118) all_42_2 = e3
% 142.06/21.11 | | | | (119) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3)
% 142.06/21.11 | | | | = all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 =
% 142.06/21.11 | | | | e2) & op(e0, e3) = all_42_1 & $i(all_42_1))
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | COMBINE_EQS: (54), (118) imply:
% 142.06/21.11 | | | | (120) all_10_2 = e3
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | SIMP: (120) implies:
% 142.06/21.11 | | | | (121) all_10_2 = e3
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | COMBINE_EQS: (16), (121) imply:
% 142.06/21.11 | | | | (122) all_46_2 = e3
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | REDUCE: (5), (121) imply:
% 142.06/21.11 | | | | (123) ~ (all_52_11 = e3)
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | REDUCE: (92), (121) imply:
% 142.06/21.11 | | | | (124) ~ (all_52_12 = e3)
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | REDUCE: (73), (121) imply:
% 142.06/21.11 | | | | (125) ~ (all_52_14 = e3)
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | REDUCE: (21), (121) imply:
% 142.06/21.11 | | | | (126) ~ (e3 = e1)
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | REDUCE: (47), (121) imply:
% 142.06/21.11 | | | | (127) op(e0, e0) = e3
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | BETA: splitting (59) gives:
% 142.06/21.11 | | | |
% 142.06/21.11 | | | | Case 1:
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | (128) ~ (all_46_2 = e3)
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | REDUCE: (122), (128) imply:
% 142.06/21.11 | | | | | (129) $false
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | CLOSE: (129) is inconsistent.
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | Case 2:
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | (130) ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0,
% 142.06/21.11 | | | | | e3) = all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~
% 142.06/21.11 | | | | | (all_46_1 = e1) & op(e0, e3) = all_46_1 & $i(all_46_1))
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | BETA: splitting (81) gives:
% 142.06/21.11 | | | | |
% 142.06/21.11 | | | | | Case 1:
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | (131) ~ (all_48_2 = e0)
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | REDUCE: (26), (131) imply:
% 142.06/21.11 | | | | | | (132) ~ (all_4_2 = e0)
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | BETA: splitting (17) gives:
% 142.06/21.11 | | | | | |
% 142.06/21.11 | | | | | | Case 1:
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | (133) all_54_10 = e3
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | REF_CLOSE: (50), (70), (133) are inconsistent by sub-proof #1112.
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | Case 2:
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | (134) ~ (all_54_10 = e3)
% 142.06/21.11 | | | | | | | (135) all_54_10 = e2 | all_54_10 = e1 | all_54_10 = e0
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | BETA: splitting (135) gives:
% 142.06/21.11 | | | | | | |
% 142.06/21.11 | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | |
% 142.06/21.11 | | | | | | | | (136) all_54_10 = e2
% 142.06/21.11 | | | | | | | |
% 142.06/21.11 | | | | | | | | REF_CLOSE: (67), (70), (136) are inconsistent by sub-proof
% 142.06/21.11 | | | | | | | | #1111.
% 142.06/21.11 | | | | | | | |
% 142.06/21.11 | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | |
% 142.06/21.11 | | | | | | | | (137) ~ (all_54_10 = e2)
% 142.06/21.11 | | | | | | | | (138) all_54_10 = e1 | all_54_10 = e0
% 142.06/21.11 | | | | | | | |
% 142.06/21.11 | | | | | | | | BETA: splitting (138) gives:
% 142.06/21.11 | | | | | | | |
% 142.06/21.11 | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | (139) all_54_10 = e1
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | COMBINE_EQS: (70), (139) imply:
% 142.06/21.11 | | | | | | | | | (140) all_4_2 = e1
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | SIMP: (140) implies:
% 142.06/21.11 | | | | | | | | | (141) all_4_2 = e1
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | REDUCE: (50), (141) imply:
% 142.06/21.11 | | | | | | | | | (142) ~ (e3 = e1)
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | REDUCE: (67), (141) imply:
% 142.06/21.11 | | | | | | | | | (143) ~ (e2 = e1)
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | SIMP: (143) implies:
% 142.06/21.11 | | | | | | | | | (144) ~ (e2 = e1)
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | REDUCE: (33), (141) imply:
% 142.06/21.11 | | | | | | | | | (145) op(e1, e1) = e1
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | BETA: splitting (46) gives:
% 142.06/21.11 | | | | | | | | |
% 142.06/21.11 | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | (146) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1
% 142.06/21.11 | | | | | | | | | | & op(e2, e3) = e1)
% 142.06/21.11 | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | BETA: splitting (146) gives:
% 142.06/21.11 | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | (147) all_57_0 = e1 & op(e3, e3) = e1
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | ALPHA: (147) implies:
% 142.06/21.11 | | | | | | | | | | | (148) op(e3, e3) = e1
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | REF_CLOSE: (53), (72), (85), (148) are inconsistent by
% 142.06/21.11 | | | | | | | | | | | sub-proof #840.
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | (149) all_57_2 = e1 & op(e2, e3) = e1
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | ALPHA: (149) implies:
% 142.06/21.11 | | | | | | | | | | | (150) all_57_2 = e1
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | BETA: splitting (43) gives:
% 142.06/21.11 | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | (151) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 142.06/21.11 | | | | | | | | | | | | & op(e2, e3) = e3)
% 142.06/21.11 | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | REF_CLOSE: (32), (84), (126), (150), (151) are inconsistent
% 142.06/21.11 | | | | | | | | | | | | by sub-proof #649.
% 142.06/21.11 | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | (152) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 142.06/21.11 | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 142.06/21.11 | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | BETA: splitting (152) gives:
% 142.06/21.11 | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | (153) all_57_6 = e3 & op(e1, e3) = e3
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | ALPHA: (153) implies:
% 142.06/21.11 | | | | | | | | | | | | | (154) all_57_6 = e3
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | BETA: splitting (87) gives:
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | (155) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.06/21.11 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | REF_CLOSE: (57), (72), (85), (144), (150), (155) are
% 142.06/21.11 | | | | | | | | | | | | | | inconsistent by sub-proof #638.
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | (156) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.06/21.11 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | BETA: splitting (156) gives:
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | (157) all_57_6 = e2 & op(e1, e3) = e2
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | REF_CLOSE: (58), (154), (157) are inconsistent by sub-proof
% 142.06/21.11 | | | | | | | | | | | | | | | #998.
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | (158) all_57_12 = e2 & op(e0, e3) = e2
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | ALPHA: (158) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | (159) all_57_12 = e2
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (12), (14), (15), (18),
% 142.06/21.11 | | | | | | | | | | | | | | | (20), (22), (25), (28), (30), (31), (32), (33),
% 142.06/21.11 | | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (42),
% 142.06/21.11 | | | | | | | | | | | | | | | (43), (44), (45), (46), (48), (49), (50), (51),
% 142.06/21.11 | | | | | | | | | | | | | | | (52), (53), (55), (57), (58), (61), (64), (66),
% 142.06/21.11 | | | | | | | | | | | | | | | (67), (68), (72), (74), (75), (76), (77), (78),
% 142.06/21.11 | | | | | | | | | | | | | | | (80), (82), (83), (84), (85), (86), (87), (91),
% 142.06/21.11 | | | | | | | | | | | | | | | (93), (94), (95), (100), (119), (124), (125),
% 142.06/21.11 | | | | | | | | | | | | | | | (126), (127), (130), (144), (145), (150), (154),
% 142.06/21.11 | | | | | | | | | | | | | | | (159) are inconsistent by sub-proof #548.
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | End of split
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | End of split
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | (160) all_57_12 = e3 & op(e0, e3) = e3
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | ALPHA: (160) implies:
% 142.06/21.11 | | | | | | | | | | | | | (161) all_57_12 = e3
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | BETA: splitting (87) gives:
% 142.06/21.11 | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | (162) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.06/21.11 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | REF_CLOSE: (57), (72), (85), (144), (150), (162) are
% 142.06/21.11 | | | | | | | | | | | | | | inconsistent by sub-proof #638.
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | (163) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.06/21.11 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | BETA: splitting (163) gives:
% 142.06/21.11 | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | (164) all_57_6 = e2 & op(e1, e3) = e2
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | ALPHA: (164) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | (165) all_57_6 = e2
% 142.06/21.11 | | | | | | | | | | | | | | | (166) op(e1, e3) = e2
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 142.06/21.11 | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | (167) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | BETA: splitting (167) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | (168) all_57_6 = e3 & op(e1, e3) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | ALPHA: (168) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (169) all_57_6 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (165), (169) imply:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (170) e3 = e2
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | SIMP: (170) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (171) e3 = e2
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | COMBINE_EQS: (161), (171) imply:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (172) all_57_12 = e2
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (43), (46), (53), (58), (72), (84), (85),
% 142.06/21.11 | | | | | | | | | | | | | | | | | (126), (144), (165), (172) are inconsistent by
% 142.06/21.11 | | | | | | | | | | | | | | | | | sub-proof #550.
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | (173) all_57_7 = e3 & op(e1, e2) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | ALPHA: (173) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (174) all_57_7 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | (175) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (126), (150), (175) are inconsistent by
% 142.06/21.11 | | | | | | | | | | | | | | | | | | sub-proof #553.
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | (176) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.06/21.11 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | BETA: splitting (176) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (177) all_57_5 = e3 & op(e2, e1) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | ALPHA: (177) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (178) all_57_5 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | (179) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (31), (32), (52), (53), (55), (57),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | (58), (72), (85), (144), (174), (179) are
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | (180) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (32), (34), (40), (53), (57), (58), (68),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | (72), (77), (100), (144), (145), (166), (178),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | | (180) are inconsistent by sub-proof #546.
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | End of split
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (181) all_57_10 = e3 & op(e2, e0) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | ALPHA: (181) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (182) all_57_10 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (32), (53), (57), (58), (72), (76), (78),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (182) are inconsistent by
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | sub-proof #650.
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | End of split
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | End of split
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | End of split
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | (183) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 142.06/21.11 | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | BETA: splitting (183) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | (184) all_57_8 = e3 & op(e1, e1) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | ALPHA: (184) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (185) op(e1, e1) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (126), (145), (185) are inconsistent by
% 142.06/21.11 | | | | | | | | | | | | | | | | | sub-proof #1096.
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | (186) all_57_11 = e3 & op(e1, e0) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | ALPHA: (186) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | (187) all_57_11 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | (188) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | BETA: splitting (188) gives:
% 142.06/21.11 | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (189) all_57_2 = e3 & op(e2, e3) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | ALPHA: (189) implies:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (190) all_57_2 = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (150), (190) imply:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (191) e3 = e1
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (14), (20), (22), (28), (30), (31),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (32), (34), (36), (38), (39), (40), (42), (43),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (46), (49), (51), (52), (53), (55), (57), (58),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (61), (64), (66), (68), (72), (74), (76), (77),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (78), (80), (84), (85), (87), (93), (95), (124),
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (145), (161), (187), (191)
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #545.
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | (192) all_57_3 = e3 & op(e2, e2) = e3
% 142.06/21.11 | | | | | | | | | | | | | | | | | | |
% 142.06/21.11 | | | | | | | | | | | | | | | | | | | ALPHA: (192) implies:
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (193) all_57_3 = e3
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (193) imply:
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (194) e3 = e1
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (14), (20), (22), (28), (30), (31),
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (32), (34), (36), (38), (39), (40), (42), (43),
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (46), (49), (51), (52), (53), (55), (57), (58),
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (61), (64), (66), (68), (72), (74), (76), (77),
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (78), (80), (84), (85), (87), (93), (95), (124),
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (145), (161), (187), (194)
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #545.
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | End of split
% 142.06/21.12 | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | Case 2:
% 142.06/21.12 | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | (195) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.06/21.12 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.06/21.12 | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | BETA: splitting (195) gives:
% 142.06/21.12 | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (196) all_57_5 = e3 & op(e2, e1) = e3
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (196) implies:
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | (197) all_57_5 = e3
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 142.06/21.12 | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | | (198) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.06/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (20), (22), (31), (32), (34), (49),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (52), (53), (55), (57), (58), (61), (68), (72),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (77), (80), (84), (85), (93), (124), (126), (144),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (145), (198) are inconsistent by sub-proof #544.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (199) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (32), (34), (40), (53), (57), (58), (68),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (72), (77), (100), (144), (145), (166), (197),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (199) are inconsistent by sub-proof #546.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (200) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (200) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (201) all_57_10 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (32), (53), (57), (58), (72), (76), (78),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (201) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | sub-proof #650.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | (202) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | REF_CLOSE: (58), (161), (202) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | #659.
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | (203) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 142.10/21.12 | | | | | | | | | | & op(e0, e3) = e1)
% 142.10/21.12 | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | BETA: splitting (203) gives:
% 142.10/21.12 | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | (204) all_57_6 = e1 & op(e1, e3) = e1
% 142.10/21.12 | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | ALPHA: (204) implies:
% 142.10/21.12 | | | | | | | | | | | (205) all_57_6 = e1
% 142.10/21.12 | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | BETA: splitting (43) gives:
% 142.10/21.12 | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | (206) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 142.10/21.12 | | | | | | | | | | | | & op(e2, e3) = e3)
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | BETA: splitting (206) gives:
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | (207) all_57_0 = e3 & op(e3, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | REF_CLOSE: (32), (84), (207) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | #1108.
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | (208) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | ALPHA: (208) implies:
% 142.10/21.12 | | | | | | | | | | | | | (209) all_57_2 = e3
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | BETA: splitting (87) gives:
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | (210) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.12 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | REF_CLOSE: (57), (58), (72), (85), (209), (210) are
% 142.10/21.12 | | | | | | | | | | | | | | inconsistent by sub-proof #634.
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | (211) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.10/21.12 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | BETA: splitting (211) gives:
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | (212) all_57_6 = e2 & op(e1, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | ALPHA: (212) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | (213) all_57_6 = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | REF_CLOSE: (144), (205), (213) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | #700.
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | (214) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | ALPHA: (214) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | (215) all_57_12 = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | (216) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | BETA: splitting (216) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | (217) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | ALPHA: (217) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (218) all_57_6 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (218) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (219) e3 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | SIMP: (219) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (220) e3 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | COMBINE_EQS: (209), (220) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (221) all_57_2 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (12), (14), (15), (18),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (20), (22), (25), (28), (30), (31), (32), (33),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (42),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (43), (44), (45), (46), (48), (49), (50), (51),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (52), (53), (55), (57), (58), (61), (64), (66),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (67), (68), (72), (74), (75), (76), (77), (78),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (80), (82), (83), (84), (85), (86), (87), (91),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (93), (94), (95), (100), (119), (124), (125),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (126), (127), (130), (144), (145), (215), (218),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (221) are inconsistent by sub-proof #548.
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | (222) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | ALPHA: (222) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (223) all_57_7 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (224) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (31), (32), (52), (53), (55), (57),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (58), (72), (85), (144), (223), (224) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (225) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | BETA: splitting (225) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (226) all_57_4 = e1 & op(e3, e1) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (226) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (227) all_57_4 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (32), (34), (53), (57), (58), (68),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (72), (77), (126), (144), (145), (227) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (228) all_57_9 = e1 & op(e3, e0) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (228) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (229) op(e3, e0) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (230) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (230) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (231) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (231) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (232) all_57_12 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (51), (57), (58), (61), (72), (74),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (85), (87), (144), (209), (229), (232) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #632.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (233) all_57_13 = e1 & op(e0, e2) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (233) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (234) all_57_13 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (235) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (53), (55), (72), (235) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #1062.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (236) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (236) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (237) all_57_7 = e0 & op(e1, e2) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (223), (237) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | #1061.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (238) all_57_13 = e0 & op(e0, e2) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (238) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (239) all_57_13 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (234), (239) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (240) e1 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (240) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (241) all_57_6 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (53), (72), (85), (126), (144), (209),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (215), (241) are inconsistent by sub-proof #773.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (242) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (32), (34), (53), (57), (58), (68),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (72), (77), (126), (127), (144), (145), (242) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | (243) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 142.10/21.12 | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | BETA: splitting (243) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | (244) all_57_8 = e3 & op(e1, e1) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | ALPHA: (244) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (245) op(e1, e1) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (126), (145), (245) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | sub-proof #1096.
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | (246) all_57_11 = e3 & op(e1, e0) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | ALPHA: (246) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (247) all_57_11 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | BETA: splitting (76) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (248) all_57_15 = e0 & op(e0, e0) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | ALPHA: (248) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (249) op(e0, e0) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (72), (127), (249) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | | sub-proof #751.
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (250) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 142.10/21.12 | | | | | | | | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 142.10/21.12 | | | | | | | | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | ALPHA: (250) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (251) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 142.10/21.12 | | | | | | | | | | | | | | | | | | e0) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | BETA: splitting (251) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (252) all_57_9 = e0 & op(e3, e0) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (252) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (253) op(e3, e0) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (39), (61), (72), (253) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | sub-proof #941.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (254) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (254) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (255) all_57_10 = e0 & op(e2, e0) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (255) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (256) all_57_10 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (257) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (20), (22), (31), (32), (34), (49),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (52), (53), (55), (57), (58), (61), (68), (72),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (77), (80), (84), (85), (93), (124), (126), (144),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (145), (257) are inconsistent by sub-proof #544.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (258) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (258) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (259) all_57_4 = e1 & op(e3, e1) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (259) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (260) all_57_4 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (32), (34), (53), (57), (58), (68),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (72), (77), (126), (144), (145), (260) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #623.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (261) all_57_9 = e1 & op(e3, e0) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | ALPHA: (261) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (262) all_57_9 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | (263) op(e3, e0) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (264) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (264) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (265) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (265) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (266) all_57_12 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (28) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (267) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (267) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (268) all_57_9 = e2 & op(e3, e0) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (268) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (269) all_57_9 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (144), (262), (269) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #815.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (270) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (270) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (271) all_57_10 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (87) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (272) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (272) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (273) all_57_0 = e2 & op(e3, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (273) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (274) op(e3, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (72), (85), (274) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #880.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (275) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (275) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (276) all_57_2 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (277) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (277) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (208), (276) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #823.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (278) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (278) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (279) all_57_3 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (49), (126), (279) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #591.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (280) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (280) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (281) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (281) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (282) all_57_5 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (283) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (30), (38), (53), (72), (283) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #640.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (284) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (284) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (285) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (57), (58), (64), (66), (72), (126), (144),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (145), (205), (247), (282), (285) are inconsistent
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #543.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (255), (271) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #563.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (286) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (286) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (287) all_57_10 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (32), (53), (57), (58), (72), (78), (126),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (127), (144), (251), (287) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #687.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (40), (51), (61), (72), (74), (144), (211),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (263), (266) are inconsistent by sub-proof #633.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (288) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (72), (127), (247), (288) are inconsistent
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #583.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (289) all_57_13 = e1 & op(e0, e2) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (289) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | (290) all_57_13 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (11) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (291) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (22), (58), (72), (144), (209), (291) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #594.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | (292) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (292) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (293) all_57_5 = e2 & op(e2, e1) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (293) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (294) all_57_5 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (66) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (295) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e1, e2) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (295) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (296) all_57_6 = e2 & op(e1, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (296) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (297) all_57_6 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (43), (46), (53), (58), (72), (84), (85),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (144), (215), (297) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #550.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (298) all_57_7 = e2 & op(e1, e2) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (298) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | (299) all_57_7 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (52) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (300) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (13), (14), (32), (53), (55), (58), (72),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (126), (144), (256), (294), (300) are inconsistent
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #542.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (301) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e2) = e0)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (301) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (302) all_57_7 = e0 & op(e1, e2) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (299), (302) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | #1017.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (303) all_57_13 = e0 & op(e0, e2) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (303) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (304) all_57_13 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (290), (304) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (305) e1 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | SIMP: (305) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (306) e1 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (306) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (307) all_57_6 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (46), (53), (72), (85), (126), (144), (209),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | (215), (307) are inconsistent by sub-proof #773.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | (308) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | e2 & op(e1, e0) = e2)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (72), (144), (145), (247), (308) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #962.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (309) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (309) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | (310) all_57_10 = e2
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (57), (256), (310) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | | #609.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (311) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (32), (34), (53), (57), (58), (68),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | (72), (77), (126), (127), (144), (145), (311) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (312) all_57_11 = e0 & op(e1, e0) = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | ALPHA: (312) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (313) all_57_11 = e0
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (57), (58), (64), (66), (72), (126), (144),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (145), (205), (313) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | #955.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | (314) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 142.10/21.12 | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | BETA: splitting (314) gives:
% 142.10/21.12 | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | (315) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | REF_CLOSE: (126), (205), (315) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | #1093.
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | (316) all_57_12 = e3 & op(e0, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | ALPHA: (316) implies:
% 142.10/21.12 | | | | | | | | | | | | | (317) all_57_12 = e3
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | BETA: splitting (87) gives:
% 142.10/21.12 | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | (318) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.12 | | | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | BETA: splitting (318) gives:
% 142.10/21.12 | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | (319) all_57_0 = e2 & op(e3, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | ALPHA: (319) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | (320) op(e3, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | REF_CLOSE: (57), (72), (85), (320) are inconsistent by
% 142.10/21.12 | | | | | | | | | | | | | | | sub-proof #880.
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | (321) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | ALPHA: (321) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | (322) all_57_2 = e2
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | BETA: splitting (64) gives:
% 142.10/21.12 | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | (323) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | & op(e1, e2) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | BETA: splitting (323) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | (324) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | ALPHA: (324) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (325) all_57_6 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | COMBINE_EQS: (205), (325) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (326) e3 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (43), (58), (84), (126), (205), (317),
% 142.10/21.12 | | | | | | | | | | | | | | | | | (322), (326) are inconsistent by sub-proof #540.
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | (327) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | ALPHA: (327) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | (328) all_57_7 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (329) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | BETA: splitting (329) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (330) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (322), (330) are inconsistent by sub-proof
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | #823.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (331) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (331) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (332) all_57_3 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (332) imply:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (333) e3 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (43), (58), (84), (126), (205), (317),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (322), (333) are inconsistent by sub-proof #540.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | (334) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.10/21.12 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | BETA: splitting (334) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (335) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | ALPHA: (335) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | (336) all_57_5 = e3
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (337) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (14), (22), (31), (32), (52), (53), (55), (57),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (58), (72), (85), (144), (328), (337) are
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #547.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | (338) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | BETA: splitting (338) gives:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (339) all_57_4 = e1 & op(e3, e1) = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | ALPHA: (339) implies:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (340) all_57_4 = e1
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (32), (34), (53), (57), (58), (68), (72),
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | (77), (144), (145), (336), (340) are inconsistent
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | | by sub-proof #628.
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.12 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (341) all_57_9 = e1 & op(e3, e0) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (341) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (342) op(e3, e0) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | (343) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (343) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (344) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (344) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (345) all_57_12 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (32), (40), (43), (51), (57), (58), (61),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (72), (74), (84), (85), (87), (126), (144), (205),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (342), (345) are inconsistent by sub-proof #606.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (346) all_57_13 = e1 & op(e0, e2) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (346) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (347) all_57_13 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | (348) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (348) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | (349) all_57_4 = e0 & op(e3, e1) = e0
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (72), (77), (349) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #981.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | (350) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (336), (350) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | #729.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | (351) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (53), (57), (58), (72), (127), (144), (145),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | (317), (347), (351) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | #539.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | (352) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (32), (34), (53), (57), (58), (68),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | (72), (77), (126), (127), (144), (145), (352) are
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (353) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | ALPHA: (353) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (354) all_57_10 = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (32), (53), (57), (58), (72), (76), (78),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (354) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | sub-proof #650.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | (355) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 =
% 142.10/21.13 | | | | | | | | | | | | | | | | e3 & op(e1, e0) = e3)
% 142.10/21.13 | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | BETA: splitting (355) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | (356) all_57_8 = e3 & op(e1, e1) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | ALPHA: (356) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | (357) op(e1, e1) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | REF_CLOSE: (72), (126), (145), (357) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | | | | | | | sub-proof #1096.
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | (358) all_57_11 = e3 & op(e1, e0) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | ALPHA: (358) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | (359) all_57_11 = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | BETA: splitting (1) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | (360) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | BETA: splitting (360) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (361) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (58), (322), (361) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | #823.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (362) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | ALPHA: (362) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (363) all_57_3 = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (49), (363) imply:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (364) e3 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (14), (20), (22), (28), (30), (31),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (32), (34), (36), (38), (39), (40), (42), (43),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (46), (49), (51), (52), (53), (55), (57), (58),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (61), (64), (66), (68), (72), (74), (76), (77),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (78), (80), (84), (85), (87), (93), (95), (124),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (145), (317), (359), (364)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #545.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | (365) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | BETA: splitting (365) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (366) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | ALPHA: (366) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (367) all_57_5 = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | BETA: splitting (42) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | (368) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (14), (20), (22), (31), (32), (34), (49),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | (52), (53), (55), (57), (58), (61), (68), (72),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | (77), (80), (84), (85), (93), (124), (126), (144),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | (145), (368) are inconsistent by sub-proof #544.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | (369) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | BETA: splitting (369) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (370) all_57_4 = e1 & op(e3, e1) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (370) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (371) all_57_4 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (20), (32), (34), (53), (57), (58), (68), (72),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (77), (144), (145), (367), (371) are inconsistent
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | by sub-proof #628.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (372) all_57_9 = e1 & op(e3, e0) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | ALPHA: (372) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | (373) op(e3, e0) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | BETA: splitting (25) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | (374) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e2) = e1)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (374) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (375) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (375) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (376) all_57_12 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (9), (32), (40), (43), (51), (57), (58), (61),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (72), (74), (84), (85), (87), (126), (144), (205),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (373), (376) are inconsistent by sub-proof #606.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (377) all_57_13 = e1 & op(e0, e2) = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | ALPHA: (377) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | (378) all_57_13 = e1
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (20) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | (379) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e0)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | BETA: splitting (379) gives:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | (380) all_57_4 = e0 & op(e3, e1) = e0
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (34), (72), (77), (380) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | sub-proof #981.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | (381) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (32), (57), (58), (64), (66), (72), (126), (144),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | (145), (205), (359), (367), (381) are inconsistent
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | | by sub-proof #543.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | (382) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | e0 & op(e0, e1) = e0)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (37), (53), (57), (58), (72), (127), (144), (145),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | (317), (378), (382) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | | #539.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | (383) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 =
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | e1 & op(e0, e0) = e1)
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (4), (20), (32), (34), (53), (57), (58), (68),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | (72), (77), (126), (127), (144), (145), (383) are
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | | inconsistent by sub-proof #549.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (384) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | ALPHA: (384) implies:
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (385) all_57_10 = e3
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (28), (32), (53), (57), (58), (72), (76), (78),
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | (126), (127), (144), (385) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | | | | | | | | | sub-proof #650.
% 142.10/21.13 | | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | (386) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.10/21.13 | | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.10/21.13 | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | BETA: splitting (386) gives:
% 142.10/21.13 | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | (387) all_57_6 = e2 & op(e1, e3) = e2
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (144), (205), (387) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | | | | | | | #1110.
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | (388) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | | REF_CLOSE: (58), (317), (388) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | | | | | | | #659.
% 142.10/21.13 | | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | (389) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | REF_CLOSE: (1), (3), (4), (9), (11), (12), (14), (15), (18),
% 142.10/21.13 | | | | | | | | | | | (20), (22), (25), (28), (30), (31), (32), (33),
% 142.10/21.13 | | | | | | | | | | | (34), (35), (36), (37), (38), (39), (40), (42),
% 142.10/21.13 | | | | | | | | | | | (43), (44), (45), (46), (48), (49), (50), (51),
% 142.10/21.13 | | | | | | | | | | | (52), (53), (55), (57), (58), (61), (64), (66),
% 142.10/21.13 | | | | | | | | | | | (67), (68), (72), (74), (75), (76), (77), (78),
% 142.10/21.13 | | | | | | | | | | | (80), (82), (83), (84), (85), (86), (87), (91),
% 142.10/21.13 | | | | | | | | | | | (93), (94), (95), (100), (119), (124), (125),
% 142.10/21.13 | | | | | | | | | | | (126), (127), (130), (144), (145), (389) are
% 142.10/21.13 | | | | | | | | | | | inconsistent by sub-proof #554.
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | (390) all_54_10 = e0
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | REF_CLOSE: (70), (132), (390) are inconsistent by sub-proof
% 142.10/21.13 | | | | | | | | | #899.
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | End of split
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | End of split
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | End of split
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | Case 2:
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | (391) all_48_2 = e0
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | COMBINE_EQS: (26), (391) imply:
% 142.10/21.13 | | | | | | (392) all_4_2 = e0
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | REDUCE: (7), (392) imply:
% 142.10/21.13 | | | | | | (393) ~ (all_52_6 = e0)
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | REDUCE: (65), (392) imply:
% 142.10/21.13 | | | | | | (394) ~ (all_52_9 = e0)
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | REDUCE: (50), (392) imply:
% 142.10/21.13 | | | | | | (395) ~ (e3 = e0)
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | REDUCE: (67), (392) imply:
% 142.10/21.13 | | | | | | (396) ~ (e2 = e0)
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | BETA: splitting (52) gives:
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | | Case 1:
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | | (397) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 &
% 142.10/21.13 | | | | | | | op(e2, e2) = e0)
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | | REF_CLOSE: (14), (22), (53), (55), (72), (397) are inconsistent by
% 142.10/21.13 | | | | | | | sub-proof #1062.
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | Case 2:
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | | (398) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 &
% 142.10/21.13 | | | | | | | op(e0, e2) = e0)
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | | BETA: splitting (398) gives:
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | (399) all_57_7 = e0 & op(e1, e2) = e0
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | ALPHA: (399) implies:
% 142.10/21.13 | | | | | | | | (400) op(e1, e2) = e0
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | REF_CLOSE: (12), (72), (393), (400) are inconsistent by
% 142.10/21.13 | | | | | | | | sub-proof #999.
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | (401) all_57_13 = e0 & op(e0, e2) = e0
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | ALPHA: (401) implies:
% 142.10/21.13 | | | | | | | | (402) op(e0, e2) = e0
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | BETA: splitting (95) gives:
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | (403) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 142.10/21.13 | | | | | | | | | op(e2, e2) = e0)
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | REF_CLOSE: (22), (30), (38), (53), (72), (403) are
% 142.10/21.13 | | | | | | | | | inconsistent by sub-proof #640.
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | (404) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 142.10/21.13 | | | | | | | | | op(e2, e0) = e0)
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | BETA: splitting (404) gives:
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | (405) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | ALPHA: (405) implies:
% 142.10/21.13 | | | | | | | | | | (406) op(e2, e1) = e0
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | REF_CLOSE: (72), (86), (394), (406) are inconsistent by
% 142.10/21.13 | | | | | | | | | | sub-proof #1091.
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | (407) all_57_10 = e0 & op(e2, e0) = e0
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | ALPHA: (407) implies:
% 142.10/21.13 | | | | | | | | | | (408) op(e2, e0) = e0
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | BETA: splitting (76) gives:
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | (409) all_57_15 = e0 & op(e0, e0) = e0
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | ALPHA: (409) implies:
% 142.10/21.13 | | | | | | | | | | | (410) op(e0, e0) = e0
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | REF_CLOSE: (32), (72), (127), (410) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | sub-proof #751.
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | (411) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 =
% 142.10/21.13 | | | | | | | | | | | e0 & op(e2, e0) = e0) | (all_57_11 = e0 &
% 142.10/21.13 | | | | | | | | | | | op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0,
% 142.10/21.13 | | | | | | | | | | | e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.10/21.13 | | | | | | | | | | | e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | ALPHA: (411) implies:
% 142.10/21.13 | | | | | | | | | | | (412) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 =
% 142.10/21.13 | | | | | | | | | | | e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 142.10/21.13 | | | | | | | | | | | e1) = e0)
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | GROUND_INST: instantiating (72) with all_52_7, e0, e2, e0,
% 142.10/21.13 | | | | | | | | | | | simplifying with (79), (402) gives:
% 142.10/21.13 | | | | | | | | | | | (413) all_52_7 = e0
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | GROUND_INST: instantiating (72) with all_52_13, e0, e0, e2,
% 142.10/21.13 | | | | | | | | | | | simplifying with (91), (408) gives:
% 142.10/21.13 | | | | | | | | | | | (414) all_52_13 = e0
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | REDUCE: (56), (413) imply:
% 142.10/21.13 | | | | | | | | | | | (415) ~ (all_52_11 = e0)
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | SIMP: (415) implies:
% 142.10/21.13 | | | | | | | | | | | (416) ~ (all_52_11 = e0)
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | REDUCE: (88), (414) imply:
% 142.10/21.13 | | | | | | | | | | | (417) ~ (e1 = e0)
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | BETA: splitting (19) gives:
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | (418) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 142.10/21.13 | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 =
% 142.10/21.13 | | | | | | | | | | | | e3) & op(e2, e2) = all_56_11 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 142.10/21.13 | | | | | | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1,
% 142.10/21.13 | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e2) = e3) | ( ~ (all_56_3 = e2) & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e3) = all_56_3 & $i(all_56_3))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_6 = e1) & op(e1, e3) = all_56_6 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e3) = all_56_10 & $i(all_56_10)))) |
% 142.10/21.13 | | | | | | | | | | | | (op(e2, e2) = all_56_11 & $i(all_56_11) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 142.10/21.13 | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 142.10/21.13 | | | | | | | | | | | | e1) = all_56_13 & $i(all_56_13))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e2) = all_56_12 & $i(all_56_12))))
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | BETA: splitting (418) gives:
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | (419) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3
% 142.10/21.13 | | | | | | | | | | | | | = e2 & op(e2, e3) = e2) | ( ~ (all_56_11 = e3)
% 142.10/21.13 | | | | | | | | | | | | | & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0,
% 142.10/21.13 | | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.10/21.13 | | | | | | | | | | | | | e0) = all_56_15 & $i(all_56_15))) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_11 = e3 & op(e2, e2) = e3) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1)
% 142.10/21.13 | | | | | | | | | | | | | = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 142.10/21.13 | | | | | | | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 &
% 142.10/21.13 | | | | | | | | | | | | | op(e0, e0) = e3) | ( ~ (all_56_10 = e0) &
% 142.10/21.13 | | | | | | | | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | ALPHA: (419) implies:
% 142.10/21.13 | | | | | | | | | | | | | (420) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_15))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | REF_CLOSE: (18), (72), (75), (127), (420) are inconsistent by
% 142.10/21.13 | | | | | | | | | | | | | sub-proof #739.
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | (421) op(e2, e2) = all_56_11 & $i(all_56_11) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9
% 142.10/21.13 | | | | | | | | | | | | | = e2) & op(e3, e3) = all_56_9 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2)
% 142.10/21.13 | | | | | | | | | | | | | = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 142.10/21.13 | | | | | | | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 142.10/21.13 | | | | | | | | | | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 142.10/21.13 | | | | | | | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.10/21.13 | | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 142.10/21.13 | | | | | | | | | | | | | = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2
% 142.10/21.13 | | | | | | | | | | | | | & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 142.10/21.13 | | | | | | | | | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | ALPHA: (421) implies:
% 142.10/21.13 | | | | | | | | | | | | | (422) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_12))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | REF_CLOSE: (18), (58), (60), (72), (75), (127), (412), (416),
% 142.10/21.13 | | | | | | | | | | | | | (422) are inconsistent by sub-proof #736.
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | (423) (op(e1, e1) = all_56_13 & $i(all_56_13) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e1) = all_56_4 & $i(all_56_4))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0,
% 142.10/21.13 | | | | | | | | | | | | e1) = all_56_14 & $i(all_56_14)))) |
% 142.10/21.13 | | | | | | | | | | | | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.10/21.13 | | | | | | | | | | | | e2) = all_56_11 & $i(all_56_11))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 142.10/21.13 | | | | | | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3,
% 142.10/21.13 | | | | | | | | | | | | e0) = all_56_2 & $i(all_56_2))) &
% 142.10/21.13 | | | | | | | | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 142.10/21.13 | | | | | | | | | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 142.10/21.13 | | | | | | | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 142.10/21.13 | | | | | | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 142.10/21.13 | | | | | | | | | | | | e0) = all_56_8 & $i(all_56_8))))
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | BETA: splitting (423) gives:
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | Case 1:
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | (424) op(e1, e1) = all_56_13 & $i(all_56_13) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9
% 142.10/21.13 | | | | | | | | | | | | | = e1) & op(e3, e3) = all_56_9 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1)
% 142.10/21.13 | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.10/21.13 | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1
% 142.10/21.13 | | | | | | | | | | | | | & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) &
% 142.10/21.13 | | | | | | | | | | | | | op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_4 = e2) & op(e2, e1) = all_56_4 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1)
% 142.10/21.13 | | | | | | | | | | | | | = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.10/21.13 | | | | | | | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1
% 142.10/21.13 | | | | | | | | | | | | | & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) &
% 142.10/21.13 | | | | | | | | | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | ALPHA: (424) implies:
% 142.10/21.13 | | | | | | | | | | | | | (425) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_14))
% 142.10/21.13 | | | | | | | | | | | | | (426) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 142.10/21.13 | | | | | | | | | | | | | (all_56_15 = e1) & op(e0, e0) = all_56_15 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_15))
% 142.10/21.13 | | | | | | | | | | | | | (427) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4
% 142.10/21.13 | | | | | | | | | | | | | = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))
% 142.10/21.13 | | | | | | | | | | | | | (428) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1
% 142.10/21.13 | | | | | | | | | | | | | = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))
% 142.10/21.13 | | | | | | | | | | | | | (429) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11
% 142.10/21.13 | | | | | | | | | | | | | = e1) & op(e2, e2) = all_56_11 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_11))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | REF_CLOSE: (2), (10), (22), (24), (27), (29), (34), (41),
% 142.10/21.13 | | | | | | | | | | | | | (53), (60), (71), (72), (77), (85), (86), (123),
% 142.10/21.13 | | | | | | | | | | | | | (126), (127), (425), (426), (427), (428), (429)
% 142.10/21.13 | | | | | | | | | | | | | are inconsistent by sub-proof #532.
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | Case 2:
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | (430) op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 142.10/21.13 | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0)
% 142.10/21.13 | | | | | | | | | | | | | = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 142.10/21.13 | | | | | | | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 142.10/21.13 | | | | | | | | | | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) &
% 142.10/21.13 | | | | | | | | | | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.10/21.13 | | | | | | | | | | | | | ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2
% 142.10/21.13 | | | | | | | | | | | | | = e3) & op(e3, e0) = all_56_2 &
% 142.10/21.13 | | | | | | | | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2)
% 142.10/21.13 | | | | | | | | | | | | | = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 142.10/21.13 | | | | | | | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 &
% 142.10/21.13 | | | | | | | | | | | | | op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 142.10/21.13 | | | | | | | | | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | ALPHA: (430) implies:
% 142.10/21.13 | | | | | | | | | | | | | (431) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9
% 142.10/21.13 | | | | | | | | | | | | | = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | | REF_CLOSE: (33), (53), (57), (58), (61), (67), (72), (83),
% 142.10/21.13 | | | | | | | | | | | | | (85), (124), (126), (127), (431) are inconsistent
% 142.10/21.13 | | | | | | | | | | | | | by sub-proof #530.
% 142.10/21.13 | | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | | |
% 142.10/21.13 | | | | | | | | | End of split
% 142.10/21.13 | | | | | | | | |
% 142.10/21.13 | | | | | | | | End of split
% 142.10/21.13 | | | | | | | |
% 142.10/21.13 | | | | | | | End of split
% 142.10/21.13 | | | | | | |
% 142.10/21.13 | | | | | | End of split
% 142.10/21.13 | | | | | |
% 142.10/21.13 | | | | | End of split
% 142.10/21.13 | | | | |
% 142.10/21.13 | | | | End of split
% 142.10/21.13 | | | |
% 142.10/21.13 | | | End of split
% 142.10/21.13 | | |
% 142.10/21.13 | | End of split
% 142.10/21.13 | |
% 142.10/21.13 | Case 2:
% 142.10/21.13 | |
% 142.10/21.13 | | (432) all_24_2 = e2
% 142.10/21.13 | |
% 142.10/21.13 | | REF_CLOSE: (21), (22), (33), (47), (53), (57), (58), (67), (72), (83), (85),
% 142.10/21.13 | | (90), (432) are inconsistent by sub-proof #524.
% 142.10/21.13 | |
% 142.10/21.13 | End of split
% 142.10/21.13 |
% 142.10/21.13 End of proof
% 142.10/21.13
% 142.10/21.13 Sub-proof #524 shows that the following formulas are inconsistent:
% 142.10/21.13 ----------------------------------------------------------------
% 142.10/21.13 (1) ~ (all_10_2 = e1)
% 142.10/21.13 (2) op(e2, e2) = e1
% 142.10/21.13 (3) op(e1, e1) = all_4_2
% 142.10/21.13 (4) all_24_2 = e2
% 142.10/21.13 (5) op(e0, e0) = all_10_2
% 142.10/21.13 (6) ~ (e1 = e0)
% 142.10/21.13 (7) ~ (e2 = e0)
% 142.10/21.13 (8) ~ (e3 = e2)
% 142.10/21.13 (9) ~ (all_4_2 = e2)
% 142.10/21.13 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.13 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.13 (11) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.13 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.13 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.13 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.13 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.13 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.13 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.13 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.13 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.13 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.13 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.13 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.13 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.13 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.13 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.13 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.13 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.13 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.13 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.13 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.13 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.13 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.13 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.13 $i(all_56_14))))
% 142.10/21.13 (12) op(e3, e3) = e0
% 142.10/21.13 (13) all_24_2 = all_10_2
% 142.10/21.13
% 142.10/21.13 Begin of proof
% 142.10/21.13 |
% 142.10/21.13 | COMBINE_EQS: (4), (13) imply:
% 142.10/21.13 | (14) all_10_2 = e2
% 142.10/21.13 |
% 142.10/21.14 | SIMP: (14) implies:
% 142.10/21.14 | (15) all_10_2 = e2
% 142.10/21.14 |
% 142.10/21.14 | REDUCE: (1), (15) imply:
% 142.10/21.14 | (16) ~ (e2 = e1)
% 142.10/21.14 |
% 142.10/21.14 | REDUCE: (5), (15) imply:
% 142.10/21.14 | (17) op(e0, e0) = e2
% 142.10/21.14 |
% 142.10/21.14 | REF_CLOSE: (2), (3), (6), (7), (8), (9), (10), (11), (12), (16), (17) are
% 142.10/21.14 | inconsistent by sub-proof #525.
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #525 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) ~ (e2 = e1)
% 142.10/21.14 (2) op(e2, e2) = e1
% 142.10/21.14 (3) op(e1, e1) = all_4_2
% 142.10/21.14 (4) ~ (e1 = e0)
% 142.10/21.14 (5) ~ (e2 = e0)
% 142.10/21.14 (6) ~ (e3 = e2)
% 142.10/21.14 (7) ~ (all_4_2 = e2)
% 142.10/21.14 (8) op(e0, e0) = e2
% 142.10/21.14 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.14 (10) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.14 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.14 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.14 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.14 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.14 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.14 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.14 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.14 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.14 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.14 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.14 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.14 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.14 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.14 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.14 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.14 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.14 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.14 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.14 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.14 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.14 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.14 $i(all_56_14))))
% 142.10/21.14 (11) op(e3, e3) = e0
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (10) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (12) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 142.10/21.14 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.10/21.14 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 142.10/21.14 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 142.10/21.14 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 142.10/21.14 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.10/21.14 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 142.10/21.14 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (4), (5), (9), (11), (12) are inconsistent by sub-proof #752.
% 142.10/21.14 | |
% 142.10/21.14 | Case 2:
% 142.10/21.14 | |
% 142.10/21.14 | | (13) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 142.10/21.14 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.10/21.14 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 142.10/21.14 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 142.10/21.14 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 142.10/21.14 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.10/21.14 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 142.10/21.14 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.10/21.14 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.10/21.14 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.10/21.14 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.10/21.14 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 142.10/21.14 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.10/21.14 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.10/21.14 | | all_56_14 & $i(all_56_14))))
% 142.10/21.14 | |
% 142.10/21.14 | | BETA: splitting (13) gives:
% 142.10/21.14 | |
% 142.10/21.14 | | Case 1:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (14) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.10/21.14 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.10/21.14 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 142.10/21.14 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 142.10/21.14 | | |
% 142.10/21.14 | | | REF_CLOSE: (3), (6), (7), (8), (9), (14) are inconsistent by sub-proof
% 142.10/21.14 | | | #529.
% 142.10/21.14 | | |
% 142.10/21.14 | | Case 2:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (15) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 142.10/21.14 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.10/21.14 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 142.10/21.14 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.10/21.14 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.10/21.14 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.10/21.14 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.10/21.14 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.10/21.14 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.10/21.14 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.10/21.14 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.10/21.14 | | |
% 142.10/21.14 | | | BETA: splitting (15) gives:
% 142.10/21.14 | | |
% 142.10/21.14 | | | Case 1:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | (16) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.10/21.14 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.10/21.14 | | | | $i(all_56_7)
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | ALPHA: (16) implies:
% 142.10/21.14 | | | | (17) op(e1, e1) = e2
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | REF_CLOSE: (3), (7), (9), (17) are inconsistent by sub-proof #1124.
% 142.10/21.14 | | | |
% 142.10/21.14 | | | Case 2:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | (18) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.10/21.14 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.10/21.14 | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.10/21.14 | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.10/21.14 | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 142.10/21.14 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.10/21.14 | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 142.10/21.14 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.10/21.14 | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.10/21.14 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.10/21.14 | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.14 | | | | $i(all_56_14))))
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | BETA: splitting (18) gives:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | Case 1:
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | | (19) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.10/21.14 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.10/21.14 | | | | | $i(all_56_5)
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | | ALPHA: (19) implies:
% 142.10/21.14 | | | | | (20) op(e2, e2) = e0
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | | REF_CLOSE: (2), (4), (9), (20) are inconsistent by sub-proof #1117.
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | Case 2:
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | | (21) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.10/21.14 | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0
% 142.10/21.14 | | | | | & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.10/21.14 | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0
% 142.10/21.14 | | | | | & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.10/21.14 | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.10/21.14 | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.10/21.14 | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | | ALPHA: (21) implies:
% 142.10/21.14 | | | | | (22) op(e0, e0) = all_56_15
% 142.10/21.14 | | | | | (23) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 142.10/21.14 | | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.14 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.10/21.14 | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 142.10/21.14 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 142.10/21.14 | | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.10/21.14 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.10/21.14 | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | | REF_CLOSE: (1), (2), (4), (6), (8), (9), (22), (23) are inconsistent
% 142.10/21.14 | | | | | by sub-proof #526.
% 142.10/21.14 | | | | |
% 142.10/21.14 | | | | End of split
% 142.10/21.14 | | | |
% 142.10/21.14 | | | End of split
% 142.10/21.14 | | |
% 142.10/21.14 | | End of split
% 142.10/21.14 | |
% 142.10/21.14 | End of split
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #526 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) ~ (e2 = e1)
% 142.10/21.14 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.10/21.14 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.10/21.14 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.10/21.14 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.10/21.14 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.10/21.14 e1) = all_56_14 & $i(all_56_14))
% 142.10/21.14 (3) op(e2, e2) = e1
% 142.10/21.14 (4) ~ (e1 = e0)
% 142.10/21.14 (5) ~ (e3 = e2)
% 142.10/21.14 (6) op(e0, e0) = e2
% 142.10/21.14 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.14 (8) op(e0, e0) = all_56_15
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | GROUND_INST: instantiating (7) with e2, all_56_15, e0, e0, simplifying with
% 142.10/21.14 | (6), (8) gives:
% 142.10/21.14 | (9) all_56_15 = e2
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (2) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (10) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.10/21.14 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.10/21.14 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 142.10/21.14 | | e2) = all_56_12 & $i(all_56_12))
% 142.10/21.14 | |
% 142.10/21.14 | | BETA: splitting (10) gives:
% 142.10/21.14 | |
% 142.10/21.14 | | Case 1:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (11) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 142.10/21.14 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.10/21.14 | | |
% 142.10/21.14 | | | REF_CLOSE: (5), (9), (11) are inconsistent by sub-proof #528.
% 142.10/21.14 | | |
% 142.10/21.14 | | Case 2:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (12) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.14 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.10/21.14 | | |
% 142.10/21.14 | | | ALPHA: (12) implies:
% 142.10/21.14 | | | (13) op(e2, e2) = e0
% 142.10/21.14 | | |
% 142.10/21.14 | | | REF_CLOSE: (3), (4), (7), (13) are inconsistent by sub-proof #1117.
% 142.10/21.14 | | |
% 142.10/21.14 | | End of split
% 142.10/21.14 | |
% 142.10/21.14 | Case 2:
% 142.10/21.14 | |
% 142.10/21.14 | | (14) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.10/21.14 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.10/21.14 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.10/21.14 | | e1) = all_56_14 & $i(all_56_14))
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (1), (9), (14) are inconsistent by sub-proof #527.
% 142.10/21.14 | |
% 142.10/21.14 | End of split
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #527 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.10/21.14 op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 142.10/21.14 e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.14 $i(all_56_14))
% 142.10/21.14 (2) all_56_15 = e2
% 142.10/21.14 (3) ~ (e2 = e1)
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (1) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (4) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.10/21.14 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (4) implies:
% 142.10/21.14 | | (5) all_56_15 = e1
% 142.10/21.14 | |
% 142.10/21.14 | | COMBINE_EQS: (2), (5) imply:
% 142.10/21.14 | | (6) e2 = e1
% 142.10/21.14 | |
% 142.10/21.14 | | REDUCE: (3), (6) imply:
% 142.10/21.14 | | (7) $false
% 142.10/21.14 | |
% 142.10/21.14 | | CLOSE: (7) is inconsistent.
% 142.10/21.14 | |
% 142.10/21.14 | Case 2:
% 142.10/21.14 | |
% 142.10/21.14 | | (8) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 142.10/21.14 | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (8) implies:
% 142.10/21.14 | | (9) all_56_15 = e1
% 142.10/21.14 | |
% 142.10/21.14 | | COMBINE_EQS: (2), (9) imply:
% 142.10/21.14 | | (10) e2 = e1
% 142.10/21.14 | |
% 142.10/21.14 | | REDUCE: (3), (10) imply:
% 142.10/21.14 | | (11) $false
% 142.10/21.14 | |
% 142.10/21.14 | | CLOSE: (11) is inconsistent.
% 142.10/21.14 | |
% 142.10/21.14 | End of split
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #528 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.10/21.14 (2) all_56_15 = e2
% 142.10/21.14 (3) ~ (e3 = e2)
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | ALPHA: (1) implies:
% 142.10/21.14 | (4) all_56_15 = e3
% 142.10/21.14 |
% 142.10/21.14 | COMBINE_EQS: (2), (4) imply:
% 142.10/21.14 | (5) e3 = e2
% 142.10/21.14 |
% 142.10/21.14 | SIMP: (5) implies:
% 142.10/21.14 | (6) e3 = e2
% 142.10/21.14 |
% 142.10/21.14 | REDUCE: (3), (6) imply:
% 142.10/21.14 | (7) $false
% 142.10/21.14 |
% 142.10/21.14 | CLOSE: (7) is inconsistent.
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #529 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) op(e1, e1) = all_4_2
% 142.10/21.14 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 &
% 142.10/21.14 op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 =
% 142.10/21.14 e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1)
% 142.10/21.14 = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 142.10/21.14 (3) ~ (e3 = e2)
% 142.10/21.14 (4) ~ (all_4_2 = e2)
% 142.10/21.14 (5) op(e0, e0) = e2
% 142.10/21.14 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (2) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (7) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0
% 142.10/21.14 | | & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (7) implies:
% 142.10/21.14 | | (8) op(e0, e0) = e3
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1066.
% 142.10/21.14 | |
% 142.10/21.14 | Case 2:
% 142.10/21.14 | |
% 142.10/21.14 | | (9) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 142.10/21.14 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (9) implies:
% 142.10/21.14 | | (10) op(e1, e1) = e2
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (1), (4), (6), (10) are inconsistent by sub-proof #1124.
% 142.10/21.14 | |
% 142.10/21.14 | End of split
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #530 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) ~ (all_52_12 = e3)
% 142.10/21.14 (2) op(e0, e0) = e3
% 142.10/21.14 (3) op(e1, e1) = all_4_2
% 142.10/21.14 (4) ~ (e1 = e0)
% 142.10/21.14 (5) ~ (e2 = e0)
% 142.10/21.14 (6) ~ (e3 = e2)
% 142.10/21.14 (7) op(e3, e0) = all_52_12
% 142.10/21.14 (8) ~ (all_4_2 = e2)
% 142.10/21.14 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.14 (10) ~ (e3 = e1)
% 142.10/21.14 (11) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.14 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.14 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.14 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.14 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.14 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.14 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.14 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.14 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.14 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.14 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.14 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.14 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.14 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.14 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.14 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.14 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.14 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.14 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.14 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.14 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.14 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.14 $i(all_56_14))))
% 142.10/21.14 (12) op(e3, e3) = e0
% 142.10/21.14 (13) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 142.10/21.14 all_56_9 & $i(all_56_9))
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (13) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (14) all_56_2 = e3 & op(e3, e0) = e3
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (14) implies:
% 142.10/21.14 | | (15) op(e3, e0) = e3
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (1), (7), (9), (15) are inconsistent by sub-proof #1105.
% 142.10/21.14 | |
% 142.10/21.14 | Case 2:
% 142.10/21.14 | |
% 142.10/21.14 | | (16) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (16) implies:
% 142.10/21.14 | | (17) ~ (all_56_9 = e0)
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (17) are
% 142.10/21.14 | | inconsistent by sub-proof #531.
% 142.10/21.14 | |
% 142.10/21.14 | End of split
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #531 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) op(e0, e0) = e3
% 142.10/21.14 (2) op(e1, e1) = all_4_2
% 142.10/21.14 (3) ~ (e1 = e0)
% 142.10/21.14 (4) ~ (e2 = e0)
% 142.10/21.14 (5) ~ (e3 = e2)
% 142.10/21.14 (6) ~ (all_4_2 = e2)
% 142.10/21.14 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.14 (8) ~ (e3 = e1)
% 142.10/21.14 (9) ~ (all_56_9 = e0)
% 142.10/21.14 (10) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.14 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.14 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.14 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.14 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.14 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.14 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.14 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.14 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.14 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.14 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.14 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.14 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.14 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.14 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.14 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.14 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.14 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.14 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.14 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.14 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.14 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.14 $i(all_56_14))))
% 142.10/21.14 (11) op(e3, e3) = e0
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (10) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (12) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 142.10/21.14 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.10/21.14 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 142.10/21.14 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 142.10/21.14 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 142.10/21.14 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.10/21.14 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 142.10/21.14 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.10/21.14 | |
% 142.10/21.14 | | REF_CLOSE: (3), (4), (7), (11), (12) are inconsistent by sub-proof #752.
% 142.10/21.14 | |
% 142.10/21.14 | Case 2:
% 142.10/21.14 | |
% 142.10/21.14 | | (13) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 142.10/21.14 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.10/21.14 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 142.10/21.14 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 142.10/21.14 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 142.10/21.14 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.10/21.14 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 142.10/21.14 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.10/21.14 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.10/21.14 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.10/21.14 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.10/21.14 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 142.10/21.14 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.10/21.14 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.10/21.14 | | all_56_14 & $i(all_56_14))))
% 142.10/21.14 | |
% 142.10/21.14 | | BETA: splitting (13) gives:
% 142.10/21.14 | |
% 142.10/21.14 | | Case 1:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (14) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.10/21.14 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.10/21.14 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 142.10/21.14 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 142.10/21.14 | | |
% 142.10/21.14 | | | BETA: splitting (14) gives:
% 142.10/21.14 | | |
% 142.10/21.14 | | | Case 1:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | (15) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.10/21.14 | | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | ALPHA: (15) implies:
% 142.10/21.14 | | | | (16) all_56_9 = e0
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | REDUCE: (9), (16) imply:
% 142.10/21.14 | | | | (17) $false
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | CLOSE: (17) is inconsistent.
% 142.10/21.14 | | | |
% 142.10/21.14 | | | Case 2:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | (18) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2,
% 142.10/21.14 | | | | e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.10/21.14 | | | | $i(all_56_4)
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | ALPHA: (18) implies:
% 142.10/21.14 | | | | (19) op(e1, e1) = e2
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | REF_CLOSE: (2), (6), (7), (19) are inconsistent by sub-proof #1124.
% 142.10/21.14 | | | |
% 142.10/21.14 | | | End of split
% 142.10/21.14 | | |
% 142.10/21.14 | | Case 2:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (20) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 142.10/21.14 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.10/21.14 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 142.10/21.14 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.10/21.14 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.10/21.14 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.10/21.14 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.10/21.14 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.10/21.14 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.14 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.10/21.14 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.10/21.14 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.10/21.14 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.10/21.14 | | |
% 142.10/21.14 | | | BETA: splitting (20) gives:
% 142.10/21.14 | | |
% 142.10/21.14 | | | Case 1:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | (21) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.10/21.14 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.10/21.14 | | | | $i(all_56_7)
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | ALPHA: (21) implies:
% 142.10/21.14 | | | | (22) op(e1, e1) = e2
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | REF_CLOSE: (2), (6), (7), (22) are inconsistent by sub-proof #1124.
% 142.10/21.14 | | | |
% 142.10/21.14 | | | Case 2:
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | (23) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.10/21.14 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.10/21.14 | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.10/21.14 | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.10/21.14 | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 142.10/21.14 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.10/21.14 | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 142.10/21.14 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.10/21.14 | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.10/21.14 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.10/21.14 | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.14 | | | | $i(all_56_14))))
% 142.10/21.14 | | | |
% 142.10/21.14 | | | | REF_CLOSE: (1), (5), (7), (8), (9), (23) are inconsistent by sub-proof
% 142.10/21.14 | | | | #645.
% 142.10/21.14 | | | |
% 142.10/21.14 | | | End of split
% 142.10/21.14 | | |
% 142.10/21.14 | | End of split
% 142.10/21.14 | |
% 142.10/21.14 | End of split
% 142.10/21.14 |
% 142.10/21.14 End of proof
% 142.10/21.14
% 142.10/21.14 Sub-proof #532 shows that the following formulas are inconsistent:
% 142.10/21.14 ----------------------------------------------------------------
% 142.10/21.14 (1) ~ (all_52_8 = all_52_11)
% 142.10/21.14 (2) ~ (all_52_8 = all_52_9)
% 142.10/21.14 (3) op(e0, e0) = e3
% 142.10/21.14 (4) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.10/21.14 all_56_11 & $i(all_56_11))
% 142.10/21.14 (5) ~ (all_52_11 = e3)
% 142.10/21.14 (6) op(e2, e2) = e1
% 142.10/21.14 (7) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 142.10/21.14 (8) ~ (all_52_9 = all_52_11)
% 142.10/21.14 (9) all_54_2 = all_52_8
% 142.10/21.14 (10) op(e3, e1) = all_52_8
% 142.10/21.14 (11) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.10/21.14 (12) ~ (e1 = e0)
% 142.10/21.14 (13) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.10/21.14 all_56_14 & $i(all_56_14))
% 142.10/21.14 (14) op(e0, e1) = all_52_11
% 142.10/21.14 (15) all_54_14 = all_52_11
% 142.10/21.14 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.14 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.14 (17) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.10/21.14 all_56_4 & $i(all_56_4))
% 142.10/21.14 (18) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 142.10/21.14 all_56_1 & $i(all_56_1))
% 142.10/21.14 (19) ~ (all_52_8 = e0)
% 142.10/21.14 (20) ~ (e3 = e1)
% 142.10/21.14 (21) op(e3, e3) = e0
% 142.10/21.14 (22) op(e2, e1) = all_52_9
% 142.10/21.14 (23) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.10/21.14 all_56_15 & $i(all_56_15))
% 142.10/21.14
% 142.10/21.14 Begin of proof
% 142.10/21.14 |
% 142.10/21.14 | BETA: splitting (4) gives:
% 142.10/21.14 |
% 142.10/21.14 | Case 1:
% 142.10/21.14 | |
% 142.10/21.14 | | (24) all_56_4 = e2 & op(e2, e1) = e2
% 142.10/21.14 | |
% 142.10/21.14 | | ALPHA: (24) implies:
% 142.10/21.14 | | (25) op(e2, e1) = e2
% 142.10/21.14 | |
% 142.10/21.14 | | BETA: splitting (18) gives:
% 142.10/21.14 | |
% 142.10/21.14 | | Case 1:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (26) all_56_9 = e1 & op(e3, e3) = e1
% 142.10/21.14 | | |
% 142.10/21.14 | | | ALPHA: (26) implies:
% 142.10/21.14 | | | (27) op(e3, e3) = e1
% 142.10/21.14 | | |
% 142.10/21.14 | | | REF_CLOSE: (12), (16), (21), (27) are inconsistent by sub-proof #840.
% 142.10/21.14 | | |
% 142.10/21.14 | | Case 2:
% 142.10/21.14 | | |
% 142.10/21.14 | | | (28) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1)
% 142.10/21.14 | | |
% 142.10/21.14 | | | ALPHA: (28) implies:
% 142.10/21.14 | | | (29) ~ (all_56_1 = e3)
% 142.10/21.14 | | | (30) op(e3, e1) = all_56_1
% 142.10/21.14 | | |
% 142.10/21.15 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (11), (13), (14),
% 142.10/21.15 | | | (15), (16), (19), (20), (22), (25), (29), (30) are inconsistent
% 142.10/21.15 | | | by sub-proof #535.
% 142.10/21.15 | | |
% 142.10/21.15 | | End of split
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (31) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (31) implies:
% 142.10/21.15 | | (32) ~ (all_56_11 = e1)
% 142.10/21.15 | | (33) op(e2, e2) = all_56_11
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (3), (4), (6), (13), (16), (17), (20), (23), (32), (33) are
% 142.10/21.15 | | inconsistent by sub-proof #533.
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #533 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) op(e0, e0) = e3
% 142.10/21.15 (2) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.10/21.15 all_56_11 & $i(all_56_11))
% 142.10/21.15 (3) op(e2, e2) = all_56_11
% 142.10/21.15 (4) op(e2, e2) = e1
% 142.10/21.15 (5) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.10/21.15 all_56_14 & $i(all_56_14))
% 142.10/21.15 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (7) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.10/21.15 all_56_4 & $i(all_56_4))
% 142.10/21.15 (8) ~ (e3 = e1)
% 142.10/21.15 (9) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.10/21.15 all_56_15 & $i(all_56_15))
% 142.10/21.15 (10) ~ (all_56_11 = e1)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (7) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (11) all_56_11 = e1 & op(e2, e2) = e1
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (11) implies:
% 142.10/21.15 | | (12) all_56_11 = e1
% 142.10/21.15 | |
% 142.10/21.15 | | REDUCE: (10), (12) imply:
% 142.10/21.15 | | (13) $false
% 142.10/21.15 | |
% 142.10/21.15 | | CLOSE: (13) is inconsistent.
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (14) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (14) implies:
% 142.10/21.15 | | (15) ~ (all_56_4 = e2)
% 142.10/21.15 | |
% 142.10/21.15 | | BETA: splitting (5) gives:
% 142.10/21.15 | |
% 142.10/21.15 | | Case 1:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (16) all_56_15 = e1 & op(e0, e0) = e1
% 142.10/21.15 | | |
% 142.10/21.15 | | | ALPHA: (16) implies:
% 142.10/21.15 | | | (17) op(e0, e0) = e1
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (1), (6), (8), (17) are inconsistent by sub-proof #732.
% 142.10/21.15 | | |
% 142.10/21.15 | | Case 2:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (18) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.10/21.15 | | |
% 142.10/21.15 | | | ALPHA: (18) implies:
% 142.10/21.15 | | | (19) ~ (all_56_14 = e0)
% 142.10/21.15 | | | (20) op(e0, e1) = all_56_14
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (2), (3), (4), (6), (9), (15), (19), (20) are inconsistent by
% 142.10/21.15 | | | sub-proof #534.
% 142.10/21.15 | | |
% 142.10/21.15 | | End of split
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #534 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) op(e0, e1) = all_56_14
% 142.10/21.15 (2) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.10/21.15 all_56_11 & $i(all_56_11))
% 142.10/21.15 (3) op(e2, e2) = all_56_11
% 142.10/21.15 (4) ~ (all_56_4 = e2)
% 142.10/21.15 (5) op(e2, e2) = e1
% 142.10/21.15 (6) ~ (all_56_14 = e0)
% 142.10/21.15 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (8) (all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.10/21.15 all_56_15 & $i(all_56_15))
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (8) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (9) all_56_14 = e0 & op(e0, e1) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (9) implies:
% 142.10/21.15 | | (10) op(e0, e1) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (1), (6), (7), (10) are inconsistent by sub-proof #973.
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | |
% 142.10/21.15 | | GROUND_INST: instantiating (7) with e1, all_56_11, e2, e2, simplifying with
% 142.10/21.15 | | (3), (5) gives:
% 142.10/21.15 | | (11) all_56_11 = e1
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (2), (4), (11) are inconsistent by sub-proof #646.
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #535 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) ~ (all_52_8 = all_52_11)
% 142.10/21.15 (2) ~ (all_52_8 = all_52_9)
% 142.10/21.15 (3) op(e0, e0) = e3
% 142.10/21.15 (4) op(e2, e1) = e2
% 142.10/21.15 (5) ~ (all_52_11 = e3)
% 142.10/21.15 (6) all_54_2 = e3 | all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 142.10/21.15 (7) ~ (all_52_9 = all_52_11)
% 142.10/21.15 (8) all_54_2 = all_52_8
% 142.10/21.15 (9) op(e3, e1) = all_52_8
% 142.10/21.15 (10) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.10/21.15 (11) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.10/21.15 all_56_14 & $i(all_56_14))
% 142.10/21.15 (12) op(e0, e1) = all_52_11
% 142.10/21.15 (13) all_54_14 = all_52_11
% 142.10/21.15 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (15) ~ (all_52_8 = e0)
% 142.10/21.15 (16) ~ (e3 = e1)
% 142.10/21.15 (17) op(e3, e1) = all_56_1
% 142.10/21.15 (18) ~ (all_56_1 = e3)
% 142.10/21.15 (19) op(e2, e1) = all_52_9
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (11) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (20) all_56_15 = e1 & op(e0, e0) = e1
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (20) implies:
% 142.10/21.15 | | (21) op(e0, e0) = e1
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (3), (14), (16), (21) are inconsistent by sub-proof #732.
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (22) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (22) implies:
% 142.10/21.15 | | (23) ~ (all_56_14 = e0)
% 142.10/21.15 | | (24) op(e0, e1) = all_56_14
% 142.10/21.15 | |
% 142.10/21.15 | | GROUND_INST: instantiating (14) with all_52_11, all_56_14, e1, e0,
% 142.10/21.15 | | simplifying with (12), (24) gives:
% 142.10/21.15 | | (25) all_56_14 = all_52_11
% 142.10/21.15 | |
% 142.10/21.15 | | GROUND_INST: instantiating (14) with all_52_9, e2, e1, e2, simplifying with
% 142.10/21.15 | | (4), (19) gives:
% 142.10/21.15 | | (26) all_52_9 = e2
% 142.10/21.15 | |
% 142.10/21.15 | | GROUND_INST: instantiating (14) with all_52_8, all_56_1, e1, e3, simplifying
% 142.10/21.15 | | with (9), (17) gives:
% 142.10/21.15 | | (27) all_56_1 = all_52_8
% 142.10/21.15 | |
% 142.10/21.15 | | REDUCE: (18), (27) imply:
% 142.10/21.15 | | (28) ~ (all_52_8 = e3)
% 142.10/21.15 | |
% 142.10/21.15 | | REDUCE: (23), (25) imply:
% 142.10/21.15 | | (29) ~ (all_52_11 = e0)
% 142.10/21.15 | |
% 142.10/21.15 | | REDUCE: (2), (26) imply:
% 142.10/21.15 | | (30) ~ (all_52_8 = e2)
% 142.10/21.15 | |
% 142.10/21.15 | | REDUCE: (7), (26) imply:
% 142.10/21.15 | | (31) ~ (all_52_11 = e2)
% 142.10/21.15 | |
% 142.10/21.15 | | SIMP: (31) implies:
% 142.10/21.15 | | (32) ~ (all_52_11 = e2)
% 142.10/21.15 | |
% 142.10/21.15 | | BETA: splitting (6) gives:
% 142.10/21.15 | |
% 142.10/21.15 | | Case 1:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (33) all_54_2 = e3
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (8), (28), (33) are inconsistent by sub-proof #538.
% 142.10/21.15 | | |
% 142.10/21.15 | | Case 2:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (34) all_54_2 = e2 | all_54_2 = e1 | all_54_2 = e0
% 142.10/21.15 | | |
% 142.10/21.15 | | | BETA: splitting (34) gives:
% 142.10/21.15 | | |
% 142.10/21.15 | | | Case 1:
% 142.10/21.15 | | | |
% 142.10/21.15 | | | | (35) all_54_2 = e2
% 142.10/21.15 | | | |
% 142.10/21.15 | | | | REF_CLOSE: (8), (30), (35) are inconsistent by sub-proof #537.
% 142.10/21.15 | | | |
% 142.10/21.15 | | | Case 2:
% 142.10/21.15 | | | |
% 142.10/21.15 | | | | (36) all_54_2 = e1 | all_54_2 = e0
% 142.10/21.15 | | | |
% 142.10/21.15 | | | | BETA: splitting (36) gives:
% 142.10/21.15 | | | |
% 142.10/21.15 | | | | Case 1:
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | (37) all_54_2 = e1
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | COMBINE_EQS: (8), (37) imply:
% 142.10/21.15 | | | | | (38) all_52_8 = e1
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | SIMP: (38) implies:
% 142.10/21.15 | | | | | (39) all_52_8 = e1
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | REDUCE: (1), (39) imply:
% 142.10/21.15 | | | | | (40) ~ (all_52_11 = e1)
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | SIMP: (40) implies:
% 142.10/21.15 | | | | | (41) ~ (all_52_11 = e1)
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | BETA: splitting (10) gives:
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | Case 1:
% 142.10/21.15 | | | | | |
% 142.10/21.15 | | | | | | (42) all_54_14 = e3
% 142.10/21.15 | | | | | |
% 142.10/21.15 | | | | | | REF_CLOSE: (5), (13), (42) are inconsistent by sub-proof #764.
% 142.10/21.15 | | | | | |
% 142.10/21.15 | | | | | Case 2:
% 142.10/21.15 | | | | | |
% 142.10/21.15 | | | | | | (43) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.10/21.15 | | | | | |
% 142.10/21.15 | | | | | | REF_CLOSE: (13), (29), (32), (41), (43) are inconsistent by
% 142.10/21.15 | | | | | | sub-proof #760.
% 142.10/21.15 | | | | | |
% 142.10/21.15 | | | | | End of split
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | Case 2:
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | (44) all_54_2 = e0
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | | REF_CLOSE: (8), (15), (44) are inconsistent by sub-proof #536.
% 142.10/21.15 | | | | |
% 142.10/21.15 | | | | End of split
% 142.10/21.15 | | | |
% 142.10/21.15 | | | End of split
% 142.10/21.15 | | |
% 142.10/21.15 | | End of split
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #536 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) all_54_2 = all_52_8
% 142.10/21.15 (2) all_54_2 = e0
% 142.10/21.15 (3) ~ (all_52_8 = e0)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (1), (2) imply:
% 142.10/21.15 | (4) all_52_8 = e0
% 142.10/21.15 |
% 142.10/21.15 | SIMP: (4) implies:
% 142.10/21.15 | (5) all_52_8 = e0
% 142.10/21.15 |
% 142.10/21.15 | REDUCE: (3), (5) imply:
% 142.10/21.15 | (6) $false
% 142.10/21.15 |
% 142.10/21.15 | CLOSE: (6) is inconsistent.
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #537 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) all_54_2 = all_52_8
% 142.10/21.15 (2) all_54_2 = e2
% 142.10/21.15 (3) ~ (all_52_8 = e2)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (1), (2) imply:
% 142.10/21.15 | (4) all_52_8 = e2
% 142.10/21.15 |
% 142.10/21.15 | SIMP: (4) implies:
% 142.10/21.15 | (5) all_52_8 = e2
% 142.10/21.15 |
% 142.10/21.15 | REDUCE: (3), (5) imply:
% 142.10/21.15 | (6) $false
% 142.10/21.15 |
% 142.10/21.15 | CLOSE: (6) is inconsistent.
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #538 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) all_54_2 = all_52_8
% 142.10/21.15 (2) all_54_2 = e3
% 142.10/21.15 (3) ~ (all_52_8 = e3)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (1), (2) imply:
% 142.10/21.15 | (4) all_52_8 = e3
% 142.10/21.15 |
% 142.10/21.15 | SIMP: (4) implies:
% 142.10/21.15 | (5) all_52_8 = e3
% 142.10/21.15 |
% 142.10/21.15 | REDUCE: (3), (5) imply:
% 142.10/21.15 | (6) $false
% 142.10/21.15 |
% 142.10/21.15 | CLOSE: (6) is inconsistent.
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #539 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) ~ (e2 = e1)
% 142.10/21.15 (2) op(e0, e0) = e3
% 142.10/21.15 (3) all_57_12 = e3
% 142.10/21.15 (4) op(e1, e1) = e1
% 142.10/21.15 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.10/21.15 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.15 (6) ~ (e1 = e0)
% 142.10/21.15 (7) all_57_13 = e1
% 142.10/21.15 (8) ~ (e2 = e0)
% 142.10/21.15 (9) ~ (e3 = e2)
% 142.10/21.15 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (11) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (11) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (12) all_57_8 = e0 & op(e1, e1) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (12) implies:
% 142.10/21.15 | | (13) op(e1, e1) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (4), (6), (10), (13) are inconsistent by sub-proof #1089.
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (14) all_57_14 = e0 & op(e0, e1) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (14) implies:
% 142.10/21.15 | | (15) all_57_14 = e0
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (10), (15) are inconsistent by
% 142.10/21.15 | | sub-proof #658.
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #540 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) all_57_12 = e3
% 142.10/21.15 (2) ~ (e3 = e0)
% 142.10/21.15 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.15 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.15 (4) ~ (e3 = e2)
% 142.10/21.15 (5) all_57_6 = e1
% 142.10/21.15 (6) ~ (e3 = e1)
% 142.10/21.15 (7) all_57_0 = e0
% 142.10/21.15 (8) all_57_2 = e2
% 142.10/21.15 (9) e3 = e1
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | SIMP: (9) implies:
% 142.10/21.15 | (10) e3 = e1
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (1), (10) imply:
% 142.10/21.15 | (11) all_57_12 = e1
% 142.10/21.15 |
% 142.10/21.15 | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (11) are inconsistent by
% 142.10/21.15 | sub-proof #541.
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #541 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) ~ (e3 = e0)
% 142.10/21.15 (2) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.15 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.15 (3) ~ (e3 = e2)
% 142.10/21.15 (4) all_57_6 = e1
% 142.10/21.15 (5) ~ (e3 = e1)
% 142.10/21.15 (6) all_57_0 = e0
% 142.10/21.15 (7) all_57_2 = e2
% 142.10/21.15 (8) all_57_12 = e1
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (2) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 142.10/21.15 | |
% 142.10/21.15 | | BETA: splitting (9) gives:
% 142.10/21.15 | |
% 142.10/21.15 | | Case 1:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (10) all_57_0 = e3 & op(e3, e3) = e3
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #1108.
% 142.10/21.15 | | |
% 142.10/21.15 | | Case 2:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (11) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (3), (7), (11) are inconsistent by sub-proof #823.
% 142.10/21.15 | | |
% 142.10/21.15 | | End of split
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.10/21.15 | | e3)
% 142.10/21.15 | |
% 142.10/21.15 | | BETA: splitting (12) gives:
% 142.10/21.15 | |
% 142.10/21.15 | | Case 1:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (13) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #1099.
% 142.10/21.15 | | |
% 142.10/21.15 | | Case 2:
% 142.10/21.15 | | |
% 142.10/21.15 | | | (14) all_57_12 = e3 & op(e0, e3) = e3
% 142.10/21.15 | | |
% 142.10/21.15 | | | REF_CLOSE: (5), (8), (14) are inconsistent by sub-proof #798.
% 142.10/21.15 | | |
% 142.10/21.15 | | End of split
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #542 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.15 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.15 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.10/21.15 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.10/21.15 (3) ~ (all_52_4 = e0)
% 142.10/21.15 (4) ~ (e2 = e1)
% 142.10/21.15 (5) ~ (e3 = e0)
% 142.10/21.15 (6) ~ (e1 = e0)
% 142.10/21.15 (7) op(e3, e2) = all_52_4
% 142.10/21.15 (8) ~ (e3 = e2)
% 142.10/21.15 (9) all_57_10 = e0
% 142.10/21.15 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (11) all_57_5 = e2
% 142.10/21.15 (12) ~ (e3 = e1)
% 142.10/21.15 (13) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (13) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (14) all_57_1 = e0 & op(e3, e2) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (3), (7), (10), (14) are inconsistent by sub-proof #1102.
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (15) all_57_3 = e0 & op(e2, e2) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (15) implies:
% 142.10/21.15 | | (16) op(e2, e2) = e0
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (16) are
% 142.10/21.15 | | inconsistent by sub-proof #934.
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #543 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) ~ (e2 = e1)
% 142.10/21.15 (2) all_57_5 = e3
% 142.10/21.15 (3) ~ (e3 = e0)
% 142.10/21.15 (4) op(e1, e1) = e1
% 142.10/21.15 (5) ~ (e2 = e0)
% 142.10/21.15 (6) ~ (e3 = e2)
% 142.10/21.15 (7) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.15 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.15 (8) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.15 (9) all_57_6 = e1
% 142.10/21.15 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (11) ~ (e3 = e1)
% 142.10/21.15 (12) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.15 (13) all_57_11 = e3
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | ALPHA: (12) implies:
% 142.10/21.15 | (14) all_57_5 = e0
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (2), (14) imply:
% 142.10/21.15 | (15) e3 = e0
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (13), (15) imply:
% 142.10/21.15 | (16) all_57_11 = e0
% 142.10/21.15 |
% 142.10/21.15 | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (16) are
% 142.10/21.15 | inconsistent by sub-proof #955.
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #544 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.15 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.15 (2) ~ (all_52_12 = e3)
% 142.10/21.15 (3) ~ (all_52_4 = e0)
% 142.10/21.15 (4) ~ (e2 = e1)
% 142.10/21.15 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 142.10/21.15 (6) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.15 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.15 (7) op(e2, e2) = e1
% 142.10/21.15 (8) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.15 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.15 (9) ~ (e3 = e0)
% 142.10/21.15 (10) op(e1, e1) = e1
% 142.10/21.15 (11) op(e3, e1) = all_52_8
% 142.10/21.15 (12) all_57_3 = e1
% 142.10/21.15 (13) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.15 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.15 (14) ~ (e1 = e0)
% 142.10/21.15 (15) op(e3, e2) = all_52_4
% 142.10/21.15 (16) ~ (e2 = e0)
% 142.10/21.15 (17) ~ (e3 = e2)
% 142.10/21.15 (18) op(e3, e0) = all_52_12
% 142.10/21.15 (19) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.15 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (21) ~ (all_52_8 = e0)
% 142.10/21.15 (22) ~ (e3 = e1)
% 142.10/21.15 (23) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.15 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.15 (24) all_57_0 = e0
% 142.10/21.15 (25) op(e3, e3) = e0
% 142.10/21.15 (26) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.15 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | BETA: splitting (5) gives:
% 142.10/21.15 |
% 142.10/21.15 | Case 1:
% 142.10/21.15 | |
% 142.10/21.15 | | (27) all_57_0 = e1 & op(e3, e3) = e1
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (27) implies:
% 142.10/21.15 | | (28) op(e3, e3) = e1
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (14), (20), (25), (28) are inconsistent by sub-proof #840.
% 142.10/21.15 | |
% 142.10/21.15 | Case 2:
% 142.10/21.15 | |
% 142.10/21.15 | | (29) all_57_1 = e1 & op(e3, e2) = e1
% 142.10/21.15 | |
% 142.10/21.15 | | ALPHA: (29) implies:
% 142.10/21.15 | | (30) all_57_1 = e1
% 142.10/21.15 | |
% 142.10/21.15 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.10/21.15 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 142.10/21.15 | | (26), (30) are inconsistent by sub-proof #618.
% 142.10/21.15 | |
% 142.10/21.15 | End of split
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #545 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.15 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.15 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.15 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.15 (3) op(e1, e3) = all_52_2
% 142.10/21.15 (4) ~ (all_52_12 = e3)
% 142.10/21.15 (5) ~ (all_52_4 = e0)
% 142.10/21.15 (6) ~ (e2 = e1)
% 142.10/21.15 (7) op(e0, e0) = e3
% 142.10/21.15 (8) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.15 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.15 (9) all_57_12 = e3
% 142.10/21.15 (10) op(e2, e2) = e1
% 142.10/21.15 (11) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.15 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.15 (12) ~ (all_52_1 = e0)
% 142.10/21.15 (13) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.15 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.15 (14) ~ (e3 = e0)
% 142.10/21.15 (15) op(e1, e1) = e1
% 142.10/21.15 (16) op(e3, e1) = all_52_8
% 142.10/21.15 (17) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.15 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.15 (18) op(e2, e3) = all_52_1
% 142.10/21.15 (19) ~ (all_52_12 = e0)
% 142.10/21.15 (20) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.15 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.15 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.15 (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.15 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.15 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.15 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.15 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.15 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.15 (24) all_57_3 = e1
% 142.10/21.15 (25) all_28_2 = e0
% 142.10/21.15 (26) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.15 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.15 (27) ~ (e1 = e0)
% 142.10/21.15 (28) op(e3, e2) = all_52_4
% 142.10/21.15 (29) ~ (e2 = e0)
% 142.10/21.15 (30) ~ (e3 = e2)
% 142.10/21.15 (31) op(e3, e0) = all_52_12
% 142.10/21.15 (32) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.15 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.15 (33) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.15 (34) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.15 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.15 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.15 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.15 (36) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.15 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.15 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.15 (37) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.15 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.15 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.15 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.15 (38) ~ (all_52_8 = e0)
% 142.10/21.15 (39) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.15 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.15 (40) ~ (e3 = e1)
% 142.10/21.15 (41) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.15 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.15 (42) all_57_0 = e0
% 142.10/21.15 (43) op(e3, e3) = e0
% 142.10/21.15 (44) all_57_11 = e3
% 142.10/21.15 (45) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.15 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.15 (46) e3 = e1
% 142.10/21.15 (47) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.15 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.15 (48) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.15 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.15
% 142.10/21.15 Begin of proof
% 142.10/21.15 |
% 142.10/21.15 | SIMP: (46) implies:
% 142.10/21.15 | (49) e3 = e1
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (9), (49) imply:
% 142.10/21.15 | (50) all_57_12 = e1
% 142.10/21.15 |
% 142.10/21.15 | COMBINE_EQS: (44), (49) imply:
% 142.10/21.15 | (51) all_57_11 = e1
% 142.10/21.15 |
% 142.10/21.15 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 142.10/21.15 | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 142.10/21.15 | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 142.10/21.15 | (36), (37), (38), (39), (40), (41), (42), (43), (45), (47), (48),
% 142.10/21.15 | (50), (51) are inconsistent by sub-proof #569.
% 142.10/21.15 |
% 142.10/21.15 End of proof
% 142.10/21.15
% 142.10/21.15 Sub-proof #546 shows that the following formulas are inconsistent:
% 142.10/21.15 ----------------------------------------------------------------
% 142.10/21.15 (1) ~ (e2 = e1)
% 142.10/21.15 (2) all_57_5 = e3
% 142.10/21.15 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.15 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.15 (4) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.15 (5) ~ (e3 = e0)
% 142.10/21.15 (6) op(e1, e1) = e1
% 142.10/21.16 (7) op(e3, e1) = all_52_8
% 142.10/21.16 (8) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.10/21.16 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.10/21.16 all_14_1 & $i(all_14_1))
% 142.10/21.16 (9) op(e1, e3) = e2
% 142.10/21.16 (10) ~ (e1 = e0)
% 142.10/21.16 (11) ~ (e2 = e0)
% 142.10/21.16 (12) ~ (e3 = e2)
% 142.10/21.16 (13) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.16 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.16 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.16 (15) ~ (all_52_8 = e0)
% 142.10/21.16 (16) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.10/21.16 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 142.10/21.16 e0) = all_28_1 & $i(all_28_1))
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (4) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (17) all_57_4 = e1 & op(e3, e1) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (17) implies:
% 142.10/21.16 | | (18) all_57_4 = e1
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (10), (11), (12), (13), (14), (15),
% 142.10/21.16 | | (18) are inconsistent by sub-proof #628.
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (19) all_57_9 = e1 & op(e3, e0) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (19) implies:
% 142.10/21.16 | | (20) op(e3, e0) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (8), (9), (14), (16), (20) are inconsistent by sub-proof #683.
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #547 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) ~ (all_52_4 = e0)
% 142.10/21.16 (2) ~ (e2 = e1)
% 142.10/21.16 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1)
% 142.10/21.16 (4) op(e2, e2) = e1
% 142.10/21.16 (5) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.16 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.16 (6) ~ (e3 = e0)
% 142.10/21.16 (7) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.16 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.16 (8) ~ (e1 = e0)
% 142.10/21.16 (9) op(e3, e2) = all_52_4
% 142.10/21.16 (10) ~ (e2 = e0)
% 142.10/21.16 (11) ~ (e3 = e2)
% 142.10/21.16 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.16 (13) op(e3, e3) = e0
% 142.10/21.16 (14) all_57_7 = e3
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (3) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (15) all_57_0 = e1 & op(e3, e3) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (15) implies:
% 142.10/21.16 | | (16) op(e3, e3) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (8), (12), (13), (16) are inconsistent by sub-proof #840.
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (17) all_57_1 = e1 & op(e3, e2) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (17) implies:
% 142.10/21.16 | | (18) all_57_1 = e1
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 142.10/21.16 | | (18) are inconsistent by sub-proof #619.
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #548 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.16 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.16 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.10/21.16 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.10/21.16 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.16 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.16 (4) op(e1, e3) = all_52_2
% 142.10/21.16 (5) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.16 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.10/21.16 (6) all_57_6 = e3
% 142.10/21.16 (7) ~ (all_52_12 = e3)
% 142.10/21.16 (8) op(e1, e2) = all_52_6
% 142.10/21.16 (9) ~ (all_52_14 = e3)
% 142.10/21.16 (10) ~ (all_52_4 = e0)
% 142.10/21.16 (11) ~ (e2 = e1)
% 142.10/21.16 (12) all_54_11 = all_52_14
% 142.10/21.16 (13) op(e0, e0) = e3
% 142.10/21.16 (14) op(e0, e3) = all_52_3
% 142.10/21.16 (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.16 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.16 (16) op(e2, e2) = e1
% 142.10/21.16 (17) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.10/21.16 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.16 e1)
% 142.10/21.16 (18) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.16 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.16 (19) ~ (all_52_1 = e0)
% 142.10/21.16 (20) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.16 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.16 (21) ~ (e3 = e0)
% 142.10/21.16 (22) op(e1, e1) = e1
% 142.10/21.16 (23) op(e1, e1) = all_4_2
% 142.10/21.16 (24) op(e3, e1) = all_52_8
% 142.10/21.16 (25) ~ (all_52_12 = all_52_14)
% 142.10/21.16 (26) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.16 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.16 (27) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.16 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.16 e2)
% 142.10/21.16 (28) op(e2, e3) = all_52_1
% 142.10/21.16 (29) ~ (all_52_12 = e0)
% 142.10/21.16 (30) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.16 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.16 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.16 (31) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.16 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.16 (32) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.16 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.16 (33) ~ (all_52_6 = all_52_14)
% 142.10/21.16 (34) ~ (all_52_13 = all_52_14)
% 142.10/21.16 (35) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.16 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.16 (36) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.16 (37) all_57_3 = e1
% 142.10/21.16 (38) ~ (all_4_2 = e3)
% 142.10/21.16 (39) all_28_2 = e0
% 142.10/21.16 (40) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.16 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.16 (41) ~ (e1 = e0)
% 142.10/21.16 (42) ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 142.10/21.16 all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e1) & op(e0,
% 142.10/21.16 e3) = all_46_1 & $i(all_46_1))
% 142.10/21.16 (43) op(e3, e2) = all_52_4
% 142.10/21.16 (44) ~ (e2 = e0)
% 142.10/21.16 (45) ~ (e3 = e2)
% 142.10/21.16 (46) op(e3, e0) = all_52_12
% 142.10/21.16 (47) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.16 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.16 (48) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.16 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.16 (49) ~ (all_4_2 = e2)
% 142.10/21.16 (50) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.16 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.16 (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.16 (52) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.16 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.16 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.16 (53) ~ (all_52_3 = e0)
% 142.10/21.16 (54) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.16 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.16 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.16 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.16 (55) ~ (all_52_8 = e0)
% 142.10/21.16 (56) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.16 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.16 (57) ~ (e3 = e1)
% 142.10/21.16 (58) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.16 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.16 (59) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 142.10/21.16 all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0,
% 142.10/21.16 e3) = all_42_1 & $i(all_42_1))
% 142.10/21.16 (60) all_57_2 = e1
% 142.10/21.16 (61) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.10/21.16 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 142.10/21.16 e0) = all_28_1 & $i(all_28_1))
% 142.10/21.16 (62) ~ (all_52_9 = e1)
% 142.10/21.16 (63) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.16 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.16 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.16 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.16 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.16 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.16 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.16 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.16 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.16 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.16 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.16 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.16 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.16 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.16 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.16 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.16 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.16 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.16 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.16 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.16 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.16 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.16 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.16 $i(all_56_14))))
% 142.10/21.16 (64) all_57_0 = e0
% 142.10/21.16 (65) op(e3, e3) = e0
% 142.10/21.16 (66) op(e2, e1) = all_52_9
% 142.10/21.16 (67) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.16 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.16 (68) op(e2, e0) = all_52_13
% 142.10/21.16 (69) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.16 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.16 (70) all_57_12 = e2
% 142.10/21.16 (71) op(e1, e0) = all_52_14
% 142.10/21.16 (72) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.16 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (17) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (73) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.10/21.16 | | e1)
% 142.10/21.16 | |
% 142.10/21.16 | | BETA: splitting (73) gives:
% 142.10/21.16 | |
% 142.10/21.16 | | Case 1:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (74) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13),
% 142.10/21.16 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.10/21.16 | | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33),
% 142.10/21.16 | | | (34), (35), (36), (37), (38), (39), (40), (41), (42), (43),
% 142.10/21.16 | | | (44), (45), (46), (47), (48), (49), (50), (51), (52), (53),
% 142.10/21.16 | | | (54), (55), (56), (57), (58), (59), (61), (62), (63), (64),
% 142.10/21.16 | | | (65), (66), (67), (68), (69), (71), (72), (74) are inconsistent
% 142.10/21.16 | | | by sub-proof #554.
% 142.10/21.16 | | |
% 142.10/21.16 | | Case 2:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (75) all_57_13 = e1 & op(e0, e2) = e1
% 142.10/21.16 | | |
% 142.10/21.16 | | | ALPHA: (75) implies:
% 142.10/21.16 | | | (76) all_57_13 = e1
% 142.10/21.16 | | |
% 142.10/21.16 | | | BETA: splitting (1) gives:
% 142.10/21.16 | | |
% 142.10/21.16 | | | Case 1:
% 142.10/21.16 | | | |
% 142.10/21.16 | | | | (77) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 142.10/21.16 | | | | = e3)
% 142.10/21.16 | | | |
% 142.10/21.16 | | | | REF_CLOSE: (37), (57), (60), (77) are inconsistent by sub-proof #553.
% 142.10/21.16 | | | |
% 142.10/21.16 | | | Case 2:
% 142.10/21.16 | | | |
% 142.10/21.16 | | | | (78) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 142.10/21.16 | | | | = e3)
% 142.10/21.16 | | | |
% 142.10/21.16 | | | | BETA: splitting (78) gives:
% 142.10/21.16 | | | |
% 142.10/21.16 | | | | Case 1:
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | (79) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | ALPHA: (79) implies:
% 142.10/21.16 | | | | | (80) all_57_5 = e3
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | BETA: splitting (54) gives:
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | Case 1:
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | (81) all_57_15 = e0 & op(e0, e0) = e0
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | ALPHA: (81) implies:
% 142.10/21.16 | | | | | | (82) op(e0, e0) = e0
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | REF_CLOSE: (13), (21), (51), (82) are inconsistent by sub-proof
% 142.10/21.16 | | | | | | #751.
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | Case 2:
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | (83) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 142.10/21.16 | | | | | | op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.10/21.16 | | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.16 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | ALPHA: (83) implies:
% 142.10/21.16 | | | | | | (84) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.16 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | BETA: splitting (5) gives:
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | | Case 1:
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | | (85) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 &
% 142.10/21.16 | | | | | | | op(e2, e2) = e2)
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | | BETA: splitting (85) gives:
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | | Case 1:
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | (86) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | ALPHA: (86) implies:
% 142.10/21.16 | | | | | | | | (87) all_57_2 = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | COMBINE_EQS: (60), (87) imply:
% 142.10/21.16 | | | | | | | | (88) e2 = e1
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | SIMP: (88) implies:
% 142.10/21.16 | | | | | | | | (89) e2 = e1
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | COMBINE_EQS: (70), (89) imply:
% 142.10/21.16 | | | | | | | | (90) all_57_12 = e1
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | BETA: splitting (27) gives:
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | Case 1:
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | | (91) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 142.10/21.16 | | | | | | | | | op(e0, e2) = e2)
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | | BETA: splitting (91) gives:
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | | Case 1:
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | (92) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | REF_CLOSE: (11), (70), (90) are inconsistent by sub-proof
% 142.10/21.16 | | | | | | | | | | #970.
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | Case 2:
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | (93) all_57_13 = e2 & op(e0, e2) = e2
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | REF_CLOSE: (11), (76), (93) are inconsistent by sub-proof
% 142.10/21.16 | | | | | | | | | | #552.
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | End of split
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | Case 2:
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | | (94) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 142.10/21.16 | | | | | | | | | op(e0, e0) = e2)
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | | BETA: splitting (94) gives:
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | | Case 1:
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | (95) all_57_14 = e2 & op(e0, e1) = e2
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | ALPHA: (95) implies:
% 142.10/21.16 | | | | | | | | | | (96) all_57_14 = e2
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | REF_CLOSE: (14), (41), (44), (51), (53), (76), (84), (96) are
% 142.10/21.16 | | | | | | | | | | inconsistent by sub-proof #551.
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | Case 2:
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | (97) all_57_15 = e2 & op(e0, e0) = e2
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | ALPHA: (97) implies:
% 142.10/21.16 | | | | | | | | | | (98) op(e0, e0) = e2
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | | REF_CLOSE: (13), (45), (51), (98) are inconsistent by
% 142.10/21.16 | | | | | | | | | | sub-proof #1066.
% 142.10/21.16 | | | | | | | | | |
% 142.10/21.16 | | | | | | | | | End of split
% 142.10/21.16 | | | | | | | | |
% 142.10/21.16 | | | | | | | | End of split
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | Case 2:
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | (99) all_57_3 = e2 & op(e2, e2) = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | ALPHA: (99) implies:
% 142.10/21.16 | | | | | | | | (100) op(e2, e2) = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | REF_CLOSE: (11), (16), (51), (100) are inconsistent by sub-proof
% 142.10/21.16 | | | | | | | | #749.
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | End of split
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | Case 2:
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | | (101) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 &
% 142.10/21.16 | | | | | | | op(e2, e0) = e2)
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | | BETA: splitting (101) gives:
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | | Case 1:
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | (102) all_57_5 = e2 & op(e2, e1) = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | ALPHA: (102) implies:
% 142.10/21.16 | | | | | | | | (103) all_57_5 = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | COMBINE_EQS: (80), (103) imply:
% 142.10/21.16 | | | | | | | | (104) e3 = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | COMBINE_EQS: (6), (104) imply:
% 142.10/21.16 | | | | | | | | (105) all_57_6 = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | REF_CLOSE: (11), (21), (32), (35), (41), (45), (51), (57), (64),
% 142.10/21.16 | | | | | | | | (65), (70), (105) are inconsistent by sub-proof #550.
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | Case 2:
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | (106) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | ALPHA: (106) implies:
% 142.10/21.16 | | | | | | | | (107) all_57_10 = e2
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | | REF_CLOSE: (16), (19), (21), (28), (41), (44), (51), (72), (80),
% 142.10/21.16 | | | | | | | | (107) are inconsistent by sub-proof #562.
% 142.10/21.16 | | | | | | | |
% 142.10/21.16 | | | | | | | End of split
% 142.10/21.16 | | | | | | |
% 142.10/21.16 | | | | | | End of split
% 142.10/21.16 | | | | | |
% 142.10/21.16 | | | | | End of split
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | Case 2:
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | (108) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | ALPHA: (108) implies:
% 142.10/21.16 | | | | | (109) all_57_10 = e3
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | | REF_CLOSE: (11), (13), (18), (21), (41), (44), (45), (51), (54), (56),
% 142.10/21.16 | | | | | (57), (109) are inconsistent by sub-proof #650.
% 142.10/21.16 | | | | |
% 142.10/21.16 | | | | End of split
% 142.10/21.16 | | | |
% 142.10/21.16 | | | End of split
% 142.10/21.16 | | |
% 142.10/21.16 | | End of split
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (110) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.16 | | e1)
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (3), (11), (13), (15), (21), (22), (24), (41), (44), (45), (50),
% 142.10/21.16 | | (51), (55), (57), (110) are inconsistent by sub-proof #549.
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #549 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.16 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.16 (2) ~ (e2 = e1)
% 142.10/21.16 (3) op(e0, e0) = e3
% 142.10/21.16 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.16 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.16 (5) ~ (e3 = e0)
% 142.10/21.16 (6) op(e1, e1) = e1
% 142.10/21.16 (7) op(e3, e1) = all_52_8
% 142.10/21.16 (8) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.16 (9) ~ (e1 = e0)
% 142.10/21.16 (10) ~ (e2 = e0)
% 142.10/21.16 (11) ~ (e3 = e2)
% 142.10/21.16 (12) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.16 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.16 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.16 (14) ~ (all_52_8 = e0)
% 142.10/21.16 (15) ~ (e3 = e1)
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (8) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (16) all_57_14 = e1 & op(e0, e1) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (16) implies:
% 142.10/21.16 | | (17) all_57_14 = e1
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 142.10/21.16 | | (15), (17) are inconsistent by sub-proof #602.
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (18) all_57_15 = e1 & op(e0, e0) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (18) implies:
% 142.10/21.16 | | (19) op(e0, e0) = e1
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (3), (13), (15), (19) are inconsistent by sub-proof #732.
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #550 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) ~ (e2 = e1)
% 142.10/21.16 (2) ~ (e3 = e0)
% 142.10/21.16 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.16 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.16 (4) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.16 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.16 (5) ~ (e1 = e0)
% 142.10/21.16 (6) all_57_6 = e2
% 142.10/21.16 (7) ~ (e3 = e2)
% 142.10/21.16 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.16 (9) ~ (e3 = e1)
% 142.10/21.16 (10) all_57_0 = e0
% 142.10/21.16 (11) op(e3, e3) = e0
% 142.10/21.16 (12) all_57_12 = e2
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (3) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 142.10/21.16 | | e3)
% 142.10/21.16 | |
% 142.10/21.16 | | BETA: splitting (13) gives:
% 142.10/21.16 | |
% 142.10/21.16 | | Case 1:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (14) all_57_0 = e3 & op(e3, e3) = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #1108.
% 142.10/21.16 | | |
% 142.10/21.16 | | Case 2:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (15) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | ALPHA: (15) implies:
% 142.10/21.16 | | | (16) all_57_2 = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (1), (4), (5), (6), (8), (9), (11), (12), (16) are inconsistent
% 142.10/21.16 | | | by sub-proof #698.
% 142.10/21.16 | | |
% 142.10/21.16 | | End of split
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (17) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.10/21.16 | | e3)
% 142.10/21.16 | |
% 142.10/21.16 | | BETA: splitting (17) gives:
% 142.10/21.16 | |
% 142.10/21.16 | | Case 1:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (18) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | ALPHA: (18) implies:
% 142.10/21.16 | | | (19) all_57_6 = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (6), (7), (19) are inconsistent by sub-proof #1004.
% 142.10/21.16 | | |
% 142.10/21.16 | | Case 2:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (20) all_57_12 = e3 & op(e0, e3) = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | ALPHA: (20) implies:
% 142.10/21.16 | | | (21) all_57_12 = e3
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #772.
% 142.10/21.16 | | |
% 142.10/21.16 | | End of split
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #551 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) op(e0, e3) = all_52_3
% 142.10/21.16 (2) all_57_14 = e2
% 142.10/21.16 (3) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.10/21.16 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.16 (4) ~ (e1 = e0)
% 142.10/21.16 (5) all_57_13 = e1
% 142.10/21.16 (6) ~ (e2 = e0)
% 142.10/21.16 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.16 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.16 (8) ~ (all_52_3 = e0)
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (3) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (9) all_57_12 = e0 & op(e0, e3) = e0
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (9) implies:
% 142.10/21.16 | | (10) op(e0, e3) = e0
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (1), (7), (8), (10) are inconsistent by sub-proof #986.
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (11) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.10/21.16 | | e0)
% 142.10/21.16 | |
% 142.10/21.16 | | BETA: splitting (11) gives:
% 142.10/21.16 | |
% 142.10/21.16 | | Case 1:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (12) all_57_13 = e0 & op(e0, e2) = e0
% 142.10/21.16 | | |
% 142.10/21.16 | | | ALPHA: (12) implies:
% 142.10/21.16 | | | (13) all_57_13 = e0
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (4), (5), (13) are inconsistent by sub-proof #721.
% 142.10/21.16 | | |
% 142.10/21.16 | | Case 2:
% 142.10/21.16 | | |
% 142.10/21.16 | | | (14) all_57_14 = e0 & op(e0, e1) = e0
% 142.10/21.16 | | |
% 142.10/21.16 | | | REF_CLOSE: (2), (6), (14) are inconsistent by sub-proof #920.
% 142.10/21.16 | | |
% 142.10/21.16 | | End of split
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #552 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) all_57_13 = e2 & op(e0, e2) = e2
% 142.10/21.16 (2) all_57_13 = e1
% 142.10/21.16 (3) ~ (e2 = e1)
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | ALPHA: (1) implies:
% 142.10/21.16 | (4) all_57_13 = e2
% 142.10/21.16 |
% 142.10/21.16 | COMBINE_EQS: (2), (4) imply:
% 142.10/21.16 | (5) e2 = e1
% 142.10/21.16 |
% 142.10/21.16 | REDUCE: (3), (5) imply:
% 142.10/21.16 | (6) $false
% 142.10/21.16 |
% 142.10/21.16 | CLOSE: (6) is inconsistent.
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #553 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.10/21.16 (2) all_57_2 = e1
% 142.10/21.16 (3) ~ (e3 = e1)
% 142.10/21.16 (4) all_57_3 = e1
% 142.10/21.16
% 142.10/21.16 Begin of proof
% 142.10/21.16 |
% 142.10/21.16 | BETA: splitting (1) gives:
% 142.10/21.16 |
% 142.10/21.16 | Case 1:
% 142.10/21.16 | |
% 142.10/21.16 | | (5) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (5) implies:
% 142.10/21.16 | | (6) all_57_2 = e3
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #701.
% 142.10/21.16 | |
% 142.10/21.16 | Case 2:
% 142.10/21.16 | |
% 142.10/21.16 | | (7) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.16 | |
% 142.10/21.16 | | ALPHA: (7) implies:
% 142.10/21.16 | | (8) all_57_3 = e3
% 142.10/21.16 | |
% 142.10/21.16 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #591.
% 142.10/21.16 | |
% 142.10/21.16 | End of split
% 142.10/21.16 |
% 142.10/21.16 End of proof
% 142.10/21.16
% 142.10/21.16 Sub-proof #554 shows that the following formulas are inconsistent:
% 142.10/21.16 ----------------------------------------------------------------
% 142.10/21.16 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.16 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.16 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.10/21.16 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.10/21.16 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.16 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.16 (4) op(e1, e3) = all_52_2
% 142.10/21.16 (5) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.16 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.10/21.16 (6) ~ (all_52_12 = e3)
% 142.10/21.16 (7) op(e1, e2) = all_52_6
% 142.10/21.16 (8) ~ (all_52_14 = e3)
% 142.10/21.16 (9) ~ (all_52_4 = e0)
% 142.10/21.16 (10) ~ (e2 = e1)
% 142.10/21.16 (11) all_54_11 = all_52_14
% 142.10/21.17 (12) op(e0, e0) = e3
% 142.10/21.17 (13) op(e0, e3) = all_52_3
% 142.10/21.17 (14) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.17 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.17 (15) op(e2, e2) = e1
% 142.10/21.17 (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.10/21.17 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.17 e1)
% 142.10/21.17 (17) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.17 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.17 (18) ~ (all_52_1 = e0)
% 142.10/21.17 (19) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.17 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.17 (20) ~ (e3 = e0)
% 142.10/21.17 (21) op(e1, e1) = e1
% 142.10/21.17 (22) op(e1, e1) = all_4_2
% 142.10/21.17 (23) op(e3, e1) = all_52_8
% 142.10/21.17 (24) ~ (all_52_12 = all_52_14)
% 142.10/21.17 (25) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.17 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.17 (26) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.17 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.17 e2)
% 142.10/21.17 (27) op(e2, e3) = all_52_1
% 142.10/21.17 (28) ~ (all_52_12 = e0)
% 142.10/21.17 (29) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.17 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.17 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.17 (30) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.17 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.17 (31) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.17 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.17 (32) ~ (all_52_6 = all_52_14)
% 142.10/21.17 (33) ~ (all_52_13 = all_52_14)
% 142.10/21.17 (34) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.17 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.17 (35) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.17 (36) all_57_3 = e1
% 142.10/21.17 (37) ~ (all_4_2 = e3)
% 142.10/21.17 (38) all_28_2 = e0
% 142.10/21.17 (39) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.17 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.17 (40) ~ (e1 = e0)
% 142.10/21.17 (41) ( ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 142.10/21.17 all_46_1 & $i(all_46_0) & $i(all_46_1)) | ( ~ (all_46_1 = e1) & op(e0,
% 142.10/21.17 e3) = all_46_1 & $i(all_46_1))
% 142.10/21.17 (42) op(e3, e2) = all_52_4
% 142.10/21.17 (43) ~ (e2 = e0)
% 142.10/21.17 (44) ~ (e3 = e2)
% 142.10/21.17 (45) op(e3, e0) = all_52_12
% 142.10/21.17 (46) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.17 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.17 (47) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.17 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.17 (48) ~ (all_4_2 = e2)
% 142.10/21.17 (49) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.17 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.17 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.17 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.17 (51) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.17 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.17 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.17 (52) ~ (all_52_3 = e0)
% 142.10/21.17 (53) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.17 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.17 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.17 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.17 (54) ~ (all_52_8 = e0)
% 142.10/21.17 (55) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.17 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.17 (56) ~ (e3 = e1)
% 142.10/21.17 (57) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.17 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.17 (58) ( ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0, e3) =
% 142.10/21.17 all_42_1 & $i(all_42_0) & $i(all_42_1)) | ( ~ (all_42_1 = e2) & op(e0,
% 142.10/21.17 e3) = all_42_1 & $i(all_42_1))
% 142.10/21.17 (59) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.10/21.17 all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3,
% 142.10/21.17 e0) = all_28_1 & $i(all_28_1))
% 142.10/21.17 (60) ~ (all_52_9 = e1)
% 142.10/21.17 (61) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.17 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.17 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.17 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.17 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.17 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.17 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.17 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.17 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.17 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.17 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.17 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.17 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.17 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.17 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.17 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.17 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.17 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.17 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.17 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.17 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.17 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.17 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.17 $i(all_56_14))))
% 142.10/21.17 (62) all_57_0 = e0
% 142.10/21.17 (63) op(e3, e3) = e0
% 142.10/21.17 (64) op(e2, e1) = all_52_9
% 142.10/21.17 (65) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.17 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.17 (66) all_57_12 = e1 & op(e0, e3) = e1
% 142.10/21.17 (67) op(e2, e0) = all_52_13
% 142.10/21.17 (68) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.17 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.17 (69) op(e1, e0) = all_52_14
% 142.10/21.17 (70) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.17 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.17
% 142.10/21.17 Begin of proof
% 142.10/21.17 |
% 142.10/21.17 | ALPHA: (66) implies:
% 142.10/21.17 | (71) all_57_12 = e1
% 142.10/21.17 | (72) op(e0, e3) = e1
% 142.10/21.17 |
% 142.10/21.17 | BETA: splitting (55) gives:
% 142.10/21.17 |
% 142.10/21.17 | Case 1:
% 142.10/21.17 | |
% 142.10/21.17 | | (73) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 142.10/21.17 | | e1)
% 142.10/21.17 | |
% 142.10/21.17 | | BETA: splitting (73) gives:
% 142.10/21.17 | |
% 142.10/21.17 | | Case 1:
% 142.10/21.17 | | |
% 142.10/21.17 | | | (74) all_57_9 = e1 & op(e3, e0) = e1
% 142.10/21.17 | | |
% 142.10/21.17 | | | ALPHA: (74) implies:
% 142.10/21.17 | | | (75) all_57_9 = e1
% 142.10/21.17 | | | (76) op(e3, e0) = e1
% 142.10/21.17 | | |
% 142.10/21.17 | | | GROUND_INST: instantiating (50) with all_52_3, e1, e3, e0, simplifying
% 142.10/21.17 | | | with (13), (72) gives:
% 142.10/21.17 | | | (77) all_52_3 = e1
% 142.10/21.17 | | |
% 142.10/21.17 | | | GROUND_INST: instantiating (50) with all_52_12, e1, e0, e3, simplifying
% 142.10/21.17 | | | with (45), (76) gives:
% 142.10/21.17 | | | (78) all_52_12 = e1
% 142.10/21.17 | | |
% 142.10/21.17 | | | REDUCE: (24), (78) imply:
% 142.10/21.17 | | | (79) ~ (all_52_14 = e1)
% 142.10/21.17 | | |
% 142.10/21.17 | | | SIMP: (79) implies:
% 142.10/21.17 | | | (80) ~ (all_52_14 = e1)
% 142.10/21.17 | | |
% 142.10/21.17 | | | REDUCE: (6), (78) imply:
% 142.10/21.17 | | | (81) ~ (e3 = e1)
% 142.10/21.17 | | |
% 142.10/21.17 | | | BETA: splitting (41) gives:
% 142.10/21.17 | | |
% 142.10/21.17 | | | Case 1:
% 142.10/21.17 | | | |
% 142.10/21.17 | | | | (82) ~ (all_46_0 = e2) & op(all_46_1, e0) = all_46_0 & op(e0, e3) =
% 142.10/21.17 | | | | all_46_1 & $i(all_46_0) & $i(all_46_1)
% 142.10/21.17 | | | |
% 142.10/21.17 | | | | ALPHA: (82) implies:
% 142.10/21.17 | | | | (83) ~ (all_46_0 = e2)
% 142.10/21.17 | | | | (84) op(e0, e3) = all_46_1
% 142.10/21.17 | | | | (85) op(all_46_1, e0) = all_46_0
% 142.10/21.17 | | | |
% 142.10/21.17 | | | | BETA: splitting (59) gives:
% 142.10/21.17 | | | |
% 142.10/21.17 | | | | Case 1:
% 142.10/21.17 | | | | |
% 142.10/21.17 | | | | | (86) ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0)
% 142.10/21.17 | | | | | = all_28_1 & $i(all_28_0) & $i(all_28_1)
% 142.10/21.17 | | | | |
% 142.10/21.17 | | | | | ALPHA: (86) implies:
% 142.10/21.17 | | | | | (87) ~ (all_28_0 = e2)
% 142.10/21.17 | | | | | (88) op(e3, e0) = all_28_1
% 142.10/21.17 | | | | | (89) op(all_28_1, e3) = all_28_0
% 142.10/21.17 | | | | |
% 142.10/21.17 | | | | | BETA: splitting (58) gives:
% 142.10/21.17 | | | | |
% 142.10/21.17 | | | | | Case 1:
% 142.10/21.17 | | | | | |
% 142.10/21.17 | | | | | | (90) ~ (all_42_0 = e1) & op(all_42_1, e0) = all_42_0 & op(e0,
% 142.10/21.17 | | | | | | e3) = all_42_1 & $i(all_42_0) & $i(all_42_1)
% 142.10/21.17 | | | | | |
% 142.10/21.17 | | | | | | ALPHA: (90) implies:
% 142.10/21.17 | | | | | | (91) op(e0, e3) = all_42_1
% 142.10/21.17 | | | | | | (92) op(all_42_1, e0) = all_42_0
% 142.10/21.17 | | | | | |
% 142.10/21.17 | | | | | | BETA: splitting (29) gives:
% 142.10/21.17 | | | | | |
% 142.10/21.17 | | | | | | Case 1:
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | (93) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3,
% 142.10/21.17 | | | | | | | e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | ALPHA: (93) implies:
% 142.10/21.17 | | | | | | | (94) op(e3, e0) = all_14_1
% 142.10/21.17 | | | | | | | (95) op(all_14_1, e3) = all_14_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with e1, all_46_1, e3, e0,
% 142.10/21.17 | | | | | | | simplifying with (72), (84) gives:
% 142.10/21.17 | | | | | | | (96) all_46_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_42_1, all_46_1, e3, e0,
% 142.10/21.17 | | | | | | | simplifying with (84), (91) gives:
% 142.10/21.17 | | | | | | | (97) all_46_1 = all_42_1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with e1, all_28_1, e0, e3,
% 142.10/21.17 | | | | | | | simplifying with (76), (88) gives:
% 142.10/21.17 | | | | | | | (98) all_28_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_14_1, all_28_1, e0, e3,
% 142.10/21.17 | | | | | | | simplifying with (88), (94) gives:
% 142.10/21.17 | | | | | | | (99) all_28_1 = all_14_1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (96), (97) imply:
% 142.10/21.17 | | | | | | | (100) all_42_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | SIMP: (100) implies:
% 142.10/21.17 | | | | | | | (101) all_42_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (98), (99) imply:
% 142.10/21.17 | | | | | | | (102) all_14_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | SIMP: (102) implies:
% 142.10/21.17 | | | | | | | (103) all_14_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (85), (96) imply:
% 142.10/21.17 | | | | | | | (104) op(e1, e0) = all_46_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (92), (101) imply:
% 142.10/21.17 | | | | | | | (105) op(e1, e0) = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (89), (98) imply:
% 142.10/21.17 | | | | | | | (106) op(e1, e3) = all_28_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (95), (103) imply:
% 142.10/21.17 | | | | | | | (107) op(e1, e3) = all_14_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_52_14, all_42_0, e0, e1,
% 142.10/21.17 | | | | | | | simplifying with (69), (105) gives:
% 142.10/21.17 | | | | | | | (108) all_52_14 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_52_14, all_46_0, e0, e1,
% 142.10/21.17 | | | | | | | simplifying with (69), (104) gives:
% 142.10/21.17 | | | | | | | (109) all_52_14 = all_46_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_52_2, all_14_0, e3, e1,
% 142.10/21.17 | | | | | | | simplifying with (4), (107) gives:
% 142.10/21.17 | | | | | | | (110) all_52_2 = all_14_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_52_2, all_28_0, e3, e1,
% 142.10/21.17 | | | | | | | simplifying with (4), (106) gives:
% 142.10/21.17 | | | | | | | (111) all_52_2 = all_28_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (110), (111) imply:
% 142.10/21.17 | | | | | | | (112) all_28_0 = all_14_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (108), (109) imply:
% 142.10/21.17 | | | | | | | (113) all_46_0 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (11), (108) imply:
% 142.10/21.17 | | | | | | | (114) all_54_11 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (32), (108) imply:
% 142.10/21.17 | | | | | | | (115) ~ (all_52_6 = all_42_0)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (33), (108) imply:
% 142.10/21.17 | | | | | | | (116) ~ (all_52_13 = all_42_0)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (8), (108) imply:
% 142.10/21.17 | | | | | | | (117) ~ (all_42_0 = e3)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (80), (108) imply:
% 142.10/21.17 | | | | | | | (118) ~ (all_42_0 = e1)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (83), (113) imply:
% 142.10/21.17 | | | | | | | (119) ~ (all_42_0 = e2)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | BETA: splitting (35) gives:
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | (120) all_54_11 = e3
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | REF_CLOSE: (114), (117), (120) are inconsistent by sub-proof
% 142.10/21.17 | | | | | | | | #637.
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | (121) ~ (all_54_11 = e3)
% 142.10/21.17 | | | | | | | | (122) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | BETA: splitting (46) gives:
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | (123) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 142.10/21.17 | | | | | | | | | op(e1, e2) = e3)
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | BETA: splitting (123) gives:
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | (124) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | ALPHA: (124) implies:
% 142.10/21.17 | | | | | | | | | | (125) all_57_6 = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | BETA: splitting (65) gives:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (126) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | BETA: splitting (126) gives:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (127) all_57_0 = e2 & op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (127) implies:
% 142.10/21.17 | | | | | | | | | | | | (128) op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (43), (50), (63), (128) are inconsistent by
% 142.10/21.17 | | | | | | | | | | | | sub-proof #880.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (129) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (129) implies:
% 142.10/21.17 | | | | | | | | | | | | (130) all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 142.10/21.17 | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 142.10/21.17 | | | | | | | | | | | | (20), (21), (22), (23), (25), (26), (27), (28),
% 142.10/21.17 | | | | | | | | | | | | (29), (30), (31), (34), (36), (37), (38), (39),
% 142.10/21.17 | | | | | | | | | | | | (40), (42), (43), (44), (45), (46), (47), (48),
% 142.10/21.17 | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 142.10/21.17 | | | | | | | | | | | | (57), (60), (61), (62), (63), (64), (65), (67),
% 142.10/21.17 | | | | | | | | | | | | (68), (70), (71), (75), (76), (114), (115), (116),
% 142.10/21.17 | | | | | | | | | | | | (117), (118), (119), (122), (125), (130) are
% 142.10/21.17 | | | | | | | | | | | | inconsistent by sub-proof #572.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (131) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.10/21.17 | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | REF_CLOSE: (10), (50), (71), (76), (87), (88), (89), (107),
% 142.10/21.17 | | | | | | | | | | | (131) are inconsistent by sub-proof #571.
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | (132) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | ALPHA: (132) implies:
% 142.10/21.17 | | | | | | | | | | (133) all_57_7 = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | BETA: splitting (65) gives:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (134) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | BETA: splitting (134) gives:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (135) all_57_0 = e2 & op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (135) implies:
% 142.10/21.17 | | | | | | | | | | | | (136) op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (43), (50), (63), (136) are inconsistent by
% 142.10/21.17 | | | | | | | | | | | | sub-proof #880.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (137) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (137) implies:
% 142.10/21.17 | | | | | | | | | | | | (138) all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 142.10/21.17 | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 142.10/21.17 | | | | | | | | | | | | (20), (21), (22), (23), (25), (26), (27), (28),
% 142.10/21.17 | | | | | | | | | | | | (29), (30), (31), (34), (36), (37), (38), (39),
% 142.10/21.17 | | | | | | | | | | | | (40), (42), (43), (44), (45), (46), (47), (48),
% 142.10/21.17 | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 142.10/21.17 | | | | | | | | | | | | (57), (60), (61), (62), (63), (64), (65), (67),
% 142.10/21.17 | | | | | | | | | | | | (68), (70), (71), (75), (76), (114), (115), (116),
% 142.10/21.17 | | | | | | | | | | | | (117), (118), (119), (122), (133), (138) are
% 142.10/21.17 | | | | | | | | | | | | inconsistent by sub-proof #570.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (139) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.10/21.17 | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | REF_CLOSE: (10), (50), (71), (76), (87), (88), (89), (107),
% 142.10/21.17 | | | | | | | | | | | (139) are inconsistent by sub-proof #571.
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | (140) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 142.10/21.17 | | | | | | | | | op(e1, e0) = e3)
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (12), (14),
% 142.10/21.17 | | | | | | | | | (15), (17), (18), (19), (20), (21), (23), (25),
% 142.10/21.17 | | | | | | | | | (27), (28), (29), (30), (31), (34), (36), (38),
% 142.10/21.17 | | | | | | | | | (39), (40), (42), (43), (44), (45), (46), (47),
% 142.10/21.17 | | | | | | | | | (49), (50), (51), (53), (54), (55), (56), (57),
% 142.10/21.17 | | | | | | | | | (62), (63), (65), (68), (70), (71), (75), (76),
% 142.10/21.17 | | | | | | | | | (114), (115), (118), (119), (122), (140) are
% 142.10/21.17 | | | | | | | | | inconsistent by sub-proof #566.
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | End of split
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | End of split
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | Case 2:
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | (141) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 & $i(all_14_1)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | ALPHA: (141) implies:
% 142.10/21.17 | | | | | | | (142) ~ (all_14_1 = e2)
% 142.10/21.17 | | | | | | | (143) op(e3, e0) = all_14_1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with e1, all_46_1, e3, e0,
% 142.10/21.17 | | | | | | | simplifying with (72), (84) gives:
% 142.10/21.17 | | | | | | | (144) all_46_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_42_1, all_46_1, e3, e0,
% 142.10/21.17 | | | | | | | simplifying with (84), (91) gives:
% 142.10/21.17 | | | | | | | (145) all_46_1 = all_42_1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with e1, all_28_1, e0, e3,
% 142.10/21.17 | | | | | | | simplifying with (76), (88) gives:
% 142.10/21.17 | | | | | | | (146) all_28_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_14_1, all_28_1, e0, e3,
% 142.10/21.17 | | | | | | | simplifying with (88), (143) gives:
% 142.10/21.17 | | | | | | | (147) all_28_1 = all_14_1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (144), (145) imply:
% 142.10/21.17 | | | | | | | (148) all_42_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | SIMP: (148) implies:
% 142.10/21.17 | | | | | | | (149) all_42_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (146), (147) imply:
% 142.10/21.17 | | | | | | | (150) all_14_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | SIMP: (150) implies:
% 142.10/21.17 | | | | | | | (151) all_14_1 = e1
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (142), (151) imply:
% 142.10/21.17 | | | | | | | (152) ~ (e2 = e1)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (85), (144) imply:
% 142.10/21.17 | | | | | | | (153) op(e1, e0) = all_46_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (92), (149) imply:
% 142.10/21.17 | | | | | | | (154) op(e1, e0) = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_52_14, all_42_0, e0, e1,
% 142.10/21.17 | | | | | | | simplifying with (69), (154) gives:
% 142.10/21.17 | | | | | | | (155) all_52_14 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | GROUND_INST: instantiating (50) with all_52_14, all_46_0, e0, e1,
% 142.10/21.17 | | | | | | | simplifying with (69), (153) gives:
% 142.10/21.17 | | | | | | | (156) all_52_14 = all_46_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (155), (156) imply:
% 142.10/21.17 | | | | | | | (157) all_46_0 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | SIMP: (157) implies:
% 142.10/21.17 | | | | | | | (158) all_46_0 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | COMBINE_EQS: (11), (155) imply:
% 142.10/21.17 | | | | | | | (159) all_54_11 = all_42_0
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (32), (155) imply:
% 142.10/21.17 | | | | | | | (160) ~ (all_52_6 = all_42_0)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (33), (155) imply:
% 142.10/21.17 | | | | | | | (161) ~ (all_52_13 = all_42_0)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (8), (155) imply:
% 142.10/21.17 | | | | | | | (162) ~ (all_42_0 = e3)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (80), (155) imply:
% 142.10/21.17 | | | | | | | (163) ~ (all_42_0 = e1)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | REDUCE: (83), (158) imply:
% 142.10/21.17 | | | | | | | (164) ~ (all_42_0 = e2)
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | BETA: splitting (35) gives:
% 142.10/21.17 | | | | | | |
% 142.10/21.17 | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | (165) all_54_11 = e3
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | REF_CLOSE: (159), (162), (165) are inconsistent by sub-proof
% 142.10/21.17 | | | | | | | | #637.
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | (166) ~ (all_54_11 = e3)
% 142.10/21.17 | | | | | | | | (167) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | BETA: splitting (46) gives:
% 142.10/21.17 | | | | | | | |
% 142.10/21.17 | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | (168) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 142.10/21.17 | | | | | | | | | op(e1, e2) = e3)
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | BETA: splitting (168) gives:
% 142.10/21.17 | | | | | | | | |
% 142.10/21.17 | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | (169) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | ALPHA: (169) implies:
% 142.10/21.17 | | | | | | | | | | (170) all_57_6 = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | BETA: splitting (65) gives:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (171) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | BETA: splitting (171) gives:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (172) all_57_0 = e2 & op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (172) implies:
% 142.10/21.17 | | | | | | | | | | | | (173) op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (43), (50), (63), (173) are inconsistent by
% 142.10/21.17 | | | | | | | | | | | | sub-proof #880.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (174) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (174) implies:
% 142.10/21.17 | | | | | | | | | | | | (175) all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 142.10/21.17 | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 142.10/21.17 | | | | | | | | | | | | (20), (21), (22), (23), (25), (26), (27), (28),
% 142.10/21.17 | | | | | | | | | | | | (29), (30), (31), (34), (36), (37), (38), (39),
% 142.10/21.17 | | | | | | | | | | | | (40), (42), (43), (44), (45), (46), (47), (48),
% 142.10/21.17 | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 142.10/21.17 | | | | | | | | | | | | (57), (60), (61), (62), (63), (64), (65), (67),
% 142.10/21.17 | | | | | | | | | | | | (68), (70), (71), (75), (76), (159), (160), (161),
% 142.10/21.17 | | | | | | | | | | | | (162), (163), (164), (167), (170), (175) are
% 142.10/21.17 | | | | | | | | | | | | inconsistent by sub-proof #572.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (176) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.10/21.17 | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | REF_CLOSE: (10), (50), (59), (71), (76), (143), (176) are
% 142.10/21.17 | | | | | | | | | | | inconsistent by sub-proof #565.
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | End of split
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | (177) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | ALPHA: (177) implies:
% 142.10/21.17 | | | | | | | | | | (178) all_57_7 = e3
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | BETA: splitting (65) gives:
% 142.10/21.17 | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | (179) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | & op(e2, e3) = e2)
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | BETA: splitting (179) gives:
% 142.10/21.17 | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 1:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (180) all_57_0 = e2 & op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (180) implies:
% 142.10/21.17 | | | | | | | | | | | | (181) op(e3, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | REF_CLOSE: (43), (50), (63), (181) are inconsistent by
% 142.10/21.17 | | | | | | | | | | | | sub-proof #880.
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | Case 2:
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | (182) all_57_2 = e2 & op(e2, e3) = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.17 | | | | | | | | | | | | ALPHA: (182) implies:
% 142.10/21.17 | | | | | | | | | | | | (183) all_57_2 = e2
% 142.10/21.17 | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10),
% 142.10/21.18 | | | | | | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19),
% 142.10/21.18 | | | | | | | | | | | | (20), (21), (22), (23), (25), (26), (27), (28),
% 142.10/21.18 | | | | | | | | | | | | (29), (30), (31), (34), (36), (37), (38), (39),
% 142.10/21.18 | | | | | | | | | | | | (40), (42), (43), (44), (45), (46), (47), (48),
% 142.10/21.18 | | | | | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (56),
% 142.10/21.18 | | | | | | | | | | | | (57), (60), (61), (62), (63), (64), (65), (67),
% 142.10/21.18 | | | | | | | | | | | | (68), (70), (71), (75), (76), (159), (160), (161),
% 142.10/21.18 | | | | | | | | | | | | (162), (163), (164), (167), (178), (183) are
% 142.10/21.18 | | | | | | | | | | | | inconsistent by sub-proof #570.
% 142.10/21.18 | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | End of split
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | (184) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.10/21.18 | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | REF_CLOSE: (10), (50), (59), (71), (76), (143), (184) are
% 142.10/21.18 | | | | | | | | | | | inconsistent by sub-proof #565.
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | End of split
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | End of split
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | (185) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 &
% 142.10/21.18 | | | | | | | | | op(e1, e0) = e3)
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (12), (14),
% 142.10/21.18 | | | | | | | | | (15), (17), (18), (19), (20), (21), (23), (25),
% 142.10/21.18 | | | | | | | | | (27), (28), (29), (30), (31), (34), (36), (38),
% 142.10/21.18 | | | | | | | | | (39), (40), (42), (43), (44), (45), (46), (47),
% 142.10/21.18 | | | | | | | | | (49), (50), (51), (53), (54), (55), (56), (57),
% 142.10/21.18 | | | | | | | | | (62), (63), (65), (68), (70), (71), (75), (76),
% 142.10/21.18 | | | | | | | | | (159), (160), (163), (164), (167), (185) are
% 142.10/21.18 | | | | | | | | | inconsistent by sub-proof #566.
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | End of split
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | End of split
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | End of split
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | Case 2:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | (186) ~ (all_42_1 = e2) & op(e0, e3) = all_42_1 & $i(all_42_1)
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | ALPHA: (186) implies:
% 142.10/21.18 | | | | | | (187) ~ (all_42_1 = e2)
% 142.10/21.18 | | | | | | (188) op(e0, e3) = all_42_1
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | BETA: splitting (29) gives:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | Case 1:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | (189) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3,
% 142.10/21.18 | | | | | | | e0) = all_14_1 & $i(all_14_0) & $i(all_14_1)
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | ALPHA: (189) implies:
% 142.10/21.18 | | | | | | | (190) op(e3, e0) = all_14_1
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 142.10/21.18 | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 142.10/21.18 | | | | | | | (21), (23), (25), (26), (27), (28), (29), (30), (31),
% 142.10/21.18 | | | | | | | (32), (33), (34), (35), (36), (38), (39), (40), (42),
% 142.10/21.18 | | | | | | | (43), (44), (45), (46), (47), (49), (50), (51), (52),
% 142.10/21.18 | | | | | | | (53), (54), (55), (56), (57), (62), (63), (65), (67),
% 142.10/21.18 | | | | | | | (68), (69), (70), (71), (72), (75), (76), (80), (83),
% 142.10/21.18 | | | | | | | (84), (85), (88), (187), (188), (190) are inconsistent
% 142.10/21.18 | | | | | | | by sub-proof #556.
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | Case 2:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | (191) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 & $i(all_14_1)
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | ALPHA: (191) implies:
% 142.10/21.18 | | | | | | | (192) op(e3, e0) = all_14_1
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11),
% 142.10/21.18 | | | | | | | (12), (13), (14), (15), (16), (17), (18), (19), (20),
% 142.10/21.18 | | | | | | | (21), (23), (25), (26), (27), (28), (29), (30), (31),
% 142.10/21.18 | | | | | | | (32), (33), (34), (35), (36), (38), (39), (40), (42),
% 142.10/21.18 | | | | | | | (43), (44), (45), (46), (47), (49), (50), (51), (52),
% 142.10/21.18 | | | | | | | (53), (54), (55), (56), (57), (62), (63), (65), (67),
% 142.10/21.18 | | | | | | | (68), (69), (70), (71), (72), (75), (76), (80), (83),
% 142.10/21.18 | | | | | | | (84), (85), (88), (187), (188), (192) are inconsistent
% 142.10/21.18 | | | | | | | by sub-proof #556.
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | End of split
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | End of split
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | Case 2:
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | (193) ~ (all_28_1 = e1) & op(e3, e0) = all_28_1 & $i(all_28_1)
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | ALPHA: (193) implies:
% 142.10/21.18 | | | | | (194) ~ (all_28_1 = e1)
% 142.10/21.18 | | | | | (195) op(e3, e0) = all_28_1
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | REF_CLOSE: (50), (76), (194), (195) are inconsistent by sub-proof
% 142.10/21.18 | | | | | #685.
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | End of split
% 142.10/21.18 | | | |
% 142.10/21.18 | | | Case 2:
% 142.10/21.18 | | | |
% 142.10/21.18 | | | | (196) ~ (all_46_1 = e1) & op(e0, e3) = all_46_1 & $i(all_46_1)
% 142.10/21.18 | | | |
% 142.10/21.18 | | | | REF_CLOSE: (50), (72), (196) are inconsistent by sub-proof #555.
% 142.10/21.18 | | | |
% 142.10/21.18 | | | End of split
% 142.10/21.18 | | |
% 142.10/21.18 | | Case 2:
% 142.10/21.18 | | |
% 142.10/21.18 | | | (197) all_57_10 = e1 & op(e2, e0) = e1
% 142.10/21.18 | | |
% 142.10/21.18 | | | ALPHA: (197) implies:
% 142.10/21.18 | | | (198) all_57_10 = e1
% 142.10/21.18 | | |
% 142.10/21.18 | | | REF_CLOSE: (1), (5), (10), (12), (15), (17), (18), (20), (27), (36), (40),
% 142.10/21.18 | | | (43), (44), (50), (53), (55), (56), (70), (198) are
% 142.10/21.18 | | | inconsistent by sub-proof #589.
% 142.10/21.18 | | |
% 142.10/21.18 | | End of split
% 142.10/21.18 | |
% 142.10/21.18 | Case 2:
% 142.10/21.18 | |
% 142.10/21.18 | | (199) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.18 | | e1)
% 142.10/21.18 | |
% 142.10/21.18 | | BETA: splitting (199) gives:
% 142.10/21.18 | |
% 142.10/21.18 | | Case 1:
% 142.10/21.18 | | |
% 142.10/21.18 | | | (200) all_57_11 = e1 & op(e1, e0) = e1
% 142.10/21.18 | | |
% 142.10/21.18 | | | ALPHA: (200) implies:
% 142.10/21.18 | | | (201) all_57_11 = e1
% 142.10/21.18 | | |
% 142.10/21.18 | | | REF_CLOSE: (1), (3), (4), (6), (9), (10), (12), (14), (15), (17), (18),
% 142.10/21.18 | | | (19), (20), (21), (23), (25), (27), (28), (29), (30), (31),
% 142.10/21.18 | | | (34), (36), (38), (39), (40), (42), (43), (44), (45), (46),
% 142.10/21.18 | | | (47), (49), (50), (51), (53), (54), (55), (56), (57), (62),
% 142.10/21.18 | | | (63), (65), (68), (70), (71), (201) are inconsistent by
% 142.10/21.18 | | | sub-proof #569.
% 142.10/21.18 | | |
% 142.10/21.18 | | Case 2:
% 142.10/21.18 | | |
% 142.10/21.18 | | | (202) all_57_15 = e1 & op(e0, e0) = e1
% 142.10/21.18 | | |
% 142.10/21.18 | | | ALPHA: (202) implies:
% 142.10/21.18 | | | (203) op(e0, e0) = e1
% 142.10/21.18 | | |
% 142.10/21.18 | | | REF_CLOSE: (12), (50), (56), (203) are inconsistent by sub-proof #732.
% 142.10/21.18 | | |
% 142.10/21.18 | | End of split
% 142.10/21.18 | |
% 142.10/21.18 | End of split
% 142.10/21.18 |
% 142.10/21.18 End of proof
% 142.10/21.18
% 142.10/21.18 Sub-proof #555 shows that the following formulas are inconsistent:
% 142.10/21.18 ----------------------------------------------------------------
% 142.10/21.18 (1) ~ (all_46_1 = e1) & op(e0, e3) = all_46_1 & $i(all_46_1)
% 142.10/21.18 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.18 (3) op(e0, e3) = e1
% 142.10/21.18
% 142.10/21.18 Begin of proof
% 142.10/21.18 |
% 142.10/21.18 | ALPHA: (1) implies:
% 142.10/21.18 | (4) ~ (all_46_1 = e1)
% 142.10/21.18 | (5) op(e0, e3) = all_46_1
% 142.10/21.18 |
% 142.10/21.18 | GROUND_INST: instantiating (2) with e1, all_46_1, e3, e0, simplifying with
% 142.10/21.18 | (3), (5) gives:
% 142.10/21.18 | (6) all_46_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (4), (6) imply:
% 142.10/21.18 | (7) $false
% 142.10/21.18 |
% 142.10/21.18 | CLOSE: (7) is inconsistent.
% 142.10/21.18 |
% 142.10/21.18 End of proof
% 142.10/21.18
% 142.10/21.18 Sub-proof #556 shows that the following formulas are inconsistent:
% 142.10/21.18 ----------------------------------------------------------------
% 142.10/21.18 (1) op(e3, e0) = e1
% 142.10/21.18 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.18 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.18 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.10/21.18 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.10/21.18 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.18 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.18 (5) op(e1, e3) = all_52_2
% 142.10/21.18 (6) ~ (all_52_14 = e1)
% 142.10/21.18 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.18 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.10/21.18 (8) ~ (all_52_12 = e3)
% 142.10/21.18 (9) op(e1, e2) = all_52_6
% 142.10/21.18 (10) ~ (all_52_14 = e3)
% 142.10/21.18 (11) ~ (all_52_4 = e0)
% 142.10/21.18 (12) all_54_11 = all_52_14
% 142.10/21.18 (13) op(e0, e0) = e3
% 142.10/21.18 (14) ~ (all_42_1 = e2)
% 142.10/21.18 (15) op(e0, e3) = all_52_3
% 142.10/21.18 (16) op(e3, e0) = all_28_1
% 142.10/21.18 (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.18 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.18 (18) op(e2, e2) = e1
% 142.10/21.18 (19) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.10/21.18 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.18 e1)
% 142.10/21.18 (20) all_57_9 = e1
% 142.10/21.18 (21) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.18 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.18 (22) ~ (all_52_1 = e0)
% 142.10/21.18 (23) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.18 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.18 (24) ~ (e3 = e0)
% 142.10/21.18 (25) op(e1, e1) = e1
% 142.10/21.18 (26) op(e0, e3) = e1
% 142.10/21.18 (27) op(e3, e1) = all_52_8
% 142.10/21.18 (28) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.18 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.18 (29) op(e3, e0) = all_14_1
% 142.10/21.18 (30) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.18 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.18 e2)
% 142.10/21.18 (31) op(e2, e3) = all_52_1
% 142.10/21.18 (32) ~ (all_52_12 = e0)
% 142.10/21.18 (33) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.18 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.18 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.18 (34) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.18 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.18 (35) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.18 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.18 (36) ~ (all_52_6 = all_52_14)
% 142.10/21.18 (37) ~ (all_52_13 = all_52_14)
% 142.10/21.18 (38) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.18 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.18 (39) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.18 (40) all_57_3 = e1
% 142.10/21.18 (41) all_28_2 = e0
% 142.10/21.18 (42) op(e0, e3) = all_42_1
% 142.10/21.18 (43) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.18 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.18 (44) ~ (e1 = e0)
% 142.10/21.18 (45) op(all_46_1, e0) = all_46_0
% 142.10/21.18 (46) op(e3, e2) = all_52_4
% 142.10/21.18 (47) ~ (e2 = e0)
% 142.10/21.18 (48) op(e0, e3) = all_46_1
% 142.10/21.18 (49) ~ (e3 = e2)
% 142.10/21.18 (50) op(e3, e0) = all_52_12
% 142.10/21.18 (51) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.18 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.18 (52) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.18 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.18 (53) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.18 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.18 (54) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.18 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.18 (55) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.18 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.18 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.18 (56) ~ (all_52_3 = e0)
% 142.10/21.18 (57) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.18 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.18 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.18 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.18 (58) ~ (all_52_8 = e0)
% 142.10/21.18 (59) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.18 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.18 (60) ~ (e3 = e1)
% 142.10/21.18 (61) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.18 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.18 (62) all_57_0 = e0
% 142.10/21.18 (63) ~ (all_46_0 = e2)
% 142.10/21.18 (64) op(e3, e3) = e0
% 142.10/21.18 (65) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.18 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.18 (66) op(e2, e0) = all_52_13
% 142.10/21.18 (67) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.18 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.18 (68) all_57_12 = e1
% 142.10/21.18 (69) op(e1, e0) = all_52_14
% 142.10/21.18 (70) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.18 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.18
% 142.10/21.18 Begin of proof
% 142.10/21.18 |
% 142.10/21.18 | GROUND_INST: instantiating (54) with e1, all_46_1, e3, e0, simplifying with
% 142.10/21.18 | (26), (48) gives:
% 142.10/21.18 | (71) all_46_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | GROUND_INST: instantiating (54) with all_42_1, all_46_1, e3, e0, simplifying
% 142.10/21.18 | with (42), (48) gives:
% 142.10/21.18 | (72) all_46_1 = all_42_1
% 142.10/21.18 |
% 142.10/21.18 | GROUND_INST: instantiating (54) with e1, all_28_1, e0, e3, simplifying with
% 142.10/21.18 | (1), (16) gives:
% 142.10/21.18 | (73) all_28_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | GROUND_INST: instantiating (54) with all_14_1, all_28_1, e0, e3, simplifying
% 142.10/21.18 | with (16), (29) gives:
% 142.10/21.18 | (74) all_28_1 = all_14_1
% 142.10/21.18 |
% 142.10/21.18 | COMBINE_EQS: (71), (72) imply:
% 142.10/21.18 | (75) all_42_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | SIMP: (75) implies:
% 142.10/21.18 | (76) all_42_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | COMBINE_EQS: (73), (74) imply:
% 142.10/21.18 | (77) all_14_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | SIMP: (77) implies:
% 142.10/21.18 | (78) all_14_1 = e1
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (14), (76) imply:
% 142.10/21.18 | (79) ~ (e2 = e1)
% 142.10/21.18 |
% 142.10/21.18 | SIMP: (79) implies:
% 142.10/21.18 | (80) ~ (e2 = e1)
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (45), (71) imply:
% 142.10/21.18 | (81) op(e1, e0) = all_46_0
% 142.10/21.18 |
% 142.10/21.18 | GROUND_INST: instantiating (54) with all_52_14, all_46_0, e0, e1, simplifying
% 142.10/21.18 | with (69), (81) gives:
% 142.10/21.18 | (82) all_52_14 = all_46_0
% 142.10/21.18 |
% 142.10/21.18 | COMBINE_EQS: (12), (82) imply:
% 142.10/21.18 | (83) all_54_11 = all_46_0
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (36), (82) imply:
% 142.10/21.18 | (84) ~ (all_52_6 = all_46_0)
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (37), (82) imply:
% 142.10/21.18 | (85) ~ (all_52_13 = all_46_0)
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (10), (82) imply:
% 142.10/21.18 | (86) ~ (all_46_0 = e3)
% 142.10/21.18 |
% 142.10/21.18 | REDUCE: (6), (82) imply:
% 142.10/21.18 | (87) ~ (all_46_0 = e1)
% 142.10/21.18 |
% 142.10/21.18 | BETA: splitting (39) gives:
% 142.10/21.18 |
% 142.10/21.18 | Case 1:
% 142.10/21.18 | |
% 142.10/21.18 | | (88) all_54_11 = e3
% 142.10/21.18 | |
% 142.10/21.18 | | COMBINE_EQS: (83), (88) imply:
% 142.10/21.18 | | (89) all_46_0 = e3
% 142.10/21.18 | |
% 142.10/21.18 | | SIMP: (89) implies:
% 142.10/21.18 | | (90) all_46_0 = e3
% 142.10/21.18 | |
% 142.10/21.18 | | REDUCE: (86), (90) imply:
% 142.10/21.18 | | (91) $false
% 142.10/21.18 | |
% 142.10/21.18 | | CLOSE: (91) is inconsistent.
% 142.10/21.18 | |
% 142.10/21.18 | Case 2:
% 142.10/21.18 | |
% 142.10/21.18 | | (92) ~ (all_54_11 = e3)
% 142.10/21.18 | | (93) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.18 | |
% 142.10/21.18 | | BETA: splitting (51) gives:
% 142.10/21.18 | |
% 142.10/21.18 | | Case 1:
% 142.10/21.18 | | |
% 142.10/21.18 | | | (94) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.10/21.18 | | | e3)
% 142.10/21.18 | | |
% 142.10/21.18 | | | BETA: splitting (94) gives:
% 142.10/21.18 | | |
% 142.10/21.18 | | | Case 1:
% 142.10/21.18 | | | |
% 142.10/21.18 | | | | (95) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.18 | | | |
% 142.10/21.18 | | | | ALPHA: (95) implies:
% 142.10/21.18 | | | | (96) all_57_6 = e3
% 142.10/21.18 | | | |
% 142.10/21.18 | | | | BETA: splitting (21) gives:
% 142.10/21.18 | | | |
% 142.10/21.18 | | | | Case 1:
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | (97) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 142.10/21.18 | | | | | e0) = e2)
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | BETA: splitting (97) gives:
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | Case 1:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | (98) all_57_9 = e2 & op(e3, e0) = e2
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | REF_CLOSE: (20), (80), (98) are inconsistent by sub-proof #636.
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | Case 2:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | (99) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | ALPHA: (99) implies:
% 142.10/21.18 | | | | | | (100) all_57_10 = e2
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | BETA: splitting (2) gives:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | Case 1:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | (101) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 142.10/21.18 | | | | | | | op(e2, e2) = e3)
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | REF_CLOSE: (1), (5), (24), (33), (35), (40), (41), (47), (49),
% 142.10/21.18 | | | | | | | (50), (54), (55), (60), (62), (64), (65), (68), (80),
% 142.10/21.18 | | | | | | | (96), (101) are inconsistent by sub-proof #564.
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | Case 2:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | (102) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 142.10/21.18 | | | | | | | op(e2, e0) = e3)
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | REF_CLOSE: (13), (18), (21), (22), (24), (31), (44), (47), (49),
% 142.10/21.18 | | | | | | | (54), (57), (59), (60), (70), (80), (100), (102) are
% 142.10/21.18 | | | | | | | inconsistent by sub-proof #561.
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | End of split
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | End of split
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | Case 2:
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | (103) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 142.10/21.18 | | | | | e0) = e2)
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | BETA: splitting (103) gives:
% 142.10/21.18 | | | | |
% 142.10/21.18 | | | | | Case 1:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | (104) all_57_11 = e2 & op(e1, e0) = e2
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | ALPHA: (104) implies:
% 142.10/21.18 | | | | | | (105) all_57_11 = e2
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | BETA: splitting (67) gives:
% 142.10/21.18 | | | | | |
% 142.10/21.18 | | | | | | Case 1:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | (106) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 142.10/21.18 | | | | | | | op(e2, e2) = e3)
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | BETA: splitting (106) gives:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | (107) all_57_1 = e3 & op(e3, e2) = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | ALPHA: (107) implies:
% 142.10/21.18 | | | | | | | | (108) all_57_1 = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | BETA: splitting (93) gives:
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | (109) all_54_11 = e2
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | REF_CLOSE: (63), (83), (109) are inconsistent by sub-proof
% 142.10/21.18 | | | | | | | | | #560.
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | (110) ~ (all_54_11 = e2)
% 142.10/21.18 | | | | | | | | | (111) all_54_11 = e1 | all_54_11 = e0
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | BETA: splitting (111) gives:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | (112) all_54_11 = e1
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REF_CLOSE: (83), (87), (112) are inconsistent by sub-proof
% 142.10/21.18 | | | | | | | | | | #559.
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | (113) all_54_11 = e0
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | COMBINE_EQS: (83), (113) imply:
% 142.10/21.18 | | | | | | | | | | (114) all_46_0 = e0
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | SIMP: (114) implies:
% 142.10/21.18 | | | | | | | | | | (115) all_46_0 = e0
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (85), (115) imply:
% 142.10/21.18 | | | | | | | | | | (116) ~ (all_52_13 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (86), (115) imply:
% 142.10/21.18 | | | | | | | | | | (117) ~ (e3 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (63), (115) imply:
% 142.10/21.18 | | | | | | | | | | (118) ~ (e2 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (87), (115) imply:
% 142.10/21.18 | | | | | | | | | | (119) ~ (e1 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REF_CLOSE: (1), (2), (4), (5), (8), (11), (13), (17), (18),
% 142.10/21.18 | | | | | | | | | | (21), (22), (23), (24), (25), (27), (31), (33),
% 142.10/21.18 | | | | | | | | | | (40), (41), (43), (46), (47), (49), (50), (53),
% 142.10/21.18 | | | | | | | | | | (54), (55), (57), (58), (59), (60), (61), (62),
% 142.10/21.18 | | | | | | | | | | (64), (65), (66), (67), (68), (70), (80), (108),
% 142.10/21.18 | | | | | | | | | | (116), (119) are inconsistent by sub-proof #607.
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | End of split
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | End of split
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | (120) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | REF_CLOSE: (1), (5), (24), (33), (35), (40), (41), (47), (49),
% 142.10/21.18 | | | | | | | | (50), (54), (55), (60), (62), (64), (65), (68), (80),
% 142.10/21.18 | | | | | | | | (96), (120) are inconsistent by sub-proof #605.
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | End of split
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | Case 2:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | (121) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 142.10/21.18 | | | | | | | op(e0, e2) = e3)
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | BETA: splitting (121) gives:
% 142.10/21.18 | | | | | | |
% 142.10/21.18 | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | (122) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | ALPHA: (122) implies:
% 142.10/21.18 | | | | | | | | (123) all_57_7 = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (13), (15),
% 142.10/21.18 | | | | | | | | (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 142.10/21.18 | | | | | | | | (27), (28), (30), (31), (32), (33), (34), (35), (38),
% 142.10/21.18 | | | | | | | | (40), (41), (43), (44), (46), (47), (49), (50), (51),
% 142.10/21.18 | | | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 142.10/21.18 | | | | | | | | (61), (62), (64), (65), (67), (68), (70), (80),
% 142.10/21.18 | | | | | | | | (105), (123) are inconsistent by sub-proof #558.
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | (124) all_57_13 = e3 & op(e0, e2) = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | ALPHA: (124) implies:
% 142.10/21.18 | | | | | | | | (125) all_57_13 = e3
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | BETA: splitting (93) gives:
% 142.10/21.18 | | | | | | | |
% 142.10/21.18 | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | (126) all_54_11 = e2
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | REF_CLOSE: (63), (83), (126) are inconsistent by sub-proof
% 142.10/21.18 | | | | | | | | | #560.
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | (127) ~ (all_54_11 = e2)
% 142.10/21.18 | | | | | | | | | (128) all_54_11 = e1 | all_54_11 = e0
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | BETA: splitting (128) gives:
% 142.10/21.18 | | | | | | | | |
% 142.10/21.18 | | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | (129) all_54_11 = e1
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REF_CLOSE: (83), (87), (129) are inconsistent by sub-proof
% 142.10/21.18 | | | | | | | | | | #559.
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | (130) all_54_11 = e0
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | COMBINE_EQS: (83), (130) imply:
% 142.10/21.18 | | | | | | | | | | (131) all_46_0 = e0
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | SIMP: (131) implies:
% 142.10/21.18 | | | | | | | | | | (132) all_46_0 = e0
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (84), (132) imply:
% 142.10/21.18 | | | | | | | | | | (133) ~ (all_52_6 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (86), (132) imply:
% 142.10/21.18 | | | | | | | | | | (134) ~ (e3 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (63), (132) imply:
% 142.10/21.18 | | | | | | | | | | (135) ~ (e2 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | REDUCE: (87), (132) imply:
% 142.10/21.18 | | | | | | | | | | (136) ~ (e1 = e0)
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | BETA: splitting (2) gives:
% 142.10/21.18 | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | (137) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.10/21.18 | | | | | | | | | | | & op(e2, e2) = e3)
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | REF_CLOSE: (1), (5), (24), (33), (35), (40), (41), (47),
% 142.10/21.18 | | | | | | | | | | | (49), (50), (54), (55), (60), (62), (64), (65),
% 142.10/21.18 | | | | | | | | | | | (68), (80), (96), (137) are inconsistent by
% 142.10/21.18 | | | | | | | | | | | sub-proof #564.
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | (138) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.10/21.18 | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | BETA: splitting (138) gives:
% 142.10/21.18 | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | (139) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.18 | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | ALPHA: (139) implies:
% 142.10/21.18 | | | | | | | | | | | | (140) all_57_5 = e3
% 142.10/21.18 | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | BETA: splitting (30) gives:
% 142.10/21.18 | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | (141) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 =
% 142.10/21.18 | | | | | | | | | | | | | e2 & op(e0, e2) = e2)
% 142.10/21.18 | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | BETA: splitting (141) gives:
% 142.10/21.18 | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | Case 1:
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | (142) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | ALPHA: (142) implies:
% 142.10/21.18 | | | | | | | | | | | | | | (143) op(e0, e3) = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | REF_CLOSE: (14), (42), (48), (54), (143) are inconsistent by
% 142.10/21.18 | | | | | | | | | | | | | | sub-proof #557.
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | (144) all_57_13 = e2 & op(e0, e2) = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | ALPHA: (144) implies:
% 142.10/21.18 | | | | | | | | | | | | | | (145) all_57_13 = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | COMBINE_EQS: (125), (145) imply:
% 142.10/21.18 | | | | | | | | | | | | | | (146) e3 = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | SIMP: (146) implies:
% 142.10/21.18 | | | | | | | | | | | | | | (147) e3 = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | COMBINE_EQS: (96), (147) imply:
% 142.10/21.18 | | | | | | | | | | | | | | (148) all_57_6 = e2
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | | REF_CLOSE: (9), (25), (28), (44), (47), (54), (105), (133),
% 142.10/21.18 | | | | | | | | | | | | | | (148) are inconsistent by sub-proof #990.
% 142.10/21.18 | | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | | End of split
% 142.10/21.18 | | | | | | | | | | | | |
% 142.10/21.18 | | | | | | | | | | | | Case 2:
% 142.10/21.18 | | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | | | (149) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 =
% 142.10/21.19 | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 142.10/21.19 | | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | | | REF_CLOSE: (13), (17), (24), (25), (27), (44), (47), (49),
% 142.10/21.19 | | | | | | | | | | | | | (54), (58), (140), (149) are inconsistent by
% 142.10/21.19 | | | | | | | | | | | | | sub-proof #576.
% 142.10/21.19 | | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | | End of split
% 142.10/21.19 | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | Case 2:
% 142.10/21.19 | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | | (150) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.19 | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | | ALPHA: (150) implies:
% 142.10/21.19 | | | | | | | | | | | | (151) all_57_10 = e3
% 142.10/21.19 | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | | REF_CLOSE: (13), (21), (24), (44), (47), (49), (54), (57),
% 142.10/21.19 | | | | | | | | | | | | (59), (60), (80), (151) are inconsistent by
% 142.10/21.19 | | | | | | | | | | | | sub-proof #650.
% 142.10/21.19 | | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | | End of split
% 142.10/21.19 | | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | | End of split
% 142.10/21.19 | | | | | | | | | |
% 142.10/21.19 | | | | | | | | | End of split
% 142.10/21.19 | | | | | | | | |
% 142.10/21.19 | | | | | | | | End of split
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | End of split
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | End of split
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | Case 2:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (152) all_57_15 = e2 & op(e0, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | ALPHA: (152) implies:
% 142.10/21.19 | | | | | | (153) op(e0, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | REF_CLOSE: (13), (49), (54), (153) are inconsistent by sub-proof
% 142.10/21.19 | | | | | | #1066.
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | End of split
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | End of split
% 142.10/21.19 | | | |
% 142.10/21.19 | | | Case 2:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | (154) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | ALPHA: (154) implies:
% 142.10/21.19 | | | | (155) all_57_7 = e3
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | BETA: splitting (21) gives:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | Case 1:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | (156) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 142.10/21.19 | | | | | e0) = e2)
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | BETA: splitting (156) gives:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | Case 1:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (157) all_57_9 = e2 & op(e3, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | REF_CLOSE: (20), (80), (157) are inconsistent by sub-proof #636.
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | Case 2:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (158) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | ALPHA: (158) implies:
% 142.10/21.19 | | | | | | (159) all_57_10 = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | BETA: splitting (2) gives:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | Case 1:
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | (160) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 142.10/21.19 | | | | | | | op(e2, e2) = e3)
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (11), (13), (15), (17),
% 142.10/21.19 | | | | | | | (18), (19), (20), (21), (22), (23), (24), (25), (27),
% 142.10/21.19 | | | | | | | (28), (30), (31), (33), (35), (38), (40), (41), (43),
% 142.10/21.19 | | | | | | | (44), (46), (47), (49), (50), (51), (52), (53), (54),
% 142.10/21.19 | | | | | | | (55), (56), (57), (58), (59), (60), (61), (62), (64),
% 142.10/21.19 | | | | | | | (65), (67), (68), (70), (80), (155), (160) are
% 142.10/21.19 | | | | | | | inconsistent by sub-proof #582.
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | Case 2:
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | (161) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 142.10/21.19 | | | | | | | op(e2, e0) = e3)
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | REF_CLOSE: (13), (18), (21), (22), (24), (31), (44), (47), (49),
% 142.10/21.19 | | | | | | | (54), (57), (59), (60), (70), (80), (159), (161) are
% 142.10/21.19 | | | | | | | inconsistent by sub-proof #561.
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | End of split
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | End of split
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | Case 2:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | (162) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 142.10/21.19 | | | | | e0) = e2)
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | BETA: splitting (162) gives:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | Case 1:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (163) all_57_11 = e2 & op(e1, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | ALPHA: (163) implies:
% 142.10/21.19 | | | | | | (164) all_57_11 = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (11), (13), (15),
% 142.10/21.19 | | | | | | (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 142.10/21.19 | | | | | | (27), (28), (30), (31), (32), (33), (34), (35), (38),
% 142.10/21.19 | | | | | | (40), (41), (43), (44), (46), (47), (49), (50), (51),
% 142.10/21.19 | | | | | | (52), (53), (54), (55), (56), (57), (58), (59), (60),
% 142.10/21.19 | | | | | | (61), (62), (64), (65), (67), (68), (70), (80), (155),
% 142.10/21.19 | | | | | | (164) are inconsistent by sub-proof #558.
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | Case 2:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (165) all_57_15 = e2 & op(e0, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | ALPHA: (165) implies:
% 142.10/21.19 | | | | | | (166) op(e0, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | REF_CLOSE: (13), (49), (54), (166) are inconsistent by sub-proof
% 142.10/21.19 | | | | | | #1066.
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | End of split
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | End of split
% 142.10/21.19 | | | |
% 142.10/21.19 | | | End of split
% 142.10/21.19 | | |
% 142.10/21.19 | | Case 2:
% 142.10/21.19 | | |
% 142.10/21.19 | | | (167) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0)
% 142.10/21.19 | | | = e3)
% 142.10/21.19 | | |
% 142.10/21.19 | | | BETA: splitting (167) gives:
% 142.10/21.19 | | |
% 142.10/21.19 | | | Case 1:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | (168) all_57_8 = e3 & op(e1, e1) = e3
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | ALPHA: (168) implies:
% 142.10/21.19 | | | | (169) op(e1, e1) = e3
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | REF_CLOSE: (25), (54), (60), (169) are inconsistent by sub-proof #1096.
% 142.10/21.19 | | | |
% 142.10/21.19 | | | Case 2:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | (170) all_57_11 = e3 & op(e1, e0) = e3
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | ALPHA: (170) implies:
% 142.10/21.19 | | | | (171) all_57_11 = e3
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | BETA: splitting (21) gives:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | Case 1:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | (172) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2,
% 142.10/21.19 | | | | | e0) = e2)
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | BETA: splitting (172) gives:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | Case 1:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (173) all_57_9 = e2 & op(e3, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | REF_CLOSE: (20), (80), (173) are inconsistent by sub-proof #636.
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | Case 2:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | (174) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | ALPHA: (174) implies:
% 142.10/21.19 | | | | | | (175) all_57_10 = e2
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | BETA: splitting (2) gives:
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | | Case 1:
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | (176) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 &
% 142.10/21.19 | | | | | | | op(e2, e2) = e3)
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | BETA: splitting (176) gives:
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | Case 1:
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | | (177) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | | ALPHA: (177) implies:
% 142.10/21.19 | | | | | | | | (178) all_57_2 = e3
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | | REF_CLOSE: (1), (5), (33), (41), (47), (49), (50), (54), (55),
% 142.10/21.19 | | | | | | | | (64), (65), (68), (80), (178) are inconsistent by
% 142.10/21.19 | | | | | | | | sub-proof #632.
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | Case 2:
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | | (179) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | | REF_CLOSE: (2), (4), (5), (8), (11), (13), (17), (18), (21),
% 142.10/21.19 | | | | | | | | (22), (23), (24), (25), (27), (28), (31), (32), (33),
% 142.10/21.19 | | | | | | | | (34), (35), (38), (40), (41), (43), (44), (46), (47),
% 142.10/21.19 | | | | | | | | (49), (50), (51), (52), (53), (54), (55), (57), (58),
% 142.10/21.19 | | | | | | | | (59), (60), (61), (62), (64), (65), (67), (68), (70),
% 142.10/21.19 | | | | | | | | (80), (171), (179) are inconsistent by sub-proof
% 142.10/21.19 | | | | | | | | #568.
% 142.10/21.19 | | | | | | | |
% 142.10/21.19 | | | | | | | End of split
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | Case 2:
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | (180) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 &
% 142.10/21.19 | | | | | | | op(e2, e0) = e3)
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | | REF_CLOSE: (13), (18), (21), (22), (24), (31), (44), (47), (49),
% 142.10/21.19 | | | | | | | (54), (57), (59), (60), (70), (80), (175), (180) are
% 142.10/21.19 | | | | | | | inconsistent by sub-proof #561.
% 142.10/21.19 | | | | | | |
% 142.10/21.19 | | | | | | End of split
% 142.10/21.19 | | | | | |
% 142.10/21.19 | | | | | End of split
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | Case 2:
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | (181) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 142.10/21.19 | | | | | e0) = e2)
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | | REF_CLOSE: (13), (49), (54), (171), (181) are inconsistent by
% 142.10/21.19 | | | | | sub-proof #567.
% 142.10/21.19 | | | | |
% 142.10/21.19 | | | | End of split
% 142.10/21.19 | | | |
% 142.10/21.19 | | | End of split
% 142.10/21.19 | | |
% 142.10/21.19 | | End of split
% 142.10/21.19 | |
% 142.10/21.19 | End of split
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #557 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) op(e0, e3) = e2
% 142.10/21.19 (2) ~ (all_42_1 = e2)
% 142.10/21.19 (3) op(e0, e3) = all_42_1
% 142.10/21.19 (4) op(e0, e3) = all_46_1
% 142.10/21.19 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | GROUND_INST: instantiating (5) with all_42_1, all_46_1, e3, e0, simplifying
% 142.10/21.19 | with (3), (4) gives:
% 142.10/21.19 | (6) all_46_1 = all_42_1
% 142.10/21.19 |
% 142.10/21.19 | GROUND_INST: instantiating (5) with e2, all_46_1, e3, e0, simplifying with
% 142.10/21.19 | (1), (4) gives:
% 142.10/21.19 | (7) all_46_1 = e2
% 142.10/21.19 |
% 142.10/21.19 | COMBINE_EQS: (6), (7) imply:
% 142.10/21.19 | (8) all_42_1 = e2
% 142.10/21.19 |
% 142.10/21.19 | SIMP: (8) implies:
% 142.10/21.19 | (9) all_42_1 = e2
% 142.10/21.19 |
% 142.10/21.19 | REDUCE: (2), (9) imply:
% 142.10/21.19 | (10) $false
% 142.10/21.19 |
% 142.10/21.19 | CLOSE: (10) is inconsistent.
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #558 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) op(e3, e0) = e1
% 142.10/21.19 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.19 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.19 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.10/21.19 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.10/21.19 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.19 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.19 (5) op(e1, e3) = all_52_2
% 142.10/21.19 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.19 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.10/21.19 (7) ~ (all_52_12 = e3)
% 142.10/21.19 (8) ~ (all_52_4 = e0)
% 142.10/21.19 (9) ~ (e2 = e1)
% 142.10/21.19 (10) op(e0, e0) = e3
% 142.10/21.19 (11) op(e0, e3) = all_52_3
% 142.10/21.19 (12) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.19 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.19 (13) op(e2, e2) = e1
% 142.10/21.19 (14) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.10/21.19 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.19 e1)
% 142.10/21.19 (15) all_57_9 = e1
% 142.10/21.19 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.19 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.19 (17) ~ (all_52_1 = e0)
% 142.10/21.19 (18) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.19 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.19 (19) ~ (e3 = e0)
% 142.10/21.19 (20) op(e1, e1) = e1
% 142.10/21.19 (21) op(e3, e1) = all_52_8
% 142.10/21.19 (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.19 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.19 (23) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.19 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.19 e2)
% 142.10/21.19 (24) op(e2, e3) = all_52_1
% 142.10/21.19 (25) ~ (all_52_12 = e0)
% 142.10/21.19 (26) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.19 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.19 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.19 (27) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.19 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.19 (28) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.19 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.19 (29) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.19 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.19 (30) all_57_3 = e1
% 142.10/21.19 (31) all_28_2 = e0
% 142.10/21.19 (32) all_57_11 = e2
% 142.10/21.19 (33) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.19 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.19 (34) ~ (e1 = e0)
% 142.10/21.19 (35) op(e3, e2) = all_52_4
% 142.10/21.19 (36) ~ (e2 = e0)
% 142.10/21.19 (37) ~ (e3 = e2)
% 142.10/21.19 (38) op(e3, e0) = all_52_12
% 142.10/21.19 (39) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.19 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.19 (40) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.19 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.19 (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.19 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.19 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.19 (43) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.19 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.19 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.19 (44) ~ (all_52_3 = e0)
% 142.10/21.19 (45) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.19 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.19 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.19 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.19 (46) ~ (all_52_8 = e0)
% 142.10/21.19 (47) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.19 (48) ~ (e3 = e1)
% 142.10/21.19 (49) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.19 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.19 (50) all_57_0 = e0
% 142.10/21.19 (51) op(e3, e3) = e0
% 142.10/21.19 (52) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.19 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.19 (53) all_57_7 = e3
% 142.10/21.19 (54) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.19 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.19 (55) all_57_12 = e1
% 142.10/21.19 (56) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.19 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | BETA: splitting (2) gives:
% 142.10/21.19 |
% 142.10/21.19 | Case 1:
% 142.10/21.19 | |
% 142.10/21.19 | | (57) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 142.10/21.19 | | e3)
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (12), (13),
% 142.10/21.19 | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23), (24),
% 142.10/21.19 | | (26), (28), (29), (30), (31), (33), (34), (35), (36), (37), (38),
% 142.10/21.19 | | (39), (40), (41), (42), (43), (44), (45), (46), (47), (48), (49),
% 142.10/21.19 | | (50), (51), (52), (53), (54), (55), (56), (57) are inconsistent
% 142.10/21.19 | | by sub-proof #582.
% 142.10/21.19 | |
% 142.10/21.19 | Case 2:
% 142.10/21.19 | |
% 142.10/21.19 | | (58) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 142.10/21.19 | | e3)
% 142.10/21.19 | |
% 142.10/21.19 | | BETA: splitting (58) gives:
% 142.10/21.19 | |
% 142.10/21.19 | | Case 1:
% 142.10/21.19 | | |
% 142.10/21.19 | | | (59) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.19 | | |
% 142.10/21.19 | | | ALPHA: (59) implies:
% 142.10/21.19 | | | (60) all_57_5 = e3
% 142.10/21.19 | | |
% 142.10/21.19 | | | BETA: splitting (45) gives:
% 142.10/21.19 | | |
% 142.10/21.19 | | | Case 1:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | (61) all_57_15 = e0 & op(e0, e0) = e0
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | ALPHA: (61) implies:
% 142.10/21.19 | | | | (62) op(e0, e0) = e0
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | REF_CLOSE: (10), (19), (42), (62) are inconsistent by sub-proof #751.
% 142.10/21.19 | | | |
% 142.10/21.19 | | | Case 2:
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | (63) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 142.10/21.19 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.10/21.19 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.10/21.19 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.10/21.19 | | | |
% 142.10/21.19 | | | | REF_CLOSE: (2), (4), (5), (7), (8), (9), (10), (12), (13), (16), (17),
% 142.10/21.19 | | | | (18), (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 142.10/21.19 | | | | (28), (29), (30), (31), (32), (33), (34), (35), (36), (37),
% 142.10/21.19 | | | | (38), (39), (40), (41), (42), (43), (46), (47), (48), (49),
% 142.10/21.19 | | | | (50), (51), (52), (53), (54), (55), (56), (60), (63) are
% 142.10/21.19 | | | | inconsistent by sub-proof #575.
% 142.10/21.19 | | | |
% 142.10/21.19 | | | End of split
% 142.10/21.19 | | |
% 142.10/21.19 | | Case 2:
% 142.10/21.19 | | |
% 142.10/21.19 | | | (64) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.19 | | |
% 142.10/21.19 | | | ALPHA: (64) implies:
% 142.10/21.19 | | | (65) all_57_10 = e3
% 142.10/21.19 | | |
% 142.10/21.19 | | | REF_CLOSE: (9), (10), (16), (19), (34), (36), (37), (42), (45), (47),
% 142.10/21.19 | | | (48), (65) are inconsistent by sub-proof #650.
% 142.10/21.19 | | |
% 142.10/21.19 | | End of split
% 142.10/21.19 | |
% 142.10/21.19 | End of split
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #559 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) all_54_11 = all_46_0
% 142.10/21.19 (2) all_54_11 = e1
% 142.10/21.19 (3) ~ (all_46_0 = e1)
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | COMBINE_EQS: (1), (2) imply:
% 142.10/21.19 | (4) all_46_0 = e1
% 142.10/21.19 |
% 142.10/21.19 | SIMP: (4) implies:
% 142.10/21.19 | (5) all_46_0 = e1
% 142.10/21.19 |
% 142.10/21.19 | REDUCE: (3), (5) imply:
% 142.10/21.19 | (6) $false
% 142.10/21.19 |
% 142.10/21.19 | CLOSE: (6) is inconsistent.
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #560 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) all_54_11 = all_46_0
% 142.10/21.19 (2) all_54_11 = e2
% 142.10/21.19 (3) ~ (all_46_0 = e2)
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | COMBINE_EQS: (1), (2) imply:
% 142.10/21.19 | (4) all_46_0 = e2
% 142.10/21.19 |
% 142.10/21.19 | SIMP: (4) implies:
% 142.10/21.19 | (5) all_46_0 = e2
% 142.10/21.19 |
% 142.10/21.19 | REDUCE: (3), (5) imply:
% 142.10/21.19 | (6) $false
% 142.10/21.19 |
% 142.10/21.19 | CLOSE: (6) is inconsistent.
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #561 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) all_57_10 = e2
% 142.10/21.19 (2) ~ (e2 = e1)
% 142.10/21.19 (3) op(e0, e0) = e3
% 142.10/21.19 (4) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.19 (5) op(e2, e2) = e1
% 142.10/21.19 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.19 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.19 (7) ~ (all_52_1 = e0)
% 142.10/21.19 (8) ~ (e3 = e0)
% 142.10/21.19 (9) op(e2, e3) = all_52_1
% 142.10/21.19 (10) ~ (e1 = e0)
% 142.10/21.19 (11) ~ (e2 = e0)
% 142.10/21.19 (12) ~ (e3 = e2)
% 142.10/21.19 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.19 (14) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.19 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.19 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.19 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.19 (15) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.19 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.19 (16) ~ (e3 = e1)
% 142.10/21.19 (17) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.19 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | BETA: splitting (4) gives:
% 142.10/21.19 |
% 142.10/21.19 | Case 1:
% 142.10/21.19 | |
% 142.10/21.19 | | (18) all_57_5 = e3 & op(e2, e1) = e3
% 142.10/21.19 | |
% 142.10/21.19 | | ALPHA: (18) implies:
% 142.10/21.19 | | (19) all_57_5 = e3
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (1), (5), (7), (8), (9), (10), (11), (13), (17), (19) are
% 142.10/21.19 | | inconsistent by sub-proof #562.
% 142.10/21.19 | |
% 142.10/21.19 | Case 2:
% 142.10/21.19 | |
% 142.10/21.19 | | (20) all_57_10 = e3 & op(e2, e0) = e3
% 142.10/21.19 | |
% 142.10/21.19 | | ALPHA: (20) implies:
% 142.10/21.19 | | (21) all_57_10 = e3
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (2), (3), (6), (8), (10), (11), (12), (13), (14), (15), (16),
% 142.10/21.19 | | (21) are inconsistent by sub-proof #650.
% 142.10/21.19 | |
% 142.10/21.19 | End of split
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #562 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) all_57_10 = e2
% 142.10/21.19 (2) all_57_5 = e3
% 142.10/21.19 (3) op(e2, e2) = e1
% 142.10/21.19 (4) ~ (all_52_1 = e0)
% 142.10/21.19 (5) ~ (e3 = e0)
% 142.10/21.19 (6) op(e2, e3) = all_52_1
% 142.10/21.19 (7) ~ (e1 = e0)
% 142.10/21.19 (8) ~ (e2 = e0)
% 142.10/21.19 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.19 (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.19 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | BETA: splitting (10) gives:
% 142.10/21.19 |
% 142.10/21.19 | Case 1:
% 142.10/21.19 | |
% 142.10/21.19 | | (11) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.10/21.19 | | e0)
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (3), (4), (6), (7), (9), (11) are inconsistent by sub-proof #640.
% 142.10/21.19 | |
% 142.10/21.19 | Case 2:
% 142.10/21.19 | |
% 142.10/21.19 | | (12) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.10/21.19 | | e0)
% 142.10/21.19 | |
% 142.10/21.19 | | BETA: splitting (12) gives:
% 142.10/21.19 | |
% 142.10/21.19 | | Case 1:
% 142.10/21.19 | | |
% 142.10/21.19 | | | (13) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.19 | | |
% 142.10/21.19 | | | REF_CLOSE: (2), (5), (13) are inconsistent by sub-proof #729.
% 142.10/21.19 | | |
% 142.10/21.19 | | Case 2:
% 142.10/21.19 | | |
% 142.10/21.19 | | | (14) all_57_10 = e0 & op(e2, e0) = e0
% 142.10/21.19 | | |
% 142.10/21.19 | | | REF_CLOSE: (1), (8), (14) are inconsistent by sub-proof #563.
% 142.10/21.19 | | |
% 142.10/21.19 | | End of split
% 142.10/21.19 | |
% 142.10/21.19 | End of split
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #563 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) all_57_10 = e0 & op(e2, e0) = e0
% 142.10/21.19 (2) all_57_10 = e2
% 142.10/21.19 (3) ~ (e2 = e0)
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | ALPHA: (1) implies:
% 142.10/21.19 | (4) all_57_10 = e0
% 142.10/21.19 |
% 142.10/21.19 | COMBINE_EQS: (2), (4) imply:
% 142.10/21.19 | (5) e2 = e0
% 142.10/21.19 |
% 142.10/21.19 | REDUCE: (3), (5) imply:
% 142.10/21.19 | (6) $false
% 142.10/21.19 |
% 142.10/21.19 | CLOSE: (6) is inconsistent.
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #564 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) op(e3, e0) = e1
% 142.10/21.19 (2) op(e1, e3) = all_52_2
% 142.10/21.19 (3) all_57_6 = e3
% 142.10/21.19 (4) ~ (e2 = e1)
% 142.10/21.19 (5) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.10/21.19 (6) ~ (e3 = e0)
% 142.10/21.19 (7) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.10/21.19 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.10/21.19 all_14_1 & $i(all_14_1))
% 142.10/21.19 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.19 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.19 (9) all_57_3 = e1
% 142.10/21.19 (10) all_28_2 = e0
% 142.10/21.19 (11) ~ (e2 = e0)
% 142.10/21.19 (12) ~ (e3 = e2)
% 142.10/21.19 (13) op(e3, e0) = all_52_12
% 142.10/21.19 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.19 (15) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.19 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.19 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.19 (16) ~ (e3 = e1)
% 142.10/21.19 (17) all_57_0 = e0
% 142.10/21.19 (18) op(e3, e3) = e0
% 142.10/21.19 (19) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.19 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.19 (20) all_57_12 = e1
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | BETA: splitting (5) gives:
% 142.10/21.19 |
% 142.10/21.19 | Case 1:
% 142.10/21.19 | |
% 142.10/21.19 | | (21) all_57_2 = e3 & op(e2, e3) = e3
% 142.10/21.19 | |
% 142.10/21.19 | | ALPHA: (21) implies:
% 142.10/21.19 | | (22) all_57_2 = e3
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (1), (2), (4), (7), (10), (11), (12), (13), (14), (15), (18),
% 142.10/21.19 | | (19), (20), (22) are inconsistent by sub-proof #632.
% 142.10/21.19 | |
% 142.10/21.19 | Case 2:
% 142.10/21.19 | |
% 142.10/21.19 | | (23) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.10/21.19 | | (14), (15), (16), (17), (18), (19), (20), (23) are inconsistent
% 142.10/21.19 | | by sub-proof #605.
% 142.10/21.19 | |
% 142.10/21.19 | End of split
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #565 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) op(e3, e0) = e1
% 142.10/21.19 (2) ~ (e2 = e1)
% 142.10/21.19 (3) op(e3, e0) = all_14_1
% 142.10/21.19 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.19 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.19 (5) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.19 (6) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) = all_28_1
% 142.10/21.19 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e0) =
% 142.10/21.19 all_28_1 & $i(all_28_1))
% 142.10/21.19 (7) all_57_12 = e1
% 142.10/21.19
% 142.10/21.19 Begin of proof
% 142.10/21.19 |
% 142.10/21.19 | BETA: splitting (5) gives:
% 142.10/21.19 |
% 142.10/21.19 | Case 1:
% 142.10/21.19 | |
% 142.10/21.19 | | (8) all_57_6 = e2 & op(e1, e3) = e2
% 142.10/21.19 | |
% 142.10/21.19 | | ALPHA: (8) implies:
% 142.10/21.19 | | (9) op(e1, e3) = e2
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (1), (3), (4), (6), (9) are inconsistent by sub-proof #684.
% 142.10/21.19 | |
% 142.10/21.19 | Case 2:
% 142.10/21.19 | |
% 142.10/21.19 | | (10) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.19 | |
% 142.10/21.19 | | REF_CLOSE: (2), (7), (10) are inconsistent by sub-proof #674.
% 142.10/21.19 | |
% 142.10/21.19 | End of split
% 142.10/21.19 |
% 142.10/21.19 End of proof
% 142.10/21.19
% 142.10/21.19 Sub-proof #566 shows that the following formulas are inconsistent:
% 142.10/21.19 ----------------------------------------------------------------
% 142.10/21.19 (1) op(e3, e0) = e1
% 142.10/21.19 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.19 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.19 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.19 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.19 (4) op(e1, e3) = all_52_2
% 142.10/21.19 (5) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.19 (6) ~ (all_52_12 = e3)
% 142.10/21.19 (7) op(e1, e2) = all_52_6
% 142.10/21.19 (8) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.19 (9) ~ (all_52_4 = e0)
% 142.10/21.19 (10) ~ (e2 = e1)
% 142.10/21.19 (11) op(e0, e0) = e3
% 142.10/21.19 (12) ~ (all_42_0 = e2)
% 142.10/21.19 (13) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.19 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.19 (14) op(e2, e2) = e1
% 142.10/21.19 (15) ~ (all_52_6 = all_42_0)
% 142.10/21.20 (16) all_57_9 = e1
% 142.10/21.20 (17) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.20 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.20 (18) ~ (all_52_1 = e0)
% 142.10/21.20 (19) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.20 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.20 (20) ~ (e3 = e0)
% 142.10/21.20 (21) op(e1, e1) = e1
% 142.10/21.20 (22) op(e3, e1) = all_52_8
% 142.10/21.20 (23) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.20 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.20 (24) op(e2, e3) = all_52_1
% 142.10/21.20 (25) ~ (all_52_12 = e0)
% 142.10/21.20 (26) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.20 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.20 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.20 (27) all_54_11 = all_42_0
% 142.10/21.20 (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.20 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.20 (29) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.20 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.20 (30) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.20 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.20 (31) all_57_3 = e1
% 142.10/21.20 (32) all_28_2 = e0
% 142.10/21.20 (33) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.20 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.20 (34) ~ (e1 = e0)
% 142.10/21.20 (35) op(e3, e2) = all_52_4
% 142.10/21.20 (36) ~ (e2 = e0)
% 142.10/21.20 (37) ~ (e3 = e2)
% 142.10/21.20 (38) op(e3, e0) = all_52_12
% 142.10/21.20 (39) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.20 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.20 (40) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.20 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.20 (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.20 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.20 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.20 (43) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.20 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.20 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.20 (44) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.20 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.20 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.20 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.20 (45) ~ (all_52_8 = e0)
% 142.10/21.20 (46) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.20 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.20 (47) ~ (e3 = e1)
% 142.10/21.20 (48) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.20 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.20 (49) all_57_0 = e0
% 142.10/21.20 (50) op(e3, e3) = e0
% 142.10/21.20 (51) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.20 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.20 (52) ~ (all_42_0 = e1)
% 142.10/21.20 (53) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.20 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.20 (54) all_57_12 = e1
% 142.10/21.20 (55) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.20 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.20
% 142.10/21.20 Begin of proof
% 142.10/21.20 |
% 142.10/21.20 | BETA: splitting (8) gives:
% 142.10/21.20 |
% 142.10/21.20 | Case 1:
% 142.10/21.20 | |
% 142.10/21.20 | | (56) all_57_8 = e3 & op(e1, e1) = e3
% 142.10/21.20 | |
% 142.10/21.20 | | ALPHA: (56) implies:
% 142.10/21.20 | | (57) op(e1, e1) = e3
% 142.10/21.20 | |
% 142.10/21.20 | | REF_CLOSE: (21), (42), (47), (57) are inconsistent by sub-proof #1096.
% 142.10/21.20 | |
% 142.10/21.20 | Case 2:
% 142.10/21.20 | |
% 142.10/21.20 | | (58) all_57_11 = e3 & op(e1, e0) = e3
% 142.10/21.20 | |
% 142.10/21.20 | | ALPHA: (58) implies:
% 142.10/21.20 | | (59) all_57_11 = e3
% 142.10/21.20 | |
% 142.10/21.20 | | BETA: splitting (17) gives:
% 142.10/21.20 | |
% 142.10/21.20 | | Case 1:
% 142.10/21.20 | | |
% 142.10/21.20 | | | (60) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.10/21.20 | | | e2)
% 142.10/21.20 | | |
% 142.10/21.20 | | | BETA: splitting (60) gives:
% 142.10/21.20 | | |
% 142.10/21.20 | | | Case 1:
% 142.10/21.20 | | | |
% 142.10/21.20 | | | | (61) all_57_9 = e2 & op(e3, e0) = e2
% 142.10/21.20 | | | |
% 142.10/21.20 | | | | REF_CLOSE: (10), (16), (61) are inconsistent by sub-proof #636.
% 142.10/21.20 | | | |
% 142.10/21.20 | | | Case 2:
% 142.10/21.20 | | | |
% 142.10/21.20 | | | | (62) all_57_10 = e2 & op(e2, e0) = e2
% 142.10/21.20 | | | |
% 142.10/21.20 | | | | ALPHA: (62) implies:
% 142.10/21.20 | | | | (63) all_57_10 = e2
% 142.10/21.20 | | | |
% 142.10/21.20 | | | | BETA: splitting (53) gives:
% 142.10/21.20 | | | |
% 142.10/21.20 | | | | Case 1:
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | | (64) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 142.10/21.20 | | | | | e2) = e3)
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | | BETA: splitting (64) gives:
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | | Case 1:
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | (65) all_57_1 = e3 & op(e3, e2) = e3
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | ALPHA: (65) implies:
% 142.10/21.20 | | | | | | (66) all_57_1 = e3
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | BETA: splitting (55) gives:
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | Case 1:
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | (67) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 142.10/21.20 | | | | | | | op(e2, e2) = e0)
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | REF_CLOSE: (14), (18), (24), (34), (42), (67) are inconsistent by
% 142.10/21.20 | | | | | | | sub-proof #640.
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | Case 2:
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | (68) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 142.10/21.20 | | | | | | | op(e2, e0) = e0)
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | BETA: splitting (68) gives:
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | (69) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | ALPHA: (69) implies:
% 142.10/21.20 | | | | | | | | (70) all_57_5 = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (13), (14),
% 142.10/21.20 | | | | | | | | (17), (19), (20), (21), (22), (26), (31), (32), (33),
% 142.10/21.20 | | | | | | | | (34), (35), (36), (37), (38), (41), (42), (43), (44),
% 142.10/21.20 | | | | | | | | (45), (46), (47), (48), (49), (50), (51), (53), (54),
% 142.10/21.20 | | | | | | | | (66), (70) are inconsistent by sub-proof #617.
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | (71) all_57_10 = e0 & op(e2, e0) = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | ALPHA: (71) implies:
% 142.10/21.20 | | | | | | | | (72) all_57_10 = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | REF_CLOSE: (36), (63), (72) are inconsistent by sub-proof #609.
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | End of split
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | End of split
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | Case 2:
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | (73) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | REF_CLOSE: (2), (3), (4), (6), (9), (10), (11), (13), (14), (17),
% 142.10/21.20 | | | | | | (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 142.10/21.20 | | | | | | (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 142.10/21.20 | | | | | | (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 142.10/21.20 | | | | | | (46), (47), (48), (49), (50), (51), (53), (54), (55),
% 142.10/21.20 | | | | | | (59), (73) are inconsistent by sub-proof #568.
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | End of split
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | Case 2:
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | | (74) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 142.10/21.20 | | | | | e2) = e3)
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | | BETA: splitting (74) gives:
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | | Case 1:
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | (75) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | ALPHA: (75) implies:
% 142.10/21.20 | | | | | | (76) all_57_7 = e3
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | BETA: splitting (55) gives:
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | Case 1:
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | (77) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 &
% 142.10/21.20 | | | | | | | op(e2, e2) = e0)
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | REF_CLOSE: (14), (18), (24), (34), (42), (77) are inconsistent by
% 142.10/21.20 | | | | | | | sub-proof #640.
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | Case 2:
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | (78) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 &
% 142.10/21.20 | | | | | | | op(e2, e0) = e0)
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | BETA: splitting (78) gives:
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | (79) all_57_5 = e0 & op(e2, e1) = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | ALPHA: (79) implies:
% 142.10/21.20 | | | | | | | | (80) all_57_5 = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | BETA: splitting (48) gives:
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | | (81) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 142.10/21.20 | | | | | | | | | op(e3, e2) = e3)
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (9), (10), (11), (13),
% 142.10/21.20 | | | | | | | | | (14), (17), (19), (20), (21), (22), (26), (31),
% 142.10/21.20 | | | | | | | | | (32), (33), (34), (35), (36), (37), (38), (41),
% 142.10/21.20 | | | | | | | | | (42), (43), (44), (45), (46), (47), (48), (49),
% 142.10/21.20 | | | | | | | | | (50), (51), (53), (54), (80), (81) are inconsistent
% 142.10/21.20 | | | | | | | | | by sub-proof #616.
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | | (82) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 142.10/21.20 | | | | | | | | | op(e3, e0) = e3)
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | | BETA: splitting (82) gives:
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | (83) all_57_4 = e3 & op(e3, e1) = e3
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | ALPHA: (83) implies:
% 142.10/21.20 | | | | | | | | | | (84) all_57_4 = e3
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | BETA: splitting (29) gives:
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | (85) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 142.10/21.20 | | | | | | | | | | | & op(e2, e3) = e3)
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | REF_CLOSE: (1), (4), (10), (20), (26), (32), (36), (37),
% 142.10/21.20 | | | | | | | | | | | (38), (42), (43), (49), (50), (51), (54), (85) are
% 142.10/21.20 | | | | | | | | | | | inconsistent by sub-proof #615.
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | (86) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 142.10/21.20 | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | BETA: splitting (86) gives:
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | (87) all_57_6 = e3 & op(e1, e3) = e3
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | ALPHA: (87) implies:
% 142.10/21.20 | | | | | | | | | | | | (88) all_57_6 = e3
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | BETA: splitting (23) gives:
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | (89) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 142.10/21.20 | | | | | | | | | | | | | & op(e1, e2) = e0)
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | BETA: splitting (89) gives:
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | (90) all_57_6 = e0 & op(e1, e3) = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | ALPHA: (90) implies:
% 142.10/21.20 | | | | | | | | | | | | | | (91) all_57_6 = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | REF_CLOSE: (20), (88), (91) are inconsistent by sub-proof
% 142.10/21.20 | | | | | | | | | | | | | | #873.
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | (92) all_57_7 = e0 & op(e1, e2) = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | REF_CLOSE: (20), (76), (92) are inconsistent by sub-proof
% 142.10/21.20 | | | | | | | | | | | | | | #1061.
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | End of split
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | (93) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 142.10/21.20 | | | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | BETA: splitting (93) gives:
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | Case 1:
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | (94) all_57_8 = e0 & op(e1, e1) = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | ALPHA: (94) implies:
% 142.10/21.20 | | | | | | | | | | | | | | (95) op(e1, e1) = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | REF_CLOSE: (21), (34), (42), (95) are inconsistent by
% 142.10/21.20 | | | | | | | | | | | | | | sub-proof #1089.
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | (96) all_57_11 = e0 & op(e1, e0) = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | ALPHA: (96) implies:
% 142.10/21.20 | | | | | | | | | | | | | | (97) all_57_11 = e0
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | | REF_CLOSE: (20), (59), (97) are inconsistent by sub-proof
% 142.10/21.20 | | | | | | | | | | | | | | #858.
% 142.10/21.20 | | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | | End of split
% 142.10/21.20 | | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | End of split
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | (98) all_57_12 = e3 & op(e0, e3) = e3
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | | REF_CLOSE: (3), (10), (13), (20), (21), (22), (34), (36),
% 142.10/21.20 | | | | | | | | | | | | (37), (41), (42), (45), (47), (54), (84), (98) are
% 142.10/21.20 | | | | | | | | | | | | inconsistent by sub-proof #610.
% 142.10/21.20 | | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | | End of split
% 142.10/21.20 | | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | End of split
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | (99) all_57_9 = e3 & op(e3, e0) = e3
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | ALPHA: (99) implies:
% 142.10/21.20 | | | | | | | | | | (100) op(e3, e0) = e3
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | | REF_CLOSE: (6), (38), (42), (100) are inconsistent by
% 142.10/21.20 | | | | | | | | | | sub-proof #1105.
% 142.10/21.20 | | | | | | | | | |
% 142.10/21.20 | | | | | | | | | End of split
% 142.10/21.20 | | | | | | | | |
% 142.10/21.20 | | | | | | | | End of split
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | Case 2:
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | (101) all_57_10 = e0 & op(e2, e0) = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | ALPHA: (101) implies:
% 142.10/21.20 | | | | | | | | (102) all_57_10 = e0
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | | REF_CLOSE: (36), (63), (102) are inconsistent by sub-proof #609.
% 142.10/21.20 | | | | | | | |
% 142.10/21.20 | | | | | | | End of split
% 142.10/21.20 | | | | | | |
% 142.10/21.20 | | | | | | End of split
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | Case 2:
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | (103) all_57_13 = e3 & op(e0, e2) = e3
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | | REF_CLOSE: (5), (7), (9), (12), (14), (15), (20), (27), (33), (34),
% 142.10/21.20 | | | | | | (35), (42), (52), (103) are inconsistent by sub-proof
% 142.10/21.20 | | | | | | #573.
% 142.10/21.20 | | | | | |
% 142.10/21.20 | | | | | End of split
% 142.10/21.20 | | | | |
% 142.10/21.20 | | | | End of split
% 142.10/21.20 | | | |
% 142.10/21.20 | | | End of split
% 142.10/21.20 | | |
% 142.10/21.20 | | Case 2:
% 142.10/21.20 | | |
% 142.10/21.20 | | | (104) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0)
% 142.10/21.20 | | | = e2)
% 142.10/21.20 | | |
% 142.10/21.20 | | | REF_CLOSE: (11), (37), (42), (59), (104) are inconsistent by sub-proof
% 142.10/21.20 | | | #567.
% 142.10/21.20 | | |
% 142.10/21.20 | | End of split
% 142.10/21.20 | |
% 142.10/21.20 | End of split
% 142.10/21.20 |
% 142.10/21.20 End of proof
% 142.10/21.20
% 142.10/21.20 Sub-proof #567 shows that the following formulas are inconsistent:
% 142.10/21.20 ----------------------------------------------------------------
% 142.10/21.20 (1) op(e0, e0) = e3
% 142.10/21.20 (2) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.20 (3) ~ (e3 = e2)
% 142.10/21.20 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.20 (5) all_57_11 = e3
% 142.10/21.20
% 142.10/21.20 Begin of proof
% 142.10/21.20 |
% 142.10/21.20 | BETA: splitting (2) gives:
% 142.10/21.20 |
% 142.10/21.20 | Case 1:
% 142.10/21.20 | |
% 142.10/21.20 | | (6) all_57_11 = e2 & op(e1, e0) = e2
% 142.10/21.20 | |
% 142.10/21.20 | | ALPHA: (6) implies:
% 142.10/21.20 | | (7) all_57_11 = e2
% 142.10/21.20 | |
% 142.10/21.20 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #1055.
% 142.10/21.20 | |
% 142.10/21.20 | Case 2:
% 142.10/21.20 | |
% 142.10/21.20 | | (8) all_57_15 = e2 & op(e0, e0) = e2
% 142.10/21.20 | |
% 142.10/21.20 | | ALPHA: (8) implies:
% 142.10/21.20 | | (9) op(e0, e0) = e2
% 142.10/21.20 | |
% 142.10/21.20 | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #1066.
% 142.10/21.20 | |
% 142.10/21.20 | End of split
% 142.10/21.20 |
% 142.10/21.20 End of proof
% 142.10/21.20
% 142.10/21.20 Sub-proof #568 shows that the following formulas are inconsistent:
% 142.10/21.20 ----------------------------------------------------------------
% 142.10/21.20 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.20 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.20 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.20 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.20 (3) op(e1, e3) = all_52_2
% 142.10/21.20 (4) ~ (all_52_12 = e3)
% 142.10/21.20 (5) ~ (all_52_4 = e0)
% 142.10/21.20 (6) ~ (e2 = e1)
% 142.10/21.20 (7) op(e0, e0) = e3
% 142.10/21.20 (8) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.20 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.20 (9) op(e2, e2) = e1
% 142.10/21.20 (10) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.20 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.20 (11) ~ (all_52_1 = e0)
% 142.10/21.20 (12) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.20 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.20 (13) ~ (e3 = e0)
% 142.10/21.20 (14) op(e1, e1) = e1
% 142.10/21.20 (15) op(e3, e1) = all_52_8
% 142.10/21.20 (16) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.20 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.20 (17) op(e2, e3) = all_52_1
% 142.10/21.20 (18) ~ (all_52_12 = e0)
% 142.10/21.20 (19) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.20 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.20 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.20 (20) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.20 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.20 (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.20 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.20 (22) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.20 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.20 (23) all_57_3 = e1
% 142.10/21.20 (24) all_28_2 = e0
% 142.10/21.20 (25) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.20 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.20 (26) ~ (e1 = e0)
% 142.10/21.20 (27) op(e3, e2) = all_52_4
% 142.10/21.20 (28) ~ (e2 = e0)
% 142.10/21.20 (29) ~ (e3 = e2)
% 142.10/21.20 (30) op(e3, e0) = all_52_12
% 142.10/21.20 (31) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.20 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.20 (32) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.20 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.20 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.20 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.20 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.20 (35) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.20 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.20 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.20 (36) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.20 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.20 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.20 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.20 (37) ~ (all_52_8 = e0)
% 142.10/21.20 (38) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.20 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.20 (39) ~ (e3 = e1)
% 142.10/21.20 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.20 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.20 (41) all_57_0 = e0
% 142.10/21.20 (42) op(e3, e3) = e0
% 142.10/21.20 (43) all_57_11 = e3
% 142.10/21.20 (44) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.20 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.20 (45) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.20 (46) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.20 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.20 (47) all_57_12 = e1
% 142.10/21.20 (48) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.20 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.20
% 142.10/21.20 Begin of proof
% 142.10/21.20 |
% 142.10/21.20 | ALPHA: (45) implies:
% 142.10/21.20 | (49) all_57_3 = e3
% 142.10/21.20 |
% 142.10/21.20 | COMBINE_EQS: (23), (49) imply:
% 142.10/21.20 | (50) e3 = e1
% 142.10/21.20 |
% 142.10/21.20 | COMBINE_EQS: (43), (50) imply:
% 142.10/21.20 | (51) all_57_11 = e1
% 142.10/21.20 |
% 142.10/21.20 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.10/21.20 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.10/21.20 | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 142.10/21.20 | (35), (36), (37), (38), (39), (40), (41), (42), (44), (46), (47),
% 142.10/21.20 | (48), (51) are inconsistent by sub-proof #569.
% 142.10/21.20 |
% 142.10/21.20 End of proof
% 142.10/21.20
% 142.10/21.20 Sub-proof #569 shows that the following formulas are inconsistent:
% 142.10/21.20 ----------------------------------------------------------------
% 142.10/21.20 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.20 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.20 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.20 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.20 (3) op(e1, e3) = all_52_2
% 142.10/21.20 (4) ~ (all_52_12 = e3)
% 142.10/21.20 (5) ~ (all_52_4 = e0)
% 142.10/21.20 (6) ~ (e2 = e1)
% 142.10/21.20 (7) op(e0, e0) = e3
% 142.10/21.20 (8) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.20 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.20 (9) op(e2, e2) = e1
% 142.10/21.20 (10) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.20 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.20 (11) ~ (all_52_1 = e0)
% 142.10/21.20 (12) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.20 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.20 (13) ~ (e3 = e0)
% 142.10/21.20 (14) op(e1, e1) = e1
% 142.10/21.20 (15) op(e3, e1) = all_52_8
% 142.10/21.20 (16) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.20 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.20 (17) op(e2, e3) = all_52_1
% 142.10/21.20 (18) ~ (all_52_12 = e0)
% 142.10/21.20 (19) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.20 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.20 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.20 (20) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.20 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.20 (21) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.20 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.20 (22) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.20 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.20 (23) all_57_3 = e1
% 142.10/21.20 (24) all_28_2 = e0
% 142.10/21.20 (25) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.20 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.20 (26) ~ (e1 = e0)
% 142.10/21.20 (27) op(e3, e2) = all_52_4
% 142.10/21.20 (28) ~ (e2 = e0)
% 142.10/21.20 (29) ~ (e3 = e2)
% 142.10/21.20 (30) op(e3, e0) = all_52_12
% 142.10/21.20 (31) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.20 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.20 (32) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.20 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.20 (33) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.20 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.20 (34) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.20 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.20 (35) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.20 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.20 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.20 (36) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.20 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.20 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.20 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.20 (37) ~ (all_52_8 = e0)
% 142.10/21.20 (38) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.20 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.20 (39) ~ (e3 = e1)
% 142.10/21.20 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.20 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.20 (41) all_57_0 = e0
% 142.10/21.20 (42) op(e3, e3) = e0
% 142.10/21.20 (43) all_57_11 = e1
% 142.10/21.20 (44) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.20 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.20 (45) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.20 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.20 (46) all_57_12 = e1
% 142.10/21.20 (47) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.20 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.20
% 142.10/21.20 Begin of proof
% 142.10/21.20 |
% 142.10/21.20 | BETA: splitting (36) gives:
% 142.10/21.20 |
% 142.10/21.20 | Case 1:
% 142.10/21.20 | |
% 142.10/21.20 | | (48) all_57_15 = e0 & op(e0, e0) = e0
% 142.10/21.20 | |
% 142.10/21.20 | | ALPHA: (48) implies:
% 142.10/21.20 | | (49) op(e0, e0) = e0
% 142.10/21.20 | |
% 142.10/21.20 | | REF_CLOSE: (7), (13), (34), (49) are inconsistent by sub-proof #751.
% 142.10/21.20 | |
% 142.10/21.20 | Case 2:
% 142.10/21.20 | |
% 142.10/21.20 | | (50) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.10/21.20 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.10/21.20 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.10/21.20 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.10/21.20 | |
% 142.10/21.20 | | ALPHA: (50) implies:
% 142.10/21.20 | | (51) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.10/21.20 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.20 | |
% 142.10/21.20 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.10/21.20 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.10/21.20 | | (24), (25), (26), (27), (28), (29), (30), (31), (32), (33), (34),
% 142.10/21.20 | | (35), (37), (38), (39), (40), (41), (42), (43), (44), (45), (46),
% 142.10/21.20 | | (47), (51) are inconsistent by sub-proof #577.
% 142.10/21.20 | |
% 142.10/21.20 | End of split
% 142.10/21.20 |
% 142.10/21.20 End of proof
% 142.10/21.20
% 142.10/21.20 Sub-proof #570 shows that the following formulas are inconsistent:
% 142.10/21.20 ----------------------------------------------------------------
% 142.10/21.20 (1) op(e3, e0) = e1
% 142.10/21.20 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.20 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.20 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.10/21.20 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.10/21.20 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.20 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.20 (5) op(e1, e3) = all_52_2
% 142.10/21.20 (6) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.20 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.20 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.10/21.20 (8) ~ (all_52_12 = e3)
% 142.10/21.20 (9) op(e1, e2) = all_52_6
% 142.10/21.20 (10) ~ (all_52_4 = e0)
% 142.10/21.20 (11) ~ (e2 = e1)
% 142.10/21.20 (12) op(e0, e0) = e3
% 142.10/21.20 (13) ~ (all_42_0 = e2)
% 142.10/21.21 (14) op(e0, e3) = all_52_3
% 142.10/21.21 (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.21 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.21 (16) op(e2, e2) = e1
% 142.10/21.21 (17) ~ (all_52_6 = all_42_0)
% 142.10/21.21 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.10/21.21 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.21 e1)
% 142.10/21.21 (19) all_57_9 = e1
% 142.10/21.21 (20) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.21 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.21 (21) ~ (all_52_1 = e0)
% 142.10/21.21 (22) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.21 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.21 (23) ~ (e3 = e0)
% 142.10/21.21 (24) op(e1, e1) = e1
% 142.10/21.21 (25) op(e1, e1) = all_4_2
% 142.10/21.21 (26) op(e3, e1) = all_52_8
% 142.10/21.21 (27) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.21 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.21 (28) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.21 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.21 e2)
% 142.10/21.21 (29) op(e2, e3) = all_52_1
% 142.10/21.21 (30) ~ (all_52_12 = e0)
% 142.10/21.21 (31) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.21 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.21 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.21 (32) all_54_11 = all_42_0
% 142.10/21.21 (33) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.21 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.21 (34) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.21 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.21 (35) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.21 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.21 (36) all_57_3 = e1
% 142.10/21.21 (37) ~ (all_4_2 = e3)
% 142.10/21.21 (38) ~ (all_52_13 = all_42_0)
% 142.10/21.21 (39) all_28_2 = e0
% 142.10/21.21 (40) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.21 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.21 (41) ~ (e1 = e0)
% 142.10/21.21 (42) op(e3, e2) = all_52_4
% 142.10/21.21 (43) ~ (e2 = e0)
% 142.10/21.21 (44) ~ (e3 = e2)
% 142.10/21.21 (45) op(e3, e0) = all_52_12
% 142.10/21.21 (46) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.21 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.21 (47) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.21 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.21 (48) ~ (all_4_2 = e2)
% 142.10/21.21 (49) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.21 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.21 (50) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.21 (51) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.21 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.21 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.21 (52) ~ (all_52_3 = e0)
% 142.10/21.21 (53) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.21 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.21 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.21 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.21 (54) ~ (all_52_8 = e0)
% 142.10/21.21 (55) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.21 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.21 (56) ~ (e3 = e1)
% 142.10/21.21 (57) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.21 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.21 (58) ~ (all_52_9 = e1)
% 142.10/21.21 (59) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.21 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.21 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.21 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.21 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.21 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.21 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.21 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.21 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.21 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.21 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.21 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.21 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.21 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.21 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.21 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.21 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.21 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.21 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.21 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.21 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.21 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.21 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.21 $i(all_56_14))))
% 142.10/21.21 (60) all_57_0 = e0
% 142.10/21.21 (61) op(e3, e3) = e0
% 142.10/21.21 (62) op(e2, e1) = all_52_9
% 142.10/21.21 (63) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.21 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.21 (64) all_57_7 = e3
% 142.10/21.21 (65) all_57_2 = e2
% 142.10/21.21 (66) ~ (all_42_0 = e1)
% 142.10/21.21 (67) ~ (all_42_0 = e3)
% 142.10/21.21 (68) op(e2, e0) = all_52_13
% 142.10/21.21 (69) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.21 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.21 (70) all_57_12 = e1
% 142.10/21.21 (71) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.21 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.21
% 142.10/21.21 Begin of proof
% 142.10/21.21 |
% 142.10/21.21 | BETA: splitting (20) gives:
% 142.10/21.21 |
% 142.10/21.21 | Case 1:
% 142.10/21.21 | |
% 142.10/21.21 | | (72) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.10/21.21 | | e2)
% 142.10/21.21 | |
% 142.10/21.21 | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (13), (15),
% 142.10/21.21 | | (16), (17), (19), (20), (21), (22), (23), (24), (26), (27), (29),
% 142.10/21.21 | | (31), (32), (34), (36), (39), (40), (41), (42), (43), (44), (45),
% 142.10/21.21 | | (49), (50), (51), (53), (54), (55), (56), (57), (60), (61), (63),
% 142.10/21.21 | | (65), (66), (69), (70), (71), (72) are inconsistent by sub-proof
% 142.10/21.21 | | #608.
% 142.10/21.21 | |
% 142.10/21.21 | Case 2:
% 142.10/21.21 | |
% 142.10/21.21 | | (73) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.21 | | e2)
% 142.10/21.21 | |
% 142.10/21.21 | | BETA: splitting (73) gives:
% 142.10/21.21 | |
% 142.10/21.21 | | Case 1:
% 142.10/21.21 | | |
% 142.10/21.21 | | | (74) all_57_11 = e2 & op(e1, e0) = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | ALPHA: (74) implies:
% 142.10/21.21 | | | (75) all_57_11 = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (10), (11), (12), (13),
% 142.10/21.21 | | | (14), (15), (16), (18), (19), (20), (21), (22), (24), (25),
% 142.10/21.21 | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 142.10/21.21 | | | (36), (37), (38), (39), (40), (42), (44), (45), (46), (47),
% 142.10/21.21 | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 142.10/21.21 | | | (58), (59), (60), (61), (62), (63), (64), (66), (67), (68),
% 142.10/21.21 | | | (69), (70), (71), (75) are inconsistent by sub-proof #574.
% 142.10/21.21 | | |
% 142.10/21.21 | | Case 2:
% 142.10/21.21 | | |
% 142.10/21.21 | | | (76) all_57_15 = e2 & op(e0, e0) = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | ALPHA: (76) implies:
% 142.10/21.21 | | | (77) op(e0, e0) = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | REF_CLOSE: (12), (44), (50), (77) are inconsistent by sub-proof #1066.
% 142.10/21.21 | | |
% 142.10/21.21 | | End of split
% 142.10/21.21 | |
% 142.10/21.21 | End of split
% 142.10/21.21 |
% 142.10/21.21 End of proof
% 142.10/21.21
% 142.10/21.21 Sub-proof #571 shows that the following formulas are inconsistent:
% 142.10/21.21 ----------------------------------------------------------------
% 142.10/21.21 (1) op(e3, e0) = e1
% 142.10/21.21 (2) ~ (e2 = e1)
% 142.10/21.21 (3) ~ (all_28_0 = e2)
% 142.10/21.21 (4) op(e3, e0) = all_28_1
% 142.10/21.21 (5) op(e1, e3) = all_14_0
% 142.10/21.21 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.21 (7) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.21 (8) op(all_28_1, e3) = all_28_0
% 142.10/21.21 (9) all_57_12 = e1
% 142.10/21.21
% 142.10/21.21 Begin of proof
% 142.10/21.21 |
% 142.10/21.21 | BETA: splitting (7) gives:
% 142.10/21.21 |
% 142.10/21.21 | Case 1:
% 142.10/21.21 | |
% 142.10/21.21 | | (10) all_57_6 = e2 & op(e1, e3) = e2
% 142.10/21.21 | |
% 142.10/21.21 | | ALPHA: (10) implies:
% 142.10/21.21 | | (11) op(e1, e3) = e2
% 142.10/21.21 | |
% 142.10/21.21 | | REF_CLOSE: (1), (3), (4), (5), (6), (8), (11) are inconsistent by sub-proof
% 142.10/21.21 | | #686.
% 142.10/21.21 | |
% 142.10/21.21 | Case 2:
% 142.10/21.21 | |
% 142.10/21.21 | | (12) all_57_12 = e2 & op(e0, e3) = e2
% 142.10/21.21 | |
% 142.10/21.21 | | REF_CLOSE: (2), (9), (12) are inconsistent by sub-proof #674.
% 142.10/21.21 | |
% 142.10/21.21 | End of split
% 142.10/21.21 |
% 142.10/21.21 End of proof
% 142.10/21.21
% 142.10/21.21 Sub-proof #572 shows that the following formulas are inconsistent:
% 142.10/21.21 ----------------------------------------------------------------
% 142.10/21.21 (1) op(e3, e0) = e1
% 142.10/21.21 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.21 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.10/21.21 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.10/21.21 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.10/21.21 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.10/21.21 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.10/21.21 (5) op(e1, e3) = all_52_2
% 142.10/21.21 (6) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.21 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.21 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.10/21.21 (8) all_57_6 = e3
% 142.10/21.21 (9) ~ (all_52_12 = e3)
% 142.10/21.21 (10) op(e1, e2) = all_52_6
% 142.10/21.21 (11) ~ (all_52_4 = e0)
% 142.10/21.21 (12) ~ (e2 = e1)
% 142.10/21.21 (13) op(e0, e0) = e3
% 142.10/21.21 (14) ~ (all_42_0 = e2)
% 142.10/21.21 (15) op(e0, e3) = all_52_3
% 142.10/21.21 (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.10/21.21 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.10/21.21 (17) op(e2, e2) = e1
% 142.10/21.21 (18) ~ (all_52_6 = all_42_0)
% 142.10/21.21 (19) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.10/21.21 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.10/21.21 e1)
% 142.10/21.21 (20) all_57_9 = e1
% 142.10/21.21 (21) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.10/21.21 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.10/21.21 (22) ~ (all_52_1 = e0)
% 142.10/21.21 (23) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.10/21.21 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.21 (24) ~ (e3 = e0)
% 142.10/21.21 (25) op(e1, e1) = e1
% 142.10/21.21 (26) op(e1, e1) = all_4_2
% 142.10/21.21 (27) op(e3, e1) = all_52_8
% 142.10/21.21 (28) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.10/21.21 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.10/21.21 (29) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.10/21.21 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.21 e2)
% 142.10/21.21 (30) op(e2, e3) = all_52_1
% 142.10/21.21 (31) ~ (all_52_12 = e0)
% 142.10/21.21 (32) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.10/21.21 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.10/21.21 e0) = all_14_1 & $i(all_14_1))
% 142.10/21.21 (33) all_54_11 = all_42_0
% 142.10/21.21 (34) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.10/21.21 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.10/21.21 (35) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.10/21.21 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.10/21.21 (36) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.10/21.21 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.10/21.21 (37) all_57_3 = e1
% 142.10/21.21 (38) ~ (all_4_2 = e3)
% 142.10/21.21 (39) ~ (all_52_13 = all_42_0)
% 142.10/21.21 (40) all_28_2 = e0
% 142.10/21.21 (41) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.21 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.10/21.21 (42) ~ (e1 = e0)
% 142.10/21.21 (43) op(e3, e2) = all_52_4
% 142.10/21.21 (44) ~ (e2 = e0)
% 142.10/21.21 (45) ~ (e3 = e2)
% 142.10/21.21 (46) op(e3, e0) = all_52_12
% 142.10/21.21 (47) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.10/21.21 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.10/21.21 (48) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.10/21.21 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.10/21.21 (49) ~ (all_4_2 = e2)
% 142.10/21.21 (50) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.10/21.21 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.10/21.21 (51) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.10/21.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.10/21.21 (52) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.10/21.21 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.10/21.21 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.10/21.21 (53) ~ (all_52_3 = e0)
% 142.10/21.21 (54) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.10/21.21 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.10/21.21 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.10/21.21 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.10/21.21 (55) ~ (all_52_8 = e0)
% 142.10/21.21 (56) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.10/21.21 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.10/21.21 (57) ~ (e3 = e1)
% 142.10/21.21 (58) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.10/21.21 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.10/21.21 (59) ~ (all_52_9 = e1)
% 142.10/21.21 (60) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.10/21.21 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.10/21.21 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.10/21.21 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.10/21.21 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.10/21.21 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.10/21.21 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.10/21.21 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.10/21.21 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.10/21.21 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.10/21.21 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.10/21.21 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.10/21.21 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.10/21.21 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.10/21.21 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.10/21.21 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.10/21.21 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.10/21.21 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.10/21.21 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.10/21.21 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.10/21.21 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.10/21.21 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.10/21.21 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.10/21.21 $i(all_56_14))))
% 142.10/21.21 (61) all_57_0 = e0
% 142.10/21.21 (62) op(e3, e3) = e0
% 142.10/21.21 (63) op(e2, e1) = all_52_9
% 142.10/21.21 (64) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.10/21.21 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.10/21.21 (65) all_57_2 = e2
% 142.10/21.21 (66) ~ (all_42_0 = e1)
% 142.10/21.21 (67) ~ (all_42_0 = e3)
% 142.10/21.21 (68) op(e2, e0) = all_52_13
% 142.10/21.21 (69) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.10/21.21 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.10/21.21 (70) all_57_12 = e1
% 142.10/21.21 (71) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.10/21.21 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.10/21.21
% 142.10/21.21 Begin of proof
% 142.10/21.21 |
% 142.10/21.21 | BETA: splitting (21) gives:
% 142.10/21.21 |
% 142.10/21.21 | Case 1:
% 142.10/21.21 | |
% 142.10/21.21 | | (72) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.10/21.21 | | e2)
% 142.10/21.21 | |
% 142.10/21.21 | | REF_CLOSE: (1), (2), (4), (5), (6), (9), (10), (11), (12), (13), (14), (16),
% 142.10/21.21 | | (17), (18), (20), (21), (22), (23), (24), (25), (27), (28), (30),
% 142.10/21.21 | | (32), (33), (35), (37), (40), (41), (42), (43), (44), (45), (46),
% 142.10/21.21 | | (50), (51), (52), (54), (55), (56), (57), (58), (61), (62), (64),
% 142.10/21.21 | | (65), (66), (69), (70), (71), (72) are inconsistent by sub-proof
% 142.10/21.21 | | #608.
% 142.10/21.21 | |
% 142.10/21.21 | Case 2:
% 142.10/21.21 | |
% 142.10/21.21 | | (73) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.10/21.21 | | e2)
% 142.10/21.21 | |
% 142.10/21.21 | | BETA: splitting (73) gives:
% 142.10/21.21 | |
% 142.10/21.21 | | Case 1:
% 142.10/21.21 | | |
% 142.10/21.21 | | | (74) all_57_11 = e2 & op(e1, e0) = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | ALPHA: (74) implies:
% 142.10/21.21 | | | (75) all_57_11 = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | BETA: splitting (69) gives:
% 142.10/21.21 | | |
% 142.10/21.21 | | | Case 1:
% 142.10/21.21 | | | |
% 142.10/21.21 | | | | (76) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 142.10/21.21 | | | | = e3)
% 142.10/21.21 | | | |
% 142.10/21.21 | | | | BETA: splitting (76) gives:
% 142.10/21.21 | | | |
% 142.10/21.21 | | | | Case 1:
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | (77) all_57_1 = e3 & op(e3, e2) = e3
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | ALPHA: (77) implies:
% 142.10/21.21 | | | | | (78) all_57_1 = e3
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | BETA: splitting (6) gives:
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | Case 1:
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | | (79) all_54_11 = e2
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | | REF_CLOSE: (14), (33), (79) are inconsistent by sub-proof #613.
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | Case 2:
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | | (80) ~ (all_54_11 = e2)
% 142.10/21.21 | | | | | | (81) all_54_11 = e1 | all_54_11 = e0
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | | BETA: splitting (81) gives:
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | | Case 1:
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | (82) all_54_11 = e1
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | REF_CLOSE: (33), (66), (82) are inconsistent by sub-proof #612.
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | Case 2:
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | (83) all_54_11 = e0
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | COMBINE_EQS: (33), (83) imply:
% 142.10/21.21 | | | | | | | (84) all_42_0 = e0
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | SIMP: (84) implies:
% 142.10/21.21 | | | | | | | (85) all_42_0 = e0
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | REDUCE: (39), (85) imply:
% 142.10/21.21 | | | | | | | (86) ~ (all_52_13 = e0)
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | REDUCE: (67), (85) imply:
% 142.10/21.21 | | | | | | | (87) ~ (e3 = e0)
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | REDUCE: (14), (85) imply:
% 142.10/21.21 | | | | | | | (88) ~ (e2 = e0)
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | REDUCE: (66), (85) imply:
% 142.10/21.21 | | | | | | | (89) ~ (e1 = e0)
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | | REF_CLOSE: (1), (2), (4), (5), (9), (11), (12), (13), (16), (17),
% 142.10/21.21 | | | | | | | (21), (22), (23), (24), (25), (27), (30), (32), (37),
% 142.10/21.21 | | | | | | | (40), (41), (43), (44), (45), (46), (50), (51), (52),
% 142.10/21.21 | | | | | | | (54), (55), (56), (57), (58), (61), (62), (64), (68),
% 142.10/21.21 | | | | | | | (69), (70), (71), (78), (86), (89) are inconsistent by
% 142.10/21.21 | | | | | | | sub-proof #607.
% 142.10/21.21 | | | | | | |
% 142.10/21.21 | | | | | | End of split
% 142.10/21.21 | | | | | |
% 142.10/21.21 | | | | | End of split
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | Case 2:
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | (90) all_57_3 = e3 & op(e2, e2) = e3
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | REF_CLOSE: (1), (5), (8), (12), (24), (32), (35), (37), (40), (44),
% 142.10/21.21 | | | | | (45), (46), (51), (52), (57), (61), (62), (64), (70), (90)
% 142.10/21.21 | | | | | are inconsistent by sub-proof #605.
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | End of split
% 142.10/21.21 | | | |
% 142.10/21.21 | | | Case 2:
% 142.10/21.21 | | | |
% 142.10/21.21 | | | | (91) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 142.10/21.21 | | | | = e3)
% 142.10/21.21 | | | |
% 142.10/21.21 | | | | BETA: splitting (91) gives:
% 142.10/21.21 | | | |
% 142.10/21.21 | | | | Case 1:
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | (92) all_57_7 = e3 & op(e1, e2) = e3
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | ALPHA: (92) implies:
% 142.10/21.21 | | | | | (93) all_57_7 = e3
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11), (12), (13),
% 142.10/21.21 | | | | | (14), (15), (16), (17), (19), (20), (21), (22), (23), (25),
% 142.10/21.21 | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 142.10/21.21 | | | | | (36), (37), (38), (39), (40), (41), (43), (45), (46), (47),
% 142.10/21.21 | | | | | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57),
% 142.10/21.21 | | | | | (58), (59), (60), (61), (62), (63), (64), (66), (67), (68),
% 142.10/21.21 | | | | | (69), (70), (71), (75), (93) are inconsistent by sub-proof
% 142.10/21.21 | | | | | #574.
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | Case 2:
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | (94) all_57_13 = e3 & op(e0, e2) = e3
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | | REF_CLOSE: (6), (10), (11), (14), (17), (18), (24), (33), (41), (42),
% 142.10/21.21 | | | | | (43), (51), (66), (94) are inconsistent by sub-proof #573.
% 142.10/21.21 | | | | |
% 142.10/21.21 | | | | End of split
% 142.10/21.21 | | | |
% 142.10/21.21 | | | End of split
% 142.10/21.21 | | |
% 142.10/21.21 | | Case 2:
% 142.10/21.21 | | |
% 142.10/21.21 | | | (95) all_57_15 = e2 & op(e0, e0) = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | ALPHA: (95) implies:
% 142.10/21.21 | | | (96) op(e0, e0) = e2
% 142.10/21.21 | | |
% 142.10/21.21 | | | REF_CLOSE: (13), (45), (51), (96) are inconsistent by sub-proof #1066.
% 142.10/21.21 | | |
% 142.10/21.21 | | End of split
% 142.10/21.21 | |
% 142.10/21.21 | End of split
% 142.10/21.21 |
% 142.10/21.21 End of proof
% 142.10/21.21
% 142.10/21.21 Sub-proof #573 shows that the following formulas are inconsistent:
% 142.10/21.21 ----------------------------------------------------------------
% 142.10/21.21 (1) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.10/21.21 (2) op(e1, e2) = all_52_6
% 142.10/21.21 (3) ~ (all_52_4 = e0)
% 142.10/21.21 (4) ~ (all_42_0 = e2)
% 142.10/21.21 (5) op(e2, e2) = e1
% 142.10/21.21 (6) ~ (all_52_6 = all_42_0)
% 142.38/21.21 (7) ~ (e3 = e0)
% 142.38/21.21 (8) all_54_11 = all_42_0
% 142.38/21.21 (9) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.21 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.21 (10) ~ (e1 = e0)
% 142.38/21.21 (11) op(e3, e2) = all_52_4
% 142.38/21.21 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.21 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.21 (13) ~ (all_42_0 = e1)
% 142.38/21.21 (14) all_57_13 = e3 & op(e0, e2) = e3
% 142.38/21.21
% 142.38/21.21 Begin of proof
% 142.38/21.21 |
% 142.38/21.21 | ALPHA: (14) implies:
% 142.38/21.21 | (15) all_57_13 = e3
% 142.38/21.21 |
% 142.38/21.21 | BETA: splitting (9) gives:
% 142.38/21.21 |
% 142.38/21.21 | Case 1:
% 142.38/21.21 | |
% 142.38/21.21 | | (16) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.38/21.21 | | e0)
% 142.38/21.21 | |
% 142.38/21.21 | | REF_CLOSE: (3), (5), (10), (11), (12), (16) are inconsistent by sub-proof
% 142.38/21.21 | | #1062.
% 142.38/21.21 | |
% 142.38/21.21 | Case 2:
% 142.38/21.21 | |
% 142.38/21.21 | | (17) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.38/21.21 | | e0)
% 142.38/21.21 | |
% 142.38/21.21 | | BETA: splitting (17) gives:
% 142.38/21.21 | |
% 142.38/21.21 | | Case 1:
% 142.38/21.21 | | |
% 142.38/21.21 | | | (18) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.21 | | |
% 142.38/21.21 | | | REF_CLOSE: (1), (2), (4), (6), (8), (12), (13), (18) are inconsistent by
% 142.38/21.21 | | | sub-proof #611.
% 142.38/21.21 | | |
% 142.38/21.21 | | Case 2:
% 142.38/21.21 | | |
% 142.38/21.21 | | | (19) all_57_13 = e0 & op(e0, e2) = e0
% 142.38/21.21 | | |
% 142.38/21.21 | | | ALPHA: (19) implies:
% 142.38/21.21 | | | (20) all_57_13 = e0
% 142.38/21.21 | | |
% 142.38/21.21 | | | REF_CLOSE: (7), (15), (20) are inconsistent by sub-proof #804.
% 142.38/21.21 | | |
% 142.38/21.21 | | End of split
% 142.38/21.21 | |
% 142.38/21.21 | End of split
% 142.38/21.21 |
% 142.38/21.21 End of proof
% 142.38/21.21
% 142.38/21.21 Sub-proof #574 shows that the following formulas are inconsistent:
% 142.38/21.21 ----------------------------------------------------------------
% 142.38/21.21 (1) op(e3, e0) = e1
% 142.38/21.21 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.21 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.21 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.38/21.21 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.38/21.21 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.21 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.21 (5) op(e1, e3) = all_52_2
% 142.38/21.21 (6) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.38/21.21 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.21 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.38/21.21 (8) ~ (all_52_12 = e3)
% 142.38/21.21 (9) ~ (all_52_4 = e0)
% 142.38/21.21 (10) ~ (e2 = e1)
% 142.38/21.21 (11) op(e0, e0) = e3
% 142.38/21.21 (12) ~ (all_42_0 = e2)
% 142.38/21.21 (13) op(e0, e3) = all_52_3
% 142.38/21.21 (14) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.21 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.21 (15) op(e2, e2) = e1
% 142.38/21.21 (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.38/21.21 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.38/21.21 e1)
% 142.38/21.21 (17) all_57_9 = e1
% 142.38/21.22 (18) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.22 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.22 (19) ~ (all_52_1 = e0)
% 142.38/21.22 (20) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.22 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.22 (21) op(e1, e1) = e1
% 142.38/21.22 (22) op(e1, e1) = all_4_2
% 142.38/21.22 (23) op(e3, e1) = all_52_8
% 142.38/21.22 (24) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.38/21.22 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.22 (25) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.22 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.38/21.22 e2)
% 142.38/21.22 (26) op(e2, e3) = all_52_1
% 142.38/21.22 (27) ~ (all_52_12 = e0)
% 142.38/21.22 (28) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.22 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.22 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.22 (29) all_54_11 = all_42_0
% 142.38/21.22 (30) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.38/21.22 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.38/21.22 (31) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.22 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.22 (32) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.22 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.22 (33) all_57_3 = e1
% 142.38/21.22 (34) ~ (all_4_2 = e3)
% 142.38/21.22 (35) ~ (all_52_13 = all_42_0)
% 142.38/21.22 (36) all_28_2 = e0
% 142.38/21.22 (37) all_57_11 = e2
% 142.38/21.22 (38) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.22 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.22 (39) op(e3, e2) = all_52_4
% 142.38/21.22 (40) ~ (e3 = e2)
% 142.38/21.22 (41) op(e3, e0) = all_52_12
% 142.38/21.22 (42) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.38/21.22 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.38/21.22 (43) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.38/21.22 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.38/21.22 (44) ~ (all_4_2 = e2)
% 142.38/21.22 (45) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.22 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.22 (46) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.22 (47) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.22 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.22 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.22 (48) ~ (all_52_3 = e0)
% 142.38/21.22 (49) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.22 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.22 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.22 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.22 (50) ~ (all_52_8 = e0)
% 142.38/21.22 (51) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.22 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.22 (52) ~ (e3 = e1)
% 142.38/21.22 (53) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.22 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.22 (54) ~ (all_52_9 = e1)
% 142.38/21.22 (55) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.38/21.22 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.38/21.22 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.38/21.22 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.38/21.22 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.38/21.22 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.38/21.22 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.38/21.22 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.38/21.22 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.38/21.22 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.38/21.22 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.38/21.22 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.38/21.22 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.38/21.22 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.38/21.22 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.38/21.22 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.38/21.22 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.38/21.22 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.38/21.22 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.38/21.22 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.22 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.38/21.22 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.38/21.22 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.38/21.22 $i(all_56_14))))
% 142.38/21.22 (56) all_57_0 = e0
% 142.38/21.22 (57) op(e3, e3) = e0
% 142.38/21.22 (58) op(e2, e1) = all_52_9
% 142.38/21.22 (59) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.22 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.22 (60) all_57_7 = e3
% 142.38/21.22 (61) ~ (all_42_0 = e1)
% 142.38/21.22 (62) ~ (all_42_0 = e3)
% 142.38/21.22 (63) op(e2, e0) = all_52_13
% 142.38/21.22 (64) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.22 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.22 (65) all_57_12 = e1
% 142.38/21.22 (66) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.22 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.22
% 142.38/21.22 Begin of proof
% 142.38/21.22 |
% 142.38/21.22 | BETA: splitting (6) gives:
% 142.38/21.22 |
% 142.38/21.22 | Case 1:
% 142.38/21.22 | |
% 142.38/21.22 | | (67) all_54_11 = e2
% 142.38/21.22 | |
% 142.38/21.22 | | REF_CLOSE: (12), (29), (67) are inconsistent by sub-proof #613.
% 142.38/21.22 | |
% 142.38/21.22 | Case 2:
% 142.38/21.22 | |
% 142.38/21.22 | | (68) ~ (all_54_11 = e2)
% 142.38/21.22 | | (69) all_54_11 = e1 | all_54_11 = e0
% 142.38/21.22 | |
% 142.38/21.22 | | BETA: splitting (69) gives:
% 142.38/21.22 | |
% 142.38/21.22 | | Case 1:
% 142.38/21.22 | | |
% 142.38/21.22 | | | (70) all_54_11 = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | REF_CLOSE: (29), (61), (70) are inconsistent by sub-proof #612.
% 142.38/21.22 | | |
% 142.38/21.22 | | Case 2:
% 142.38/21.22 | | |
% 142.38/21.22 | | | (71) all_54_11 = e0
% 142.38/21.22 | | |
% 142.38/21.22 | | | COMBINE_EQS: (29), (71) imply:
% 142.38/21.22 | | | (72) all_42_0 = e0
% 142.38/21.22 | | |
% 142.38/21.22 | | | SIMP: (72) implies:
% 142.38/21.22 | | | (73) all_42_0 = e0
% 142.38/21.22 | | |
% 142.38/21.22 | | | REDUCE: (35), (73) imply:
% 142.38/21.22 | | | (74) ~ (all_52_13 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | REDUCE: (62), (73) imply:
% 142.38/21.22 | | | (75) ~ (e3 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | SIMP: (75) implies:
% 142.38/21.22 | | | (76) ~ (e3 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | REDUCE: (12), (73) imply:
% 142.38/21.22 | | | (77) ~ (e2 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | SIMP: (77) implies:
% 142.38/21.22 | | | (78) ~ (e2 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | REDUCE: (61), (73) imply:
% 142.38/21.22 | | | (79) ~ (e1 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | SIMP: (79) implies:
% 142.38/21.22 | | | (80) ~ (e1 = e0)
% 142.38/21.22 | | |
% 142.38/21.22 | | | BETA: splitting (2) gives:
% 142.38/21.22 | | |
% 142.38/21.22 | | | Case 1:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | (81) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2)
% 142.38/21.22 | | | | = e3)
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (9), (10), (11), (13), (14),
% 142.38/21.22 | | | | (15), (16), (17), (18), (19), (20), (21), (23), (24), (25),
% 142.38/21.22 | | | | (26), (28), (31), (32), (33), (36), (38), (39), (40), (41),
% 142.38/21.22 | | | | (42), (43), (45), (46), (47), (48), (49), (50), (51), (52),
% 142.38/21.22 | | | | (53), (56), (57), (59), (60), (64), (65), (66), (76), (78),
% 142.38/21.22 | | | | (80), (81) are inconsistent by sub-proof #582.
% 142.38/21.22 | | | |
% 142.38/21.22 | | | Case 2:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | (82) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0)
% 142.38/21.22 | | | | = e3)
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | BETA: splitting (82) gives:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | Case 1:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | (83) all_57_5 = e3 & op(e2, e1) = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | ALPHA: (83) implies:
% 142.38/21.22 | | | | | (84) all_57_5 = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | BETA: splitting (49) gives:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | Case 1:
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | | (85) all_57_15 = e0 & op(e0, e0) = e0
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | | ALPHA: (85) implies:
% 142.38/21.22 | | | | | | (86) op(e0, e0) = e0
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | | REF_CLOSE: (15), (19), (22), (26), (34), (44), (46), (54), (55),
% 142.38/21.22 | | | | | | (57), (58), (63), (66), (74), (76), (78), (80), (86) are
% 142.38/21.22 | | | | | | inconsistent by sub-proof #639.
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | Case 2:
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | | (87) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 142.38/21.22 | | | | | | op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.38/21.22 | | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.22 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | | REF_CLOSE: (2), (4), (5), (8), (9), (10), (11), (14), (15), (18),
% 142.38/21.22 | | | | | | (19), (20), (21), (23), (24), (25), (26), (27), (28),
% 142.38/21.22 | | | | | | (30), (31), (32), (33), (36), (37), (38), (39), (40),
% 142.38/21.22 | | | | | | (41), (42), (43), (45), (46), (47), (50), (51), (52),
% 142.38/21.22 | | | | | | (53), (56), (57), (59), (60), (64), (65), (66), (76),
% 142.38/21.22 | | | | | | (78), (80), (84), (87) are inconsistent by sub-proof
% 142.38/21.22 | | | | | | #575.
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | End of split
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | Case 2:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | (88) all_57_10 = e3 & op(e2, e0) = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | ALPHA: (88) implies:
% 142.38/21.22 | | | | | (89) all_57_10 = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | REF_CLOSE: (10), (11), (18), (40), (46), (49), (51), (52), (76), (78),
% 142.38/21.22 | | | | | (80), (89) are inconsistent by sub-proof #650.
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | End of split
% 142.38/21.22 | | | |
% 142.38/21.22 | | | End of split
% 142.38/21.22 | | |
% 142.38/21.22 | | End of split
% 142.38/21.22 | |
% 142.38/21.22 | End of split
% 142.38/21.22 |
% 142.38/21.22 End of proof
% 142.38/21.22
% 142.38/21.22 Sub-proof #575 shows that the following formulas are inconsistent:
% 142.38/21.22 ----------------------------------------------------------------
% 142.38/21.22 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.22 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.22 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.22 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.22 (3) op(e1, e3) = all_52_2
% 142.38/21.22 (4) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.38/21.22 (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 & op(e0, e3) =
% 142.38/21.22 e0) | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 142.38/21.22 e1) = e0))
% 142.38/21.22 (5) ~ (all_52_12 = e3)
% 142.38/21.22 (6) ~ (all_52_4 = e0)
% 142.38/21.22 (7) ~ (e2 = e1)
% 142.38/21.22 (8) op(e0, e0) = e3
% 142.38/21.22 (9) all_57_5 = e3
% 142.38/21.22 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.22 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.22 (11) op(e2, e2) = e1
% 142.38/21.22 (12) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.22 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.22 (13) ~ (all_52_1 = e0)
% 142.38/21.22 (14) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.22 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.22 (15) ~ (e3 = e0)
% 142.38/21.22 (16) op(e1, e1) = e1
% 142.38/21.22 (17) op(e3, e1) = all_52_8
% 142.38/21.22 (18) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.38/21.22 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.22 (19) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.22 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.38/21.22 e2)
% 142.38/21.22 (20) op(e2, e3) = all_52_1
% 142.38/21.22 (21) ~ (all_52_12 = e0)
% 142.38/21.22 (22) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.22 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.22 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.22 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.38/21.22 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.38/21.22 (24) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.22 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.22 (25) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.22 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.22 (26) all_57_3 = e1
% 142.38/21.22 (27) all_28_2 = e0
% 142.38/21.22 (28) all_57_11 = e2
% 142.38/21.22 (29) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.22 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.22 (30) ~ (e1 = e0)
% 142.38/21.22 (31) op(e3, e2) = all_52_4
% 142.38/21.22 (32) ~ (e2 = e0)
% 142.38/21.22 (33) ~ (e3 = e2)
% 142.38/21.22 (34) op(e3, e0) = all_52_12
% 142.38/21.22 (35) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.38/21.22 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.38/21.22 (36) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.38/21.22 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.38/21.22 (37) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.22 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.22 (38) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.22 (39) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.22 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.22 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.22 (40) ~ (all_52_8 = e0)
% 142.38/21.22 (41) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.22 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.22 (42) ~ (e3 = e1)
% 142.38/21.22 (43) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.22 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.22 (44) all_57_0 = e0
% 142.38/21.22 (45) op(e3, e3) = e0
% 142.38/21.22 (46) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.22 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.22 (47) all_57_7 = e3
% 142.38/21.22 (48) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.22 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.22 (49) all_57_12 = e1
% 142.38/21.22 (50) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.22 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.22
% 142.38/21.22 Begin of proof
% 142.38/21.22 |
% 142.38/21.22 | ALPHA: (4) implies:
% 142.38/21.22 | (51) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.22 | | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.22 |
% 142.38/21.22 | BETA: splitting (19) gives:
% 142.38/21.22 |
% 142.38/21.22 | Case 1:
% 142.38/21.22 | |
% 142.38/21.22 | | (52) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.38/21.22 | | e2)
% 142.38/21.22 | |
% 142.38/21.22 | | BETA: splitting (52) gives:
% 142.38/21.22 | |
% 142.38/21.22 | | Case 1:
% 142.38/21.22 | | |
% 142.38/21.22 | | | (53) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.22 | | |
% 142.38/21.22 | | | ALPHA: (53) implies:
% 142.38/21.22 | | | (54) all_57_12 = e2
% 142.38/21.22 | | |
% 142.38/21.22 | | | COMBINE_EQS: (49), (54) imply:
% 142.38/21.22 | | | (55) e2 = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | SIMP: (55) implies:
% 142.38/21.22 | | | (56) e2 = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | COMBINE_EQS: (28), (56) imply:
% 142.38/21.22 | | | (57) all_57_11 = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (10), (11), (12), (13),
% 142.38/21.22 | | | (14), (15), (16), (17), (18), (20), (21), (22), (23), (24),
% 142.38/21.22 | | | (25), (26), (27), (29), (30), (31), (32), (33), (34), (35),
% 142.38/21.22 | | | (36), (37), (38), (39), (40), (41), (42), (43), (44), (45),
% 142.38/21.22 | | | (46), (48), (49), (50), (51), (57) are inconsistent by
% 142.38/21.22 | | | sub-proof #577.
% 142.38/21.22 | | |
% 142.38/21.22 | | Case 2:
% 142.38/21.22 | | |
% 142.38/21.22 | | | (58) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.22 | | |
% 142.38/21.22 | | | ALPHA: (58) implies:
% 142.38/21.22 | | | (59) all_57_13 = e2
% 142.38/21.22 | | |
% 142.38/21.22 | | | REF_CLOSE: (6), (11), (15), (29), (30), (31), (32), (38), (47), (59) are
% 142.38/21.22 | | | inconsistent by sub-proof #1059.
% 142.38/21.22 | | |
% 142.38/21.22 | | End of split
% 142.38/21.22 | |
% 142.38/21.22 | Case 2:
% 142.38/21.22 | |
% 142.38/21.22 | | (60) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.38/21.22 | | e2)
% 142.38/21.22 | |
% 142.38/21.22 | | REF_CLOSE: (8), (9), (10), (15), (16), (17), (30), (32), (33), (38), (40),
% 142.38/21.22 | | (60) are inconsistent by sub-proof #576.
% 142.38/21.22 | |
% 142.38/21.22 | End of split
% 142.38/21.22 |
% 142.38/21.22 End of proof
% 142.38/21.22
% 142.38/21.22 Sub-proof #576 shows that the following formulas are inconsistent:
% 142.38/21.22 ----------------------------------------------------------------
% 142.38/21.22 (1) op(e0, e0) = e3
% 142.38/21.22 (2) all_57_5 = e3
% 142.38/21.22 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.22 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.22 (4) ~ (e3 = e0)
% 142.38/21.22 (5) op(e1, e1) = e1
% 142.38/21.22 (6) op(e3, e1) = all_52_8
% 142.38/21.22 (7) ~ (e1 = e0)
% 142.38/21.22 (8) ~ (e2 = e0)
% 142.38/21.22 (9) ~ (e3 = e2)
% 142.38/21.22 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.22 (11) ~ (all_52_8 = e0)
% 142.38/21.22 (12) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.22
% 142.38/21.22 Begin of proof
% 142.38/21.22 |
% 142.38/21.22 | BETA: splitting (12) gives:
% 142.38/21.22 |
% 142.38/21.22 | Case 1:
% 142.38/21.22 | |
% 142.38/21.22 | | (13) all_57_14 = e2 & op(e0, e1) = e2
% 142.38/21.22 | |
% 142.38/21.22 | | ALPHA: (13) implies:
% 142.38/21.22 | | (14) all_57_14 = e2
% 142.38/21.22 | |
% 142.38/21.22 | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (10), (11), (14) are
% 142.38/21.22 | | inconsistent by sub-proof #630.
% 142.38/21.22 | |
% 142.38/21.22 | Case 2:
% 142.38/21.22 | |
% 142.38/21.22 | | (15) all_57_15 = e2 & op(e0, e0) = e2
% 142.38/21.22 | |
% 142.38/21.22 | | ALPHA: (15) implies:
% 142.38/21.22 | | (16) op(e0, e0) = e2
% 142.38/21.22 | |
% 142.38/21.22 | | REF_CLOSE: (1), (9), (10), (16) are inconsistent by sub-proof #1066.
% 142.38/21.22 | |
% 142.38/21.22 | End of split
% 142.38/21.22 |
% 142.38/21.22 End of proof
% 142.38/21.22
% 142.38/21.22 Sub-proof #577 shows that the following formulas are inconsistent:
% 142.38/21.22 ----------------------------------------------------------------
% 142.38/21.22 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.22 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.22 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.22 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.22 (3) op(e1, e3) = all_52_2
% 142.38/21.22 (4) ~ (all_52_12 = e3)
% 142.38/21.22 (5) ~ (all_52_4 = e0)
% 142.38/21.22 (6) ~ (e2 = e1)
% 142.38/21.22 (7) op(e0, e0) = e3
% 142.38/21.22 (8) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.22 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.22 (9) op(e2, e2) = e1
% 142.38/21.22 (10) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.22 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.22 (11) ~ (all_52_1 = e0)
% 142.38/21.22 (12) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.22 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.22 (13) ~ (e3 = e0)
% 142.38/21.22 (14) op(e1, e1) = e1
% 142.38/21.22 (15) op(e3, e1) = all_52_8
% 142.38/21.22 (16) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.38/21.22 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.22 (17) op(e2, e3) = all_52_1
% 142.38/21.22 (18) ~ (all_52_12 = e0)
% 142.38/21.22 (19) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.22 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.22 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.22 (20) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.38/21.22 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.22 (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.38/21.22 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.38/21.22 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.22 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.22 (23) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.22 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.22 (24) all_57_3 = e1
% 142.38/21.22 (25) all_28_2 = e0
% 142.38/21.22 (26) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.22 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.22 (27) ~ (e1 = e0)
% 142.38/21.22 (28) op(e3, e2) = all_52_4
% 142.38/21.22 (29) ~ (e2 = e0)
% 142.38/21.22 (30) ~ (e3 = e2)
% 142.38/21.22 (31) op(e3, e0) = all_52_12
% 142.38/21.22 (32) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.38/21.22 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.38/21.22 (33) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.38/21.22 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.38/21.22 (34) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.22 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.22 (35) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.22 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.22 (36) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.22 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.22 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.22 (37) ~ (all_52_8 = e0)
% 142.38/21.22 (38) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.22 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.22 (39) ~ (e3 = e1)
% 142.38/21.22 (40) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.22 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.22 (41) all_57_0 = e0
% 142.38/21.22 (42) op(e3, e3) = e0
% 142.38/21.22 (43) all_57_11 = e1
% 142.38/21.22 (44) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.22 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.22 (45) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.22 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.22 (46) all_57_12 = e1
% 142.38/21.22 (47) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.22 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.22
% 142.38/21.22 Begin of proof
% 142.38/21.22 |
% 142.38/21.22 | BETA: splitting (21) gives:
% 142.38/21.22 |
% 142.38/21.22 | Case 1:
% 142.38/21.22 | |
% 142.38/21.22 | | (48) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) =
% 142.38/21.22 | | e1)
% 142.38/21.22 | |
% 142.38/21.22 | | BETA: splitting (48) gives:
% 142.38/21.22 | |
% 142.38/21.22 | | Case 1:
% 142.38/21.22 | | |
% 142.38/21.22 | | | (49) all_57_0 = e1 & op(e3, e3) = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | ALPHA: (49) implies:
% 142.38/21.22 | | | (50) op(e3, e3) = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | REF_CLOSE: (27), (35), (42), (50) are inconsistent by sub-proof #840.
% 142.38/21.22 | | |
% 142.38/21.22 | | Case 2:
% 142.38/21.22 | | |
% 142.38/21.22 | | | (51) all_57_1 = e1 & op(e3, e2) = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | ALPHA: (51) implies:
% 142.38/21.22 | | | (52) all_57_1 = e1
% 142.38/21.22 | | |
% 142.38/21.22 | | | BETA: splitting (40) gives:
% 142.38/21.22 | | |
% 142.38/21.22 | | | Case 1:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | (53) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 142.38/21.22 | | | | = e3)
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | BETA: splitting (53) gives:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | Case 1:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | (54) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | REF_CLOSE: (13), (41), (54) are inconsistent by sub-proof #1108.
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | Case 2:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | (55) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | REF_CLOSE: (39), (52), (55) are inconsistent by sub-proof #724.
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | End of split
% 142.38/21.22 | | | |
% 142.38/21.22 | | | Case 2:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | (56) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 142.38/21.22 | | | | = e3)
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | BETA: splitting (56) gives:
% 142.38/21.22 | | | |
% 142.38/21.22 | | | | Case 1:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | (57) all_57_4 = e3 & op(e3, e1) = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | ALPHA: (57) implies:
% 142.38/21.22 | | | | | (58) all_57_4 = e3
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | BETA: splitting (45) gives:
% 142.38/21.22 | | | | |
% 142.38/21.22 | | | | | Case 1:
% 142.38/21.22 | | | | | |
% 142.38/21.22 | | | | | | (59) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 142.38/21.22 | | | | | | e2) = e3)
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | REF_CLOSE: (2), (6), (8), (13), (14), (15), (24), (27), (29), (30),
% 142.38/21.23 | | | | | | (34), (35), (37), (39), (52), (58), (59) are inconsistent
% 142.38/21.23 | | | | | | by sub-proof #621.
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | Case 2:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | (60) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 142.38/21.23 | | | | | | e2) = e3)
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | BETA: splitting (60) gives:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | Case 1:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | (61) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | ALPHA: (61) implies:
% 142.38/21.23 | | | | | | | (62) all_57_7 = e3
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | REF_CLOSE: (5), (6), (9), (12), (13), (26), (27), (28), (29),
% 142.38/21.23 | | | | | | | (30), (35), (52), (62) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | #619.
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | Case 2:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | (63) all_57_13 = e3 & op(e0, e2) = e3
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | ALPHA: (63) implies:
% 142.38/21.23 | | | | | | | (64) all_57_13 = e3
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | BETA: splitting (12) gives:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | (65) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 142.38/21.23 | | | | | | | | op(e2, e2) = e2)
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | REF_CLOSE: (6), (9), (35), (52), (65) are inconsistent by
% 142.38/21.23 | | | | | | | | sub-proof #620.
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | (66) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 142.38/21.23 | | | | | | | | op(e0, e2) = e2)
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | BETA: splitting (66) gives:
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | (67) all_57_7 = e2 & op(e1, e2) = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | ALPHA: (67) implies:
% 142.38/21.23 | | | | | | | | | (68) all_57_7 = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | BETA: splitting (32) gives:
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | (69) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 &
% 142.38/21.23 | | | | | | | | | | op(e1, e2) = e3)
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | BETA: splitting (69) gives:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (70) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (70) implies:
% 142.38/21.23 | | | | | | | | | | | (71) all_57_6 = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | BETA: splitting (44) gives:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | (72) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.38/21.23 | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | BETA: splitting (72) gives:
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | (73) all_57_0 = e2 & op(e3, e3) = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | ALPHA: (73) implies:
% 142.38/21.23 | | | | | | | | | | | | | (74) op(e3, e3) = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | REF_CLOSE: (29), (35), (42), (74) are inconsistent by
% 142.38/21.23 | | | | | | | | | | | | | sub-proof #880.
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | (75) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | ALPHA: (75) implies:
% 142.38/21.23 | | | | | | | | | | | | | (76) all_57_2 = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | BETA: splitting (1) gives:
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | (77) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.38/21.23 | | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | BETA: splitting (77) gives:
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | (78) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | ALPHA: (78) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | (79) all_57_2 = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | COMBINE_EQS: (76), (79) imply:
% 142.38/21.23 | | | | | | | | | | | | | | | (80) e3 = e2
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | SIMP: (80) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | (81) e3 = e2
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | COMBINE_EQS: (71), (81) imply:
% 142.38/21.23 | | | | | | | | | | | | | | | (82) all_57_6 = e2
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | REF_CLOSE: (13), (22), (30), (39), (41), (46), (76), (82) are
% 142.38/21.23 | | | | | | | | | | | | | | | inconsistent by sub-proof #614.
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | (83) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | REF_CLOSE: (2), (6), (8), (13), (14), (15), (24), (27), (29),
% 142.38/21.23 | | | | | | | | | | | | | | | (30), (34), (35), (37), (39), (58), (83) are
% 142.38/21.23 | | | | | | | | | | | | | | | inconsistent by sub-proof #622.
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | (84) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.38/21.23 | | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | BETA: splitting (84) gives:
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | (85) all_57_5 = e3 & op(e2, e1) = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | ALPHA: (85) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | (86) all_57_5 = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | BETA: splitting (47) gives:
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | (87) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | & op(e2, e2) = e0)
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | REF_CLOSE: (9), (11), (17), (27), (35), (87) are inconsistent
% 142.38/21.23 | | | | | | | | | | | | | | | | by sub-proof #640.
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | (88) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 =
% 142.38/21.23 | | | | | | | | | | | | | | | | e0 & op(e2, e0) = e0)
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | BETA: splitting (88) gives:
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | (89) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | ALPHA: (89) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | (90) all_57_5 = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (90) imply:
% 142.38/21.23 | | | | | | | | | | | | | | | | | (91) e3 = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | COMBINE_EQS: (71), (91) imply:
% 142.38/21.23 | | | | | | | | | | | | | | | | | (92) all_57_6 = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (14), (30), (32), (35), (39), (43), (68),
% 142.38/21.23 | | | | | | | | | | | | | | | | | (92) are inconsistent by sub-proof #866.
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | (93) all_57_10 = e0 & op(e2, e0) = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | ALPHA: (93) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | (94) all_57_10 = e0
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | BETA: splitting (10) gives:
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | (95) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 =
% 142.38/21.23 | | | | | | | | | | | | | | | | | | e2 & op(e2, e0) = e2)
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | BETA: splitting (95) gives:
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | (96) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | ALPHA: (96) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | (97) all_57_9 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | BETA: splitting (34) gives:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | (98) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | & op(e2, e1) = e2)
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | BETA: splitting (98) gives:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (99) all_57_4 = e2 & op(e3, e1) = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (99) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (100) all_57_4 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (39), (40), (41), (52), (97), (100)
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #580.
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (101) all_57_5 = e2 & op(e2, e1) = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | ALPHA: (101) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (102) all_57_5 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (86), (102) imply:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (103) e3 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | SIMP: (103) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (104) e3 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | COMBINE_EQS: (58), (104) imply:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | (105) all_57_4 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (13), (30), (39), (40), (41), (52), (97), (105)
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | | are inconsistent by sub-proof #580.
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | (106) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 =
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | e2 & op(e0, e1) = e2)
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (8), (13), (14), (15), (27), (29), (35),
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | (37), (86), (106) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | | #629.
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | (107) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | ALPHA: (107) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | (108) all_57_10 = e2
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | REF_CLOSE: (29), (94), (108) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | | | | | | | | | | | | | #609.
% 142.38/21.23 | | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | (109) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 =
% 142.38/21.23 | | | | | | | | | | | | | | | | | | e2 & op(e0, e0) = e2)
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (30), (35), (43), (109) are inconsistent
% 142.38/21.23 | | | | | | | | | | | | | | | | | | by sub-proof #579.
% 142.38/21.23 | | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | (110) all_57_10 = e3 & op(e2, e0) = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | ALPHA: (110) implies:
% 142.38/21.23 | | | | | | | | | | | | | | | (111) all_57_10 = e3
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | | REF_CLOSE: (6), (7), (10), (13), (20), (27), (29), (30),
% 142.38/21.23 | | | | | | | | | | | | | | | (35), (38), (39), (111) are inconsistent by
% 142.38/21.23 | | | | | | | | | | | | | | | sub-proof #687.
% 142.38/21.23 | | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | (112) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.38/21.23 | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | BETA: splitting (112) gives:
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | (113) all_57_6 = e2 & op(e1, e3) = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | REF_CLOSE: (30), (71), (113) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | | | | | | | #998.
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | (114) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | ALPHA: (114) implies:
% 142.38/21.23 | | | | | | | | | | | | | (115) all_57_12 = e2
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | | REF_CLOSE: (6), (46), (115) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | | | | | | | #970.
% 142.38/21.23 | | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (116) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (116) implies:
% 142.38/21.23 | | | | | | | | | | | (117) all_57_7 = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (12), (13), (26), (27), (28), (29),
% 142.38/21.23 | | | | | | | | | | | (30), (35), (52), (117) are inconsistent by
% 142.38/21.23 | | | | | | | | | | | sub-proof #619.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | (118) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3
% 142.38/21.23 | | | | | | | | | | & op(e1, e0) = e3)
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | BETA: splitting (118) gives:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (119) all_57_8 = e3 & op(e1, e1) = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (119) implies:
% 142.38/21.23 | | | | | | | | | | | (120) op(e1, e1) = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (14), (35), (39), (120) are inconsistent by
% 142.38/21.23 | | | | | | | | | | | sub-proof #1096.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (121) all_57_11 = e3 & op(e1, e0) = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (121) implies:
% 142.38/21.23 | | | | | | | | | | | (122) all_57_11 = e3
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | COMBINE_EQS: (43), (122) imply:
% 142.38/21.23 | | | | | | | | | | | (123) e3 = e1
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | COMBINE_EQS: (58), (123) imply:
% 142.38/21.23 | | | | | | | | | | | (124) all_57_4 = e1
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (2), (6), (8), (13), (14), (15), (27), (29), (30),
% 142.38/21.23 | | | | | | | | | | | (34), (35), (37), (39), (124) are inconsistent by
% 142.38/21.23 | | | | | | | | | | | sub-proof #623.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | (125) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | ALPHA: (125) implies:
% 142.38/21.23 | | | | | | | | | (126) all_57_13 = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | REF_CLOSE: (30), (64), (126) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | | | #1068.
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | End of split
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | End of split
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | End of split
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | End of split
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | Case 2:
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | (127) all_57_9 = e3 & op(e3, e0) = e3
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | ALPHA: (127) implies:
% 142.38/21.23 | | | | | (128) op(e3, e0) = e3
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | REF_CLOSE: (4), (31), (35), (128) are inconsistent by sub-proof #1105.
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | End of split
% 142.38/21.23 | | | |
% 142.38/21.23 | | | End of split
% 142.38/21.23 | | |
% 142.38/21.23 | | End of split
% 142.38/21.23 | |
% 142.38/21.23 | Case 2:
% 142.38/21.23 | |
% 142.38/21.23 | | (129) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) =
% 142.38/21.23 | | e1)
% 142.38/21.23 | |
% 142.38/21.23 | | BETA: splitting (129) gives:
% 142.38/21.23 | |
% 142.38/21.23 | | Case 1:
% 142.38/21.23 | | |
% 142.38/21.23 | | | (130) all_57_4 = e1 & op(e3, e1) = e1
% 142.38/21.23 | | |
% 142.38/21.23 | | | ALPHA: (130) implies:
% 142.38/21.23 | | | (131) all_57_4 = e1
% 142.38/21.23 | | |
% 142.38/21.23 | | | REF_CLOSE: (2), (6), (8), (13), (14), (15), (27), (29), (30), (34), (35),
% 142.38/21.23 | | | (37), (39), (131) are inconsistent by sub-proof #623.
% 142.38/21.23 | | |
% 142.38/21.23 | | Case 2:
% 142.38/21.23 | | |
% 142.38/21.23 | | | (132) all_57_9 = e1 & op(e3, e0) = e1
% 142.38/21.23 | | |
% 142.38/21.23 | | | ALPHA: (132) implies:
% 142.38/21.23 | | | (133) all_57_9 = e1
% 142.38/21.23 | | | (134) op(e3, e0) = e1
% 142.38/21.23 | | |
% 142.38/21.23 | | | BETA: splitting (16) gives:
% 142.38/21.23 | | |
% 142.38/21.23 | | | Case 1:
% 142.38/21.23 | | | |
% 142.38/21.23 | | | | (135) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2)
% 142.38/21.23 | | | | = e0)
% 142.38/21.23 | | | |
% 142.38/21.23 | | | | BETA: splitting (135) gives:
% 142.38/21.23 | | | |
% 142.38/21.23 | | | | Case 1:
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | (136) all_57_6 = e0 & op(e1, e3) = e0
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | ALPHA: (136) implies:
% 142.38/21.23 | | | | | (137) all_57_6 = e0
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | BETA: splitting (44) gives:
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | Case 1:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | (138) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2,
% 142.38/21.23 | | | | | | e3) = e2)
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | BETA: splitting (138) gives:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | Case 1:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | (139) all_57_0 = e2 & op(e3, e3) = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | ALPHA: (139) implies:
% 142.38/21.23 | | | | | | | (140) op(e3, e3) = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | REF_CLOSE: (29), (35), (42), (140) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | #880.
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | Case 2:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | (141) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | ALPHA: (141) implies:
% 142.38/21.23 | | | | | | | (142) all_57_2 = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | BETA: splitting (10) gives:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | (143) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 142.38/21.23 | | | | | | | | op(e2, e0) = e2)
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | BETA: splitting (143) gives:
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | (144) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | ALPHA: (144) implies:
% 142.38/21.23 | | | | | | | | | (145) all_57_9 = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | REF_CLOSE: (6), (133), (145) are inconsistent by sub-proof
% 142.38/21.23 | | | | | | | | | #815.
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | (146) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | ALPHA: (146) implies:
% 142.38/21.23 | | | | | | | | | (147) all_57_10 = e2
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | BETA: splitting (33) gives:
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | (148) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2
% 142.38/21.23 | | | | | | | | | | & op(e1, e2) = e2)
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | BETA: splitting (148) gives:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (149) all_57_6 = e2 & op(e1, e3) = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (149) implies:
% 142.38/21.23 | | | | | | | | | | | (150) all_57_6 = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (13), (22), (30), (39), (41), (46), (142), (150)
% 142.38/21.23 | | | | | | | | | | | are inconsistent by sub-proof #614.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (151) all_57_7 = e2 & op(e1, e2) = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (151) implies:
% 142.38/21.23 | | | | | | | | | | | (152) all_57_7 = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (13), (14), (30), (32), (35), (39), (43), (137),
% 142.38/21.23 | | | | | | | | | | | (152) are inconsistent by sub-proof #866.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | (153) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2
% 142.38/21.23 | | | | | | | | | | & op(e1, e0) = e2)
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | BETA: splitting (153) gives:
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 1:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (154) all_57_8 = e2 & op(e1, e1) = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (154) implies:
% 142.38/21.23 | | | | | | | | | | | (155) op(e1, e1) = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (6), (14), (35), (155) are inconsistent by
% 142.38/21.23 | | | | | | | | | | | sub-proof #1085.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | (156) all_57_11 = e2 & op(e1, e0) = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | ALPHA: (156) implies:
% 142.38/21.23 | | | | | | | | | | | (157) all_57_11 = e2
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | COMBINE_EQS: (43), (157) imply:
% 142.38/21.23 | | | | | | | | | | | (158) e2 = e1
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | COMBINE_EQS: (147), (158) imply:
% 142.38/21.23 | | | | | | | | | | | (159) all_57_10 = e1
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | | REF_CLOSE: (18), (20), (27), (29), (31), (35), (157), (159)
% 142.38/21.23 | | | | | | | | | | | are inconsistent by sub-proof #716.
% 142.38/21.23 | | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | | |
% 142.38/21.23 | | | | | | | | | End of split
% 142.38/21.23 | | | | | | | | |
% 142.38/21.23 | | | | | | | | End of split
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | Case 2:
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | (160) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 142.38/21.23 | | | | | | | | op(e0, e0) = e2)
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | | REF_CLOSE: (6), (7), (30), (35), (43), (160) are inconsistent by
% 142.38/21.23 | | | | | | | | sub-proof #579.
% 142.38/21.23 | | | | | | | |
% 142.38/21.23 | | | | | | | End of split
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | End of split
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | Case 2:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | (161) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 142.38/21.23 | | | | | | op(e0, e3) = e2)
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | REF_CLOSE: (3), (6), (13), (19), (22), (23), (25), (27), (30), (31),
% 142.38/21.23 | | | | | | (35), (36), (39), (41), (42), (134), (137), (161) are
% 142.38/21.23 | | | | | | inconsistent by sub-proof #585.
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | End of split
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | Case 2:
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | (162) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | ALPHA: (162) implies:
% 142.38/21.23 | | | | | (163) all_57_7 = e0
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | BETA: splitting (33) gives:
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | | Case 1:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | (164) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 142.38/21.23 | | | | | | e2) = e2)
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | BETA: splitting (164) gives:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | Case 1:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | (165) all_57_6 = e2 & op(e1, e3) = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | ALPHA: (165) implies:
% 142.38/21.23 | | | | | | | (166) op(e1, e3) = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | REF_CLOSE: (3), (19), (25), (31), (35), (36), (134), (166) are
% 142.38/21.23 | | | | | | | inconsistent by sub-proof #654.
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | Case 2:
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | (167) all_57_7 = e2 & op(e1, e2) = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | ALPHA: (167) implies:
% 142.38/21.23 | | | | | | | (168) all_57_7 = e2
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | | REF_CLOSE: (29), (163), (168) are inconsistent by sub-proof #578.
% 142.38/21.23 | | | | | | |
% 142.38/21.23 | | | | | | End of split
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | Case 2:
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | (169) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 142.38/21.23 | | | | | | op(e1, e0) = e2)
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | | REF_CLOSE: (6), (14), (35), (43), (169) are inconsistent by
% 142.38/21.23 | | | | | | sub-proof #809.
% 142.38/21.23 | | | | | |
% 142.38/21.23 | | | | | End of split
% 142.38/21.23 | | | | |
% 142.38/21.23 | | | | End of split
% 142.38/21.23 | | | |
% 142.38/21.23 | | | Case 2:
% 142.38/21.23 | | | |
% 142.38/21.23 | | | | (170) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 142.38/21.23 | | | | e0) = e0)
% 142.38/21.23 | | | |
% 142.38/21.23 | | | | REF_CLOSE: (14), (27), (35), (43), (170) are inconsistent by sub-proof
% 142.38/21.23 | | | | #807.
% 142.38/21.23 | | | |
% 142.38/21.23 | | | End of split
% 142.38/21.23 | | |
% 142.38/21.23 | | End of split
% 142.38/21.23 | |
% 142.38/21.23 | End of split
% 142.38/21.23 |
% 142.38/21.23 End of proof
% 142.38/21.23
% 142.38/21.23 Sub-proof #578 shows that the following formulas are inconsistent:
% 142.38/21.23 ----------------------------------------------------------------
% 142.38/21.23 (1) all_57_7 = e2
% 142.38/21.23 (2) all_57_7 = e0
% 142.38/21.23 (3) ~ (e2 = e0)
% 142.38/21.23
% 142.38/21.23 Begin of proof
% 142.38/21.23 |
% 142.38/21.23 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.23 | (4) e2 = e0
% 142.38/21.23 |
% 142.38/21.23 | SIMP: (4) implies:
% 142.38/21.23 | (5) e2 = e0
% 142.38/21.23 |
% 142.38/21.23 | REDUCE: (3), (5) imply:
% 142.38/21.23 | (6) $false
% 142.38/21.23 |
% 142.38/21.23 | CLOSE: (6) is inconsistent.
% 142.38/21.23 |
% 142.38/21.23 End of proof
% 142.38/21.23
% 142.38/21.23 Sub-proof #579 shows that the following formulas are inconsistent:
% 142.38/21.23 ----------------------------------------------------------------
% 142.38/21.23 (1) ~ (e2 = e1)
% 142.38/21.23 (2) op(e0, e0) = e3
% 142.38/21.23 (3) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.23 (4) ~ (e3 = e2)
% 142.38/21.23 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.23 (6) all_57_11 = e1
% 142.38/21.23
% 142.38/21.23 Begin of proof
% 142.38/21.23 |
% 142.38/21.23 | BETA: splitting (3) gives:
% 142.38/21.23 |
% 142.38/21.23 | Case 1:
% 142.38/21.23 | |
% 142.38/21.23 | | (7) all_57_11 = e2 & op(e1, e0) = e2
% 142.38/21.23 | |
% 142.38/21.23 | | ALPHA: (7) implies:
% 142.38/21.23 | | (8) all_57_11 = e2
% 142.38/21.23 | |
% 142.38/21.23 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #810.
% 142.38/21.23 | |
% 142.38/21.23 | Case 2:
% 142.38/21.23 | |
% 142.38/21.23 | | (9) all_57_15 = e2 & op(e0, e0) = e2
% 142.38/21.23 | |
% 142.38/21.23 | | ALPHA: (9) implies:
% 142.38/21.23 | | (10) op(e0, e0) = e2
% 142.38/21.23 | |
% 142.38/21.23 | | REF_CLOSE: (2), (4), (5), (10) are inconsistent by sub-proof #1066.
% 142.38/21.23 | |
% 142.38/21.23 | End of split
% 142.38/21.23 |
% 142.38/21.23 End of proof
% 142.38/21.23
% 142.38/21.23 Sub-proof #580 shows that the following formulas are inconsistent:
% 142.38/21.23 ----------------------------------------------------------------
% 142.38/21.23 (1) all_57_4 = e2
% 142.38/21.23 (2) ~ (e3 = e0)
% 142.38/21.23 (3) all_57_1 = e1
% 142.38/21.23 (4) all_57_9 = e2
% 142.38/21.23 (5) ~ (e3 = e2)
% 142.38/21.23 (6) ~ (e3 = e1)
% 142.38/21.23 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.23 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.23 (8) all_57_0 = e0
% 142.38/21.23
% 142.38/21.23 Begin of proof
% 142.38/21.23 |
% 142.38/21.23 | BETA: splitting (7) gives:
% 142.38/21.23 |
% 142.38/21.23 | Case 1:
% 142.38/21.23 | |
% 142.38/21.23 | | (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 142.38/21.23 | |
% 142.38/21.23 | | BETA: splitting (9) gives:
% 142.38/21.23 | |
% 142.38/21.23 | | Case 1:
% 142.38/21.23 | | |
% 142.38/21.23 | | | (10) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.23 | | |
% 142.38/21.23 | | | REF_CLOSE: (2), (8), (10) are inconsistent by sub-proof #1108.
% 142.38/21.23 | | |
% 142.38/21.23 | | Case 2:
% 142.38/21.23 | | |
% 142.38/21.23 | | | (11) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.23 | | |
% 142.38/21.23 | | | REF_CLOSE: (3), (6), (11) are inconsistent by sub-proof #724.
% 142.38/21.23 | | |
% 142.38/21.23 | | End of split
% 142.38/21.23 | |
% 142.38/21.23 | Case 2:
% 142.38/21.23 | |
% 142.38/21.23 | | (12) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 142.38/21.23 | | e3)
% 142.38/21.23 | |
% 142.38/21.23 | | BETA: splitting (12) gives:
% 142.38/21.23 | |
% 142.38/21.23 | | Case 1:
% 142.38/21.23 | | |
% 142.38/21.23 | | | (13) all_57_4 = e3 & op(e3, e1) = e3
% 142.38/21.23 | | |
% 142.38/21.23 | | | ALPHA: (13) implies:
% 142.38/21.23 | | | (14) all_57_4 = e3
% 142.38/21.23 | | |
% 142.38/21.23 | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #821.
% 142.38/21.23 | | |
% 142.38/21.23 | | Case 2:
% 142.38/21.23 | | |
% 142.38/21.23 | | | (15) all_57_9 = e3 & op(e3, e0) = e3
% 142.38/21.23 | | |
% 142.38/21.23 | | | ALPHA: (15) implies:
% 142.38/21.23 | | | (16) all_57_9 = e3
% 142.38/21.23 | | |
% 142.38/21.23 | | | REF_CLOSE: (4), (5), (16) are inconsistent by sub-proof #581.
% 142.38/21.23 | | |
% 142.38/21.23 | | End of split
% 142.38/21.23 | |
% 142.38/21.23 | End of split
% 142.38/21.23 |
% 142.38/21.23 End of proof
% 142.38/21.23
% 142.38/21.23 Sub-proof #581 shows that the following formulas are inconsistent:
% 142.38/21.23 ----------------------------------------------------------------
% 142.38/21.23 (1) all_57_9 = e3
% 142.38/21.23 (2) all_57_9 = e2
% 142.38/21.23 (3) ~ (e3 = e2)
% 142.38/21.23
% 142.38/21.23 Begin of proof
% 142.38/21.23 |
% 142.38/21.23 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.23 | (4) e3 = e2
% 142.38/21.23 |
% 142.38/21.23 | SIMP: (4) implies:
% 142.38/21.23 | (5) e3 = e2
% 142.38/21.23 |
% 142.38/21.23 | REDUCE: (3), (5) imply:
% 142.38/21.23 | (6) $false
% 142.38/21.23 |
% 142.38/21.23 | CLOSE: (6) is inconsistent.
% 142.38/21.23 |
% 142.38/21.23 End of proof
% 142.38/21.23
% 142.38/21.23 Sub-proof #582 shows that the following formulas are inconsistent:
% 142.38/21.23 ----------------------------------------------------------------
% 142.38/21.23 (1) op(e3, e0) = e1
% 142.38/21.23 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.23 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.23 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.38/21.23 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.38/21.23 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.23 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.23 (5) op(e1, e3) = all_52_2
% 142.38/21.23 (6) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.23 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.38/21.23 (7) ~ (all_52_4 = e0)
% 142.38/21.23 (8) ~ (e2 = e1)
% 142.38/21.23 (9) op(e0, e0) = e3
% 142.38/21.23 (10) op(e0, e3) = all_52_3
% 142.38/21.23 (11) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.23 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.23 (12) op(e2, e2) = e1
% 142.38/21.23 (13) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.38/21.23 (14) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.38/21.23 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.38/21.23 e1)
% 142.38/21.23 (15) all_57_9 = e1
% 142.38/21.23 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.23 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.23 (17) ~ (all_52_1 = e0)
% 142.38/21.23 (18) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.23 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.23 (19) ~ (e3 = e0)
% 142.38/21.23 (20) op(e1, e1) = e1
% 142.38/21.23 (21) op(e3, e1) = all_52_8
% 142.38/21.23 (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.38/21.23 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.23 (23) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.23 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.38/21.23 e2)
% 142.38/21.23 (24) op(e2, e3) = all_52_1
% 142.38/21.23 (25) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.23 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.23 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.23 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.23 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.23 (27) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.23 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.23 (28) all_57_3 = e1
% 142.38/21.23 (29) all_28_2 = e0
% 142.38/21.23 (30) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.23 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.23 (31) ~ (e1 = e0)
% 142.38/21.23 (32) op(e3, e2) = all_52_4
% 142.38/21.23 (33) ~ (e2 = e0)
% 142.38/21.23 (34) ~ (e3 = e2)
% 142.38/21.23 (35) op(e3, e0) = all_52_12
% 142.38/21.23 (36) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.38/21.23 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.38/21.23 (37) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.38/21.23 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.38/21.23 (38) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.23 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.23 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.23 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.23 (40) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.23 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.23 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.23 (41) ~ (all_52_3 = e0)
% 142.38/21.23 (42) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.23 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.23 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.23 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.23 (43) ~ (all_52_8 = e0)
% 142.38/21.23 (44) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.23 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.23 (45) ~ (e3 = e1)
% 142.38/21.23 (46) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.23 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.23 (47) all_57_0 = e0
% 142.38/21.23 (48) op(e3, e3) = e0
% 142.38/21.23 (49) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.23 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.23 (50) all_57_7 = e3
% 142.38/21.23 (51) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.23 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.23 (52) all_57_12 = e1
% 142.38/21.23 (53) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.23 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.23
% 142.38/21.23 Begin of proof
% 142.38/21.23 |
% 142.38/21.23 | BETA: splitting (13) gives:
% 142.38/21.23 |
% 142.38/21.23 | Case 1:
% 142.38/21.23 | |
% 142.38/21.23 | | (54) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.23 | |
% 142.38/21.23 | | ALPHA: (54) implies:
% 142.38/21.23 | | (55) all_57_2 = e3
% 142.38/21.23 | |
% 142.38/21.23 | | REF_CLOSE: (1), (5), (8), (25), (29), (33), (34), (35), (39), (40), (48),
% 142.38/21.23 | | (49), (52), (55) are inconsistent by sub-proof #632.
% 142.38/21.23 | |
% 142.38/21.23 | Case 2:
% 142.38/21.23 | |
% 142.38/21.23 | | (56) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.24 | |
% 142.38/21.24 | | ALPHA: (56) implies:
% 142.38/21.24 | | (57) all_57_3 = e3
% 142.38/21.24 | |
% 142.38/21.24 | | COMBINE_EQS: (28), (57) imply:
% 142.38/21.24 | | (58) e3 = e1
% 142.38/21.24 | |
% 142.38/21.24 | | COMBINE_EQS: (50), (58) imply:
% 142.38/21.24 | | (59) all_57_7 = e1
% 142.38/21.24 | |
% 142.38/21.24 | | BETA: splitting (36) gives:
% 142.38/21.24 | |
% 142.38/21.24 | | Case 1:
% 142.38/21.24 | | |
% 142.38/21.24 | | | (60) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.38/21.24 | | | e3)
% 142.38/21.24 | | |
% 142.38/21.24 | | | BETA: splitting (60) gives:
% 142.38/21.24 | | |
% 142.38/21.24 | | | Case 1:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | (61) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | ALPHA: (61) implies:
% 142.38/21.24 | | | | (62) all_57_6 = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | BETA: splitting (30) gives:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | Case 1:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | (63) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 142.38/21.24 | | | | | e2) = e0)
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | REF_CLOSE: (7), (12), (31), (32), (39), (63) are inconsistent by
% 142.38/21.24 | | | | | sub-proof #1062.
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | Case 2:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | (64) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 142.38/21.24 | | | | | e2) = e0)
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | BETA: splitting (64) gives:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | Case 1:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | (65) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | REF_CLOSE: (31), (59), (65) are inconsistent by sub-proof #604.
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | Case 2:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | (66) all_57_13 = e0 & op(e0, e2) = e0
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | ALPHA: (66) implies:
% 142.38/21.24 | | | | | | (67) all_57_13 = e0
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | BETA: splitting (23) gives:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | Case 1:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | (68) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 &
% 142.38/21.24 | | | | | | | op(e0, e2) = e2)
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | BETA: splitting (68) gives:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (69) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | ALPHA: (69) implies:
% 142.38/21.24 | | | | | | | | (70) all_57_12 = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | REF_CLOSE: (8), (52), (70) are inconsistent by sub-proof #970.
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (71) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | ALPHA: (71) implies:
% 142.38/21.24 | | | | | | | | (72) all_57_13 = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | COMBINE_EQS: (67), (72) imply:
% 142.38/21.24 | | | | | | | | (73) e2 = e0
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | REDUCE: (33), (73) imply:
% 142.38/21.24 | | | | | | | | (74) $false
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | CLOSE: (74) is inconsistent.
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | End of split
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | Case 2:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | (75) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 &
% 142.38/21.24 | | | | | | | op(e0, e0) = e2)
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | BETA: splitting (75) gives:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (76) all_57_14 = e2 & op(e0, e1) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | ALPHA: (76) implies:
% 142.38/21.24 | | | | | | | | (77) all_57_14 = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | BETA: splitting (49) gives:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (78) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 142.38/21.24 | | | | | | | | | op(e2, e3) = e2)
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | BETA: splitting (78) gives:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (79) all_57_0 = e2 & op(e3, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (79) implies:
% 142.38/21.24 | | | | | | | | | | (80) op(e3, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (33), (39), (48), (80) are inconsistent by
% 142.38/21.24 | | | | | | | | | | sub-proof #880.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (81) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (81) implies:
% 142.38/21.24 | | | | | | | | | | (82) all_57_2 = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12),
% 142.38/21.24 | | | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21),
% 142.38/21.24 | | | | | | | | | | (22), (24), (26), (27), (28), (31), (33), (34),
% 142.38/21.24 | | | | | | | | | | (36), (37), (38), (39), (41), (42), (43), (44),
% 142.38/21.24 | | | | | | | | | | (45), (46), (47), (48), (51), (53), (59), (62),
% 142.38/21.24 | | | | | | | | | | (67), (77), (82) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | | #587.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (83) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 142.38/21.24 | | | | | | | | | op(e0, e3) = e2)
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | BETA: splitting (83) gives:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (84) all_57_6 = e2 & op(e1, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (84) implies:
% 142.38/21.24 | | | | | | | | | | (85) op(e1, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (1), (5), (25), (29), (35), (39), (40), (85) are
% 142.38/21.24 | | | | | | | | | | inconsistent by sub-proof #654.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (86) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (86) implies:
% 142.38/21.24 | | | | | | | | | | (87) all_57_12 = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | COMBINE_EQS: (52), (87) imply:
% 142.38/21.24 | | | | | | | | | | (88) e2 = e1
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | SIMP: (88) implies:
% 142.38/21.24 | | | | | | | | | | (89) e2 = e1
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | COMBINE_EQS: (77), (89) imply:
% 142.38/21.24 | | | | | | | | | | (90) all_57_14 = e1
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (4), (8), (11), (19), (20), (21), (31), (33),
% 142.38/21.24 | | | | | | | | | | (34), (38), (39), (43), (45), (90) are
% 142.38/21.24 | | | | | | | | | | inconsistent by sub-proof #602.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | End of split
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (91) all_57_15 = e2 & op(e0, e0) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | ALPHA: (91) implies:
% 142.38/21.24 | | | | | | | | (92) op(e0, e0) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | REF_CLOSE: (9), (34), (39), (92) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | #1066.
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | End of split
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | End of split
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | End of split
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | End of split
% 142.38/21.24 | | | |
% 142.38/21.24 | | | Case 2:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | (93) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | REF_CLOSE: (45), (59), (93) are inconsistent by sub-proof #586.
% 142.38/21.24 | | | |
% 142.38/21.24 | | | End of split
% 142.38/21.24 | | |
% 142.38/21.24 | | Case 2:
% 142.38/21.24 | | |
% 142.38/21.24 | | | (94) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.38/21.24 | | | e3)
% 142.38/21.24 | | |
% 142.38/21.24 | | | BETA: splitting (94) gives:
% 142.38/21.24 | | |
% 142.38/21.24 | | | Case 1:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | (95) all_57_8 = e3 & op(e1, e1) = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | ALPHA: (95) implies:
% 142.38/21.24 | | | | (96) op(e1, e1) = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | REF_CLOSE: (20), (39), (45), (96) are inconsistent by sub-proof #1096.
% 142.38/21.24 | | | |
% 142.38/21.24 | | | Case 2:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | (97) all_57_11 = e3 & op(e1, e0) = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | ALPHA: (97) implies:
% 142.38/21.24 | | | | (98) all_57_11 = e3
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | BETA: splitting (30) gives:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | Case 1:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | (99) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2,
% 142.38/21.24 | | | | | e2) = e0)
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | REF_CLOSE: (7), (12), (31), (32), (39), (99) are inconsistent by
% 142.38/21.24 | | | | | sub-proof #1062.
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | Case 2:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | (100) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0,
% 142.38/21.24 | | | | | e2) = e0)
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | BETA: splitting (100) gives:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | Case 1:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | (101) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | REF_CLOSE: (31), (59), (101) are inconsistent by sub-proof #604.
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | Case 2:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | (102) all_57_13 = e0 & op(e0, e2) = e0
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | ALPHA: (102) implies:
% 142.38/21.24 | | | | | | (103) all_57_13 = e0
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | BETA: splitting (16) gives:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | Case 1:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | (104) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 &
% 142.38/21.24 | | | | | | | op(e2, e0) = e2)
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | BETA: splitting (104) gives:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (105) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | ALPHA: (105) implies:
% 142.38/21.24 | | | | | | | | (106) all_57_9 = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | REF_CLOSE: (8), (15), (106) are inconsistent by sub-proof #815.
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (107) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | ALPHA: (107) implies:
% 142.38/21.24 | | | | | | | | (108) all_57_10 = e2
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | BETA: splitting (23) gives:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (109) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2
% 142.38/21.24 | | | | | | | | | & op(e0, e2) = e2)
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | BETA: splitting (109) gives:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (110) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (110) implies:
% 142.38/21.24 | | | | | | | | | | (111) all_57_12 = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | COMBINE_EQS: (52), (111) imply:
% 142.38/21.24 | | | | | | | | | | (112) e2 = e1
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | COMBINE_EQS: (108), (112) imply:
% 142.38/21.24 | | | | | | | | | | (113) all_57_10 = e1
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (2), (6), (8), (9), (12), (16), (17), (19), (24),
% 142.38/21.24 | | | | | | | | | | (28), (31), (33), (34), (39), (42), (44), (45),
% 142.38/21.24 | | | | | | | | | | (53), (113) are inconsistent by sub-proof #589.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (114) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (33), (103), (114) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | | #588.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (115) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2
% 142.38/21.24 | | | | | | | | | & op(e0, e0) = e2)
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | BETA: splitting (115) gives:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (116) all_57_14 = e2 & op(e0, e1) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (116) implies:
% 142.38/21.24 | | | | | | | | | | (117) all_57_14 = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | BETA: splitting (22) gives:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | (118) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 142.38/21.24 | | | | | | | | | | | & op(e1, e2) = e0)
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | BETA: splitting (118) gives:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | (119) all_57_6 = e0 & op(e1, e3) = e0
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | ALPHA: (119) implies:
% 142.38/21.24 | | | | | | | | | | | | (120) all_57_6 = e0
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | BETA: splitting (49) gives:
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | (121) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2
% 142.38/21.24 | | | | | | | | | | | | | & op(e2, e3) = e2)
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | BETA: splitting (121) gives:
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | (122) all_57_0 = e2 & op(e3, e3) = e2
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | ALPHA: (122) implies:
% 142.38/21.24 | | | | | | | | | | | | | | (123) op(e3, e3) = e2
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | REF_CLOSE: (33), (39), (48), (123) are inconsistent by
% 142.38/21.24 | | | | | | | | | | | | | | sub-proof #880.
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | (124) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | ALPHA: (124) implies:
% 142.38/21.24 | | | | | | | | | | | | | | (125) all_57_2 = e2
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | BETA: splitting (26) gives:
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | (126) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3
% 142.38/21.24 | | | | | | | | | | | | | | | & op(e2, e3) = e3)
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | REF_CLOSE: (1), (5), (8), (19), (25), (29), (33), (34), (35),
% 142.38/21.24 | | | | | | | | | | | | | | | (39), (40), (47), (48), (49), (52), (126) are
% 142.38/21.24 | | | | | | | | | | | | | | | inconsistent by sub-proof #615.
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | (127) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 =
% 142.38/21.24 | | | | | | | | | | | | | | | e3 & op(e0, e3) = e3)
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | BETA: splitting (127) gives:
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | | (128) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | | ALPHA: (128) implies:
% 142.38/21.24 | | | | | | | | | | | | | | | | (129) all_57_6 = e3
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | | REF_CLOSE: (2), (3), (4), (6), (8), (9), (10), (11), (12),
% 142.38/21.24 | | | | | | | | | | | | | | | | (14), (15), (16), (17), (18), (19), (20), (21),
% 142.38/21.24 | | | | | | | | | | | | | | | | (22), (24), (26), (27), (28), (31), (33), (34),
% 142.38/21.24 | | | | | | | | | | | | | | | | (36), (37), (38), (39), (41), (42), (43), (44),
% 142.38/21.24 | | | | | | | | | | | | | | | | (45), (46), (47), (48), (51), (53), (59), (103),
% 142.38/21.24 | | | | | | | | | | | | | | | | (117), (125), (129) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | | | | | | | | #587.
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | | (130) all_57_12 = e3 & op(e0, e3) = e3
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | | ALPHA: (130) implies:
% 142.38/21.24 | | | | | | | | | | | | | | | | (131) all_57_12 = e3
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | | REF_CLOSE: (8), (9), (14), (31), (39), (45), (103), (117),
% 142.38/21.24 | | | | | | | | | | | | | | | | (131) are inconsistent by sub-proof #709.
% 142.38/21.24 | | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | (132) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 =
% 142.38/21.24 | | | | | | | | | | | | | e2 & op(e0, e3) = e2)
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | | REF_CLOSE: (1), (5), (8), (19), (25), (26), (27), (29), (31),
% 142.38/21.24 | | | | | | | | | | | | | (34), (35), (39), (40), (45), (47), (48), (120),
% 142.38/21.24 | | | | | | | | | | | | | (132) are inconsistent by sub-proof #585.
% 142.38/21.24 | | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | (133) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | REF_CLOSE: (31), (59), (133) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | | | | #604.
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | (134) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 142.38/21.24 | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | BETA: splitting (134) gives:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | (135) all_57_8 = e0 & op(e1, e1) = e0
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | ALPHA: (135) implies:
% 142.38/21.24 | | | | | | | | | | | | (136) op(e1, e1) = e0
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | REF_CLOSE: (20), (31), (39), (136) are inconsistent by
% 142.38/21.24 | | | | | | | | | | | | sub-proof #1089.
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | (137) all_57_11 = e0 & op(e1, e0) = e0
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | | REF_CLOSE: (19), (98), (137) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | | | | #584.
% 142.38/21.24 | | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (138) all_57_15 = e2 & op(e0, e0) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | ALPHA: (138) implies:
% 142.38/21.24 | | | | | | | | | | (139) op(e0, e0) = e2
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | REF_CLOSE: (9), (34), (39), (139) are inconsistent by
% 142.38/21.24 | | | | | | | | | | sub-proof #1066.
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | End of split
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | End of split
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | Case 2:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | (140) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 &
% 142.38/21.24 | | | | | | | op(e0, e0) = e2)
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | REF_CLOSE: (9), (34), (39), (98), (140) are inconsistent by
% 142.38/21.24 | | | | | | | sub-proof #583.
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | End of split
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | End of split
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | End of split
% 142.38/21.24 | | | |
% 142.38/21.24 | | | End of split
% 142.38/21.24 | | |
% 142.38/21.24 | | End of split
% 142.38/21.24 | |
% 142.38/21.24 | End of split
% 142.38/21.24 |
% 142.38/21.24 End of proof
% 142.38/21.24
% 142.38/21.24 Sub-proof #583 shows that the following formulas are inconsistent:
% 142.38/21.24 ----------------------------------------------------------------
% 142.38/21.24 (1) op(e0, e0) = e3
% 142.38/21.24 (2) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.24 (3) ~ (e3 = e2)
% 142.38/21.24 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.24 (5) all_57_11 = e3
% 142.38/21.24
% 142.38/21.24 Begin of proof
% 142.38/21.24 |
% 142.38/21.24 | BETA: splitting (2) gives:
% 142.38/21.24 |
% 142.38/21.24 | Case 1:
% 142.38/21.24 | |
% 142.38/21.24 | | (6) all_57_11 = e2 & op(e1, e0) = e2
% 142.38/21.24 | |
% 142.38/21.24 | | REF_CLOSE: (3), (5), (6) are inconsistent by sub-proof #963.
% 142.38/21.24 | |
% 142.38/21.24 | Case 2:
% 142.38/21.24 | |
% 142.38/21.24 | | (7) all_57_15 = e2 & op(e0, e0) = e2
% 142.38/21.24 | |
% 142.38/21.24 | | ALPHA: (7) implies:
% 142.38/21.24 | | (8) op(e0, e0) = e2
% 142.38/21.24 | |
% 142.38/21.24 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1066.
% 142.38/21.24 | |
% 142.38/21.24 | End of split
% 142.38/21.24 |
% 142.38/21.24 End of proof
% 142.38/21.24
% 142.38/21.24 Sub-proof #584 shows that the following formulas are inconsistent:
% 142.38/21.24 ----------------------------------------------------------------
% 142.38/21.24 (1) all_57_11 = e0 & op(e1, e0) = e0
% 142.38/21.24 (2) all_57_11 = e3
% 142.38/21.24 (3) ~ (e3 = e0)
% 142.38/21.24
% 142.38/21.24 Begin of proof
% 142.38/21.24 |
% 142.38/21.24 | ALPHA: (1) implies:
% 142.38/21.24 | (4) all_57_11 = e0
% 142.38/21.24 |
% 142.38/21.24 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.24 | (5) e3 = e0
% 142.38/21.24 |
% 142.38/21.24 | REDUCE: (3), (5) imply:
% 142.38/21.24 | (6) $false
% 142.38/21.24 |
% 142.38/21.24 | CLOSE: (6) is inconsistent.
% 142.38/21.24 |
% 142.38/21.24 End of proof
% 142.38/21.24
% 142.38/21.24 Sub-proof #585 shows that the following formulas are inconsistent:
% 142.38/21.24 ----------------------------------------------------------------
% 142.38/21.24 (1) op(e3, e0) = e1
% 142.38/21.24 (2) op(e1, e3) = all_52_2
% 142.38/21.24 (3) ~ (e2 = e1)
% 142.38/21.24 (4) ~ (e3 = e0)
% 142.38/21.24 (5) all_57_6 = e0
% 142.38/21.24 (6) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.38/21.24 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.38/21.24 all_14_1 & $i(all_14_1))
% 142.38/21.24 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.24 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.24 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.24 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.24 (9) all_28_2 = e0
% 142.38/21.24 (10) ~ (e1 = e0)
% 142.38/21.24 (11) ~ (e3 = e2)
% 142.38/21.24 (12) op(e3, e0) = all_52_12
% 142.38/21.24 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.24 (14) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.24 (15) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.24 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.24 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.24 (16) ~ (e3 = e1)
% 142.38/21.24 (17) all_57_0 = e0
% 142.38/21.24 (18) op(e3, e3) = e0
% 142.38/21.24
% 142.38/21.24 Begin of proof
% 142.38/21.24 |
% 142.38/21.24 | BETA: splitting (14) gives:
% 142.38/21.24 |
% 142.38/21.24 | Case 1:
% 142.38/21.24 | |
% 142.38/21.24 | | (19) all_57_6 = e2 & op(e1, e3) = e2
% 142.38/21.24 | |
% 142.38/21.24 | | ALPHA: (19) implies:
% 142.38/21.24 | | (20) op(e1, e3) = e2
% 142.38/21.24 | |
% 142.38/21.24 | | REF_CLOSE: (1), (2), (6), (9), (12), (13), (15), (20) are inconsistent by
% 142.38/21.24 | | sub-proof #654.
% 142.38/21.24 | |
% 142.38/21.24 | Case 2:
% 142.38/21.24 | |
% 142.38/21.24 | | (21) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.24 | |
% 142.38/21.24 | | ALPHA: (21) implies:
% 142.38/21.24 | | (22) all_57_12 = e2
% 142.38/21.24 | |
% 142.38/21.24 | | REF_CLOSE: (3), (4), (5), (7), (8), (10), (11), (13), (16), (17), (18), (22)
% 142.38/21.24 | | are inconsistent by sub-proof #771.
% 142.38/21.24 | |
% 142.38/21.24 | End of split
% 142.38/21.24 |
% 142.38/21.24 End of proof
% 142.38/21.24
% 142.38/21.24 Sub-proof #586 shows that the following formulas are inconsistent:
% 142.38/21.24 ----------------------------------------------------------------
% 142.38/21.24 (1) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.24 (2) all_57_7 = e1
% 142.38/21.24 (3) ~ (e3 = e1)
% 142.38/21.24
% 142.38/21.24 Begin of proof
% 142.38/21.24 |
% 142.38/21.24 | ALPHA: (1) implies:
% 142.38/21.24 | (4) all_57_7 = e3
% 142.38/21.24 |
% 142.38/21.24 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.24 | (5) e3 = e1
% 142.38/21.24 |
% 142.38/21.24 | REDUCE: (3), (5) imply:
% 142.38/21.24 | (6) $false
% 142.38/21.24 |
% 142.38/21.24 | CLOSE: (6) is inconsistent.
% 142.38/21.24 |
% 142.38/21.24 End of proof
% 142.38/21.24
% 142.38/21.24 Sub-proof #587 shows that the following formulas are inconsistent:
% 142.38/21.24 ----------------------------------------------------------------
% 142.38/21.24 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.24 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.24 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.38/21.24 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.38/21.24 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.24 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.24 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.24 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.38/21.24 (5) all_57_6 = e3
% 142.38/21.24 (6) ~ (e2 = e1)
% 142.38/21.24 (7) op(e0, e0) = e3
% 142.38/21.24 (8) op(e0, e3) = all_52_3
% 142.38/21.24 (9) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.24 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.24 (10) all_57_14 = e2
% 142.38/21.24 (11) op(e2, e2) = e1
% 142.38/21.24 (12) all_57_7 = e1
% 142.38/21.24 (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.38/21.24 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.38/21.24 e1)
% 142.38/21.24 (14) all_57_9 = e1
% 142.38/21.24 (15) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.24 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.24 (16) ~ (all_52_1 = e0)
% 142.38/21.24 (17) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.24 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.24 (18) all_57_13 = e0
% 142.38/21.24 (19) ~ (e3 = e0)
% 142.38/21.24 (20) op(e1, e1) = e1
% 142.38/21.24 (21) op(e3, e1) = all_52_8
% 142.38/21.24 (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.38/21.24 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.24 (23) op(e2, e3) = all_52_1
% 142.38/21.24 (24) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.24 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.24 (25) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.24 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.24 (26) all_57_3 = e1
% 142.38/21.24 (27) ~ (e1 = e0)
% 142.38/21.24 (28) ~ (e2 = e0)
% 142.38/21.24 (29) ~ (e3 = e2)
% 142.38/21.24 (30) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.38/21.24 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.38/21.24 (31) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.38/21.24 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.38/21.24 (32) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.24 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.24 (33) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.24 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.24 (34) ~ (all_52_3 = e0)
% 142.38/21.24 (35) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.24 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.24 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.24 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.24 (36) ~ (all_52_8 = e0)
% 142.38/21.24 (37) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.24 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.24 (38) ~ (e3 = e1)
% 142.38/21.24 (39) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.24 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.24 (40) all_57_0 = e0
% 142.38/21.24 (41) op(e3, e3) = e0
% 142.38/21.24 (42) all_57_2 = e2
% 142.38/21.24 (43) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.24 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.24 (44) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.24 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.24
% 142.38/21.24 Begin of proof
% 142.38/21.24 |
% 142.38/21.24 | BETA: splitting (22) gives:
% 142.38/21.24 |
% 142.38/21.24 | Case 1:
% 142.38/21.24 | |
% 142.38/21.24 | | (45) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 142.38/21.24 | | e0)
% 142.38/21.24 | |
% 142.38/21.24 | | BETA: splitting (45) gives:
% 142.38/21.24 | |
% 142.38/21.24 | | Case 1:
% 142.38/21.24 | | |
% 142.38/21.24 | | | (46) all_57_6 = e0 & op(e1, e3) = e0
% 142.38/21.24 | | |
% 142.38/21.24 | | | REF_CLOSE: (5), (19), (46) are inconsistent by sub-proof #603.
% 142.38/21.24 | | |
% 142.38/21.24 | | Case 2:
% 142.38/21.24 | | |
% 142.38/21.24 | | | (47) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.24 | | |
% 142.38/21.24 | | | REF_CLOSE: (12), (27), (47) are inconsistent by sub-proof #604.
% 142.38/21.24 | | |
% 142.38/21.24 | | End of split
% 142.38/21.24 | |
% 142.38/21.24 | Case 2:
% 142.38/21.24 | |
% 142.38/21.24 | | (48) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.38/21.24 | | e0)
% 142.38/21.24 | |
% 142.38/21.24 | | BETA: splitting (48) gives:
% 142.38/21.24 | |
% 142.38/21.24 | | Case 1:
% 142.38/21.24 | | |
% 142.38/21.24 | | | (49) all_57_8 = e0 & op(e1, e1) = e0
% 142.38/21.24 | | |
% 142.38/21.24 | | | ALPHA: (49) implies:
% 142.38/21.24 | | | (50) op(e1, e1) = e0
% 142.38/21.24 | | |
% 142.38/21.24 | | | REF_CLOSE: (20), (27), (33), (50) are inconsistent by sub-proof #1089.
% 142.38/21.24 | | |
% 142.38/21.24 | | Case 2:
% 142.38/21.24 | | |
% 142.38/21.24 | | | (51) all_57_11 = e0 & op(e1, e0) = e0
% 142.38/21.24 | | |
% 142.38/21.24 | | | ALPHA: (51) implies:
% 142.38/21.24 | | | (52) all_57_11 = e0
% 142.38/21.24 | | |
% 142.38/21.24 | | | BETA: splitting (15) gives:
% 142.38/21.24 | | |
% 142.38/21.24 | | | Case 1:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | (53) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0)
% 142.38/21.24 | | | | = e2)
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | BETA: splitting (53) gives:
% 142.38/21.24 | | | |
% 142.38/21.24 | | | | Case 1:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | (54) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | ALPHA: (54) implies:
% 142.38/21.24 | | | | | (55) all_57_9 = e2
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | COMBINE_EQS: (14), (55) imply:
% 142.38/21.24 | | | | | (56) e2 = e1
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | SIMP: (56) implies:
% 142.38/21.24 | | | | | (57) e2 = e1
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | COMBINE_EQS: (10), (57) imply:
% 142.38/21.24 | | | | | (58) all_57_14 = e1
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | REF_CLOSE: (3), (6), (9), (19), (20), (21), (27), (28), (29), (32),
% 142.38/21.24 | | | | | (33), (36), (38), (58) are inconsistent by sub-proof #602.
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | Case 2:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | (59) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | ALPHA: (59) implies:
% 142.38/21.24 | | | | | (60) all_57_10 = e2
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | BETA: splitting (17) gives:
% 142.38/21.24 | | | | |
% 142.38/21.24 | | | | | Case 1:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | (61) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 142.38/21.24 | | | | | | e2) = e2)
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | BETA: splitting (61) gives:
% 142.38/21.24 | | | | | |
% 142.38/21.24 | | | | | | Case 1:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | (62) all_57_1 = e2 & op(e3, e2) = e2
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | ALPHA: (62) implies:
% 142.38/21.24 | | | | | | | (63) all_57_1 = e2
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | BETA: splitting (39) gives:
% 142.38/21.24 | | | | | | |
% 142.38/21.24 | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (64) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 &
% 142.38/21.24 | | | | | | | | op(e3, e2) = e3)
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | BETA: splitting (64) gives:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (65) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | REF_CLOSE: (19), (40), (65) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | #1108.
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (66) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | REF_CLOSE: (5), (6), (19), (20), (24), (25), (27), (28), (29),
% 142.38/21.24 | | | | | | | | | (30), (31), (33), (38), (40), (41), (42), (52),
% 142.38/21.24 | | | | | | | | | (63), (66) are inconsistent by sub-proof #601.
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | End of split
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | (67) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 &
% 142.38/21.24 | | | | | | | | op(e3, e0) = e3)
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | BETA: splitting (67) gives:
% 142.38/21.24 | | | | | | | |
% 142.38/21.24 | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | (68) all_57_4 = e3 & op(e3, e1) = e3
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | ALPHA: (68) implies:
% 142.38/21.24 | | | | | | | | | (69) all_57_4 = e3
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | BETA: splitting (43) gives:
% 142.38/21.24 | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (70) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 142.38/21.24 | | | | | | | | | | op(e2, e2) = e3)
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | BETA: splitting (70) gives:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | (71) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | REF_CLOSE: (5), (6), (19), (20), (24), (25), (27), (28),
% 142.38/21.24 | | | | | | | | | | | (29), (30), (31), (33), (38), (40), (41), (42),
% 142.38/21.24 | | | | | | | | | | | (52), (63), (71) are inconsistent by sub-proof
% 142.38/21.24 | | | | | | | | | | | #601.
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | (72) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (19), (20), (21), (26), (27), (28),
% 142.38/21.24 | | | | | | | | | | | (29), (32), (33), (36), (38), (69), (72) are
% 142.38/21.24 | | | | | | | | | | | inconsistent by sub-proof #622.
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | End of split
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | Case 2:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | (73) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3
% 142.38/21.24 | | | | | | | | | | & op(e0, e2) = e3)
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | BETA: splitting (73) gives:
% 142.38/21.24 | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | Case 1:
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | (74) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | ALPHA: (74) implies:
% 142.38/21.24 | | | | | | | | | | | (75) all_57_7 = e3
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | COMBINE_EQS: (12), (75) imply:
% 142.38/21.24 | | | | | | | | | | | (76) e3 = e1
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | SIMP: (76) implies:
% 142.38/21.24 | | | | | | | | | | | (77) e3 = e1
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | COMBINE_EQS: (69), (77) imply:
% 142.38/21.24 | | | | | | | | | | | (78) all_57_4 = e1
% 142.38/21.24 | | | | | | | | | | |
% 142.38/21.24 | | | | | | | | | | | REF_CLOSE: (3), (6), (9), (19), (20), (21), (27), (28), (29),
% 142.38/21.24 | | | | | | | | | | | (32), (33), (36), (38), (78) are inconsistent by
% 142.38/21.24 | | | | | | | | | | | sub-proof #623.
% 142.38/21.25 | | | | | | | | | | |
% 142.38/21.25 | | | | | | | | | | Case 2:
% 142.38/21.25 | | | | | | | | | | |
% 142.38/21.25 | | | | | | | | | | | (79) all_57_13 = e3 & op(e0, e2) = e3
% 142.38/21.25 | | | | | | | | | | |
% 142.38/21.25 | | | | | | | | | | | REF_CLOSE: (18), (19), (79) are inconsistent by sub-proof
% 142.38/21.25 | | | | | | | | | | | #600.
% 142.38/21.25 | | | | | | | | | | |
% 142.38/21.25 | | | | | | | | | | End of split
% 142.38/21.25 | | | | | | | | | |
% 142.38/21.25 | | | | | | | | | End of split
% 142.38/21.25 | | | | | | | | |
% 142.38/21.25 | | | | | | | | Case 2:
% 142.38/21.25 | | | | | | | | |
% 142.38/21.25 | | | | | | | | | (80) all_57_9 = e3 & op(e3, e0) = e3
% 142.38/21.25 | | | | | | | | |
% 142.38/21.25 | | | | | | | | | REF_CLOSE: (6), (7), (15), (27), (28), (29), (33), (37), (38),
% 142.38/21.25 | | | | | | | | | (52), (80) are inconsistent by sub-proof #595.
% 142.38/21.25 | | | | | | | | |
% 142.38/21.25 | | | | | | | | End of split
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | End of split
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | Case 2:
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | (81) all_57_3 = e2 & op(e2, e2) = e2
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | ALPHA: (81) implies:
% 142.38/21.25 | | | | | | | (82) op(e2, e2) = e2
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | REF_CLOSE: (6), (11), (33), (82) are inconsistent by sub-proof
% 142.38/21.25 | | | | | | | #749.
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | End of split
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | Case 2:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (83) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 142.38/21.25 | | | | | | e2) = e2)
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | BETA: splitting (83) gives:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | Case 1:
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | (84) all_57_7 = e2 & op(e1, e2) = e2
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | ALPHA: (84) implies:
% 142.38/21.25 | | | | | | | (85) all_57_7 = e2
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | COMBINE_EQS: (12), (85) imply:
% 142.38/21.25 | | | | | | | (86) e2 = e1
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | SIMP: (86) implies:
% 142.38/21.25 | | | | | | | (87) e2 = e1
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | COMBINE_EQS: (60), (87) imply:
% 142.38/21.25 | | | | | | | (88) all_57_10 = e1
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | REF_CLOSE: (1), (4), (6), (7), (11), (15), (16), (19), (23), (26),
% 142.38/21.25 | | | | | | | (27), (28), (29), (33), (35), (37), (38), (44), (88)
% 142.38/21.25 | | | | | | | are inconsistent by sub-proof #589.
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | Case 2:
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | (89) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | REF_CLOSE: (18), (28), (89) are inconsistent by sub-proof #588.
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | End of split
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | End of split
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | End of split
% 142.38/21.25 | | | |
% 142.38/21.25 | | | Case 2:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | (90) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0,
% 142.38/21.25 | | | | e0) = e2)
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | BETA: splitting (90) gives:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | Case 1:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (91) all_57_11 = e2 & op(e1, e0) = e2
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | ALPHA: (91) implies:
% 142.38/21.25 | | | | | (92) all_57_11 = e2
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | REF_CLOSE: (28), (52), (92) are inconsistent by sub-proof #996.
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | Case 2:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (93) all_57_15 = e2 & op(e0, e0) = e2
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | ALPHA: (93) implies:
% 142.38/21.25 | | | | | (94) op(e0, e0) = e2
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | BETA: splitting (35) gives:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | Case 1:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (95) all_57_15 = e0 & op(e0, e0) = e0
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | ALPHA: (95) implies:
% 142.38/21.25 | | | | | | (96) op(e0, e0) = e0
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | REF_CLOSE: (28), (33), (94), (96) are inconsistent by sub-proof
% 142.38/21.25 | | | | | | #1094.
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | Case 2:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (97) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 142.38/21.25 | | | | | | op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.38/21.25 | | | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.25 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | ALPHA: (97) implies:
% 142.38/21.25 | | | | | | (98) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.25 | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | BETA: splitting (98) gives:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | Case 1:
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | (99) all_57_12 = e0 & op(e0, e3) = e0
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | ALPHA: (99) implies:
% 142.38/21.25 | | | | | | | (100) op(e0, e3) = e0
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | REF_CLOSE: (8), (33), (34), (100) are inconsistent by sub-proof
% 142.38/21.25 | | | | | | | #986.
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | Case 2:
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | (101) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 142.38/21.25 | | | | | | | op(e0, e1) = e0)
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | BETA: splitting (101) gives:
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | | Case 1:
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | | (102) all_57_13 = e0 & op(e0, e2) = e0
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | | REF_CLOSE: (2), (6), (10), (13), (18), (19), (27), (29), (33),
% 142.38/21.25 | | | | | | | | (38), (94) are inconsistent by sub-proof #802.
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | Case 2:
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | | (103) all_57_14 = e0 & op(e0, e1) = e0
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | | REF_CLOSE: (10), (28), (103) are inconsistent by sub-proof #920.
% 142.38/21.25 | | | | | | | |
% 142.38/21.25 | | | | | | | End of split
% 142.38/21.25 | | | | | | |
% 142.38/21.25 | | | | | | End of split
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | End of split
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | End of split
% 142.38/21.25 | | | |
% 142.38/21.25 | | | End of split
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #588 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.25 (2) all_57_13 = e0
% 142.38/21.25 (3) ~ (e2 = e0)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (1) implies:
% 142.38/21.25 | (4) all_57_13 = e2
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.25 | (5) e2 = e0
% 142.38/21.25 |
% 142.38/21.25 | SIMP: (5) implies:
% 142.38/21.25 | (6) e2 = e0
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (6) imply:
% 142.38/21.25 | (7) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (7) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #589 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.25 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.25 (2) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.25 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.38/21.25 (3) ~ (e2 = e1)
% 142.38/21.25 (4) op(e0, e0) = e3
% 142.38/21.25 (5) op(e2, e2) = e1
% 142.38/21.25 (6) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.25 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.25 (7) ~ (all_52_1 = e0)
% 142.38/21.25 (8) ~ (e3 = e0)
% 142.38/21.25 (9) all_57_10 = e1
% 142.38/21.25 (10) op(e2, e3) = all_52_1
% 142.38/21.25 (11) all_57_3 = e1
% 142.38/21.25 (12) ~ (e1 = e0)
% 142.38/21.25 (13) ~ (e2 = e0)
% 142.38/21.25 (14) ~ (e3 = e2)
% 142.38/21.25 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25 (16) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.25 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.25 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.25 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.25 (17) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.25 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.25 (18) ~ (e3 = e1)
% 142.38/21.25 (19) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.25 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (16) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (20) all_57_15 = e0 & op(e0, e0) = e0
% 142.38/21.25 | |
% 142.38/21.25 | | ALPHA: (20) implies:
% 142.38/21.25 | | (21) op(e0, e0) = e0
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (4), (8), (15), (21) are inconsistent by sub-proof #751.
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (22) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.38/21.25 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.38/21.25 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.38/21.25 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.38/21.25 | |
% 142.38/21.25 | | ALPHA: (22) implies:
% 142.38/21.25 | | (23) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.38/21.25 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (19) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (24) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.38/21.25 | | | e0)
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (5), (7), (10), (12), (15), (24) are inconsistent by sub-proof
% 142.38/21.25 | | | #640.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (25) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.38/21.25 | | | e0)
% 142.38/21.25 | | |
% 142.38/21.25 | | | BETA: splitting (25) gives:
% 142.38/21.25 | | |
% 142.38/21.25 | | | Case 1:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | (26) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | ALPHA: (26) implies:
% 142.38/21.25 | | | | (27) all_57_5 = e0
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | BETA: splitting (1) gives:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | Case 1:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (28) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2,
% 142.38/21.25 | | | | | e2) = e3)
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | BETA: splitting (28) gives:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | Case 1:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (29) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | ALPHA: (29) implies:
% 142.38/21.25 | | | | | | (30) all_57_2 = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | REF_CLOSE: (2), (3), (5), (9), (13), (14), (15), (27), (30) are
% 142.38/21.25 | | | | | | inconsistent by sub-proof #592.
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | Case 2:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (31) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | ALPHA: (31) implies:
% 142.38/21.25 | | | | | | (32) all_57_3 = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | REF_CLOSE: (11), (18), (32) are inconsistent by sub-proof #591.
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | End of split
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | Case 2:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (33) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2,
% 142.38/21.25 | | | | | e0) = e3)
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | BETA: splitting (33) gives:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | Case 1:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (34) all_57_5 = e3 & op(e2, e1) = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | ALPHA: (34) implies:
% 142.38/21.25 | | | | | | (35) all_57_5 = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | REF_CLOSE: (8), (27), (35) are inconsistent by sub-proof #1041.
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | Case 2:
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | (36) all_57_10 = e3 & op(e2, e0) = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | ALPHA: (36) implies:
% 142.38/21.25 | | | | | | (37) all_57_10 = e3
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | | REF_CLOSE: (3), (4), (6), (8), (12), (13), (14), (15), (17), (18),
% 142.38/21.25 | | | | | | (23), (37) are inconsistent by sub-proof #687.
% 142.38/21.25 | | | | | |
% 142.38/21.25 | | | | | End of split
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | End of split
% 142.38/21.25 | | | |
% 142.38/21.25 | | | Case 2:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | (38) all_57_10 = e0 & op(e2, e0) = e0
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | ALPHA: (38) implies:
% 142.38/21.25 | | | | (39) all_57_10 = e0
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | REF_CLOSE: (9), (12), (39) are inconsistent by sub-proof #590.
% 142.38/21.25 | | | |
% 142.38/21.25 | | | End of split
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #590 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_10 = e1
% 142.38/21.25 (2) all_57_10 = e0
% 142.38/21.25 (3) ~ (e1 = e0)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.25 | (4) e1 = e0
% 142.38/21.25 |
% 142.38/21.25 | SIMP: (4) implies:
% 142.38/21.25 | (5) e1 = e0
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #591 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_3 = e3
% 142.38/21.25 (2) all_57_3 = e1
% 142.38/21.25 (3) ~ (e3 = e1)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.25 | (4) e3 = e1
% 142.38/21.25 |
% 142.38/21.25 | SIMP: (4) implies:
% 142.38/21.25 | (5) e3 = e1
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #592 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.25 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.38/21.25 (2) ~ (e2 = e1)
% 142.38/21.25 (3) all_57_5 = e0
% 142.38/21.25 (4) op(e2, e2) = e1
% 142.38/21.25 (5) all_57_10 = e1
% 142.38/21.25 (6) ~ (e2 = e0)
% 142.38/21.25 (7) ~ (e3 = e2)
% 142.38/21.25 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25 (9) all_57_2 = e3
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (1) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (10) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 142.38/21.25 | | e2)
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (2), (4), (7), (8), (9), (10) are inconsistent by sub-proof #594.
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (11) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.38/21.25 | | e2)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (11) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (12) all_57_5 = e2 & op(e2, e1) = e2
% 142.38/21.25 | | |
% 142.38/21.25 | | | ALPHA: (12) implies:
% 142.38/21.25 | | | (13) all_57_5 = e2
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (3), (6), (13) are inconsistent by sub-proof #1042.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (14) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (2), (5), (14) are inconsistent by sub-proof #593.
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #593 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.25 (2) all_57_10 = e1
% 142.38/21.25 (3) ~ (e2 = e1)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (1) implies:
% 142.38/21.25 | (4) all_57_10 = e2
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.25 | (5) e2 = e1
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #594 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) ~ (e2 = e1)
% 142.38/21.25 (2) op(e2, e2) = e1
% 142.38/21.25 (3) ~ (e3 = e2)
% 142.38/21.25 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 142.38/21.25 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25 (6) all_57_2 = e3
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (4) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (7) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #635.
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (8) all_57_3 = e2 & op(e2, e2) = e2
% 142.38/21.25 | |
% 142.38/21.25 | | ALPHA: (8) implies:
% 142.38/21.25 | | (9) op(e2, e2) = e2
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (1), (2), (5), (9) are inconsistent by sub-proof #749.
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #595 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_11 = e0
% 142.38/21.25 (2) ~ (e2 = e1)
% 142.38/21.25 (3) op(e0, e0) = e3
% 142.38/21.25 (4) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.25 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.25 (5) ~ (e1 = e0)
% 142.38/21.25 (6) ~ (e2 = e0)
% 142.38/21.25 (7) all_57_9 = e3 & op(e3, e0) = e3
% 142.38/21.25 (8) ~ (e3 = e2)
% 142.38/21.25 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25 (10) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.25 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.25 (11) ~ (e3 = e1)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (7) implies:
% 142.38/21.25 | (12) all_57_9 = e3
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (10) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (13) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 142.38/21.25 | | e1)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (13) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (14) all_57_9 = e1 & op(e3, e0) = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (11), (12), (14) are inconsistent by sub-proof #599.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (15) all_57_10 = e1 & op(e2, e0) = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | ALPHA: (15) implies:
% 142.38/21.25 | | | (16) all_57_10 = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (12), (16) are inconsistent
% 142.38/21.25 | | | by sub-proof #597.
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (17) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.38/21.25 | | e1)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (17) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (18) all_57_11 = e1 & op(e1, e0) = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (1), (5), (18) are inconsistent by sub-proof #596.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (19) all_57_15 = e1 & op(e0, e0) = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | ALPHA: (19) implies:
% 142.38/21.25 | | | (20) op(e0, e0) = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (3), (9), (11), (20) are inconsistent by sub-proof #732.
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #596 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_11 = e1 & op(e1, e0) = e1
% 142.38/21.25 (2) all_57_11 = e0
% 142.38/21.25 (3) ~ (e1 = e0)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (1) implies:
% 142.38/21.25 | (4) all_57_11 = e1
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.25 | (5) e1 = e0
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #597 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_11 = e0
% 142.38/21.25 (2) ~ (e2 = e1)
% 142.38/21.25 (3) op(e0, e0) = e3
% 142.38/21.25 (4) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.25 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.25 (5) all_57_10 = e1
% 142.38/21.25 (6) ~ (e2 = e0)
% 142.38/21.25 (7) ~ (e3 = e2)
% 142.38/21.25 (8) all_57_9 = e3
% 142.38/21.25 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (4) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (10) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.38/21.25 | | e2)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (10) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (11) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (7), (8), (11) are inconsistent by sub-proof #598.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (12) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.25 | | |
% 142.38/21.25 | | | ALPHA: (12) implies:
% 142.38/21.25 | | | (13) all_57_10 = e2
% 142.38/21.25 | | |
% 142.38/21.25 | | | COMBINE_EQS: (5), (13) imply:
% 142.38/21.25 | | | (14) e2 = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | SIMP: (14) implies:
% 142.38/21.25 | | | (15) e2 = e1
% 142.38/21.25 | | |
% 142.38/21.25 | | | REDUCE: (2), (15) imply:
% 142.38/21.25 | | | (16) $false
% 142.38/21.25 | | |
% 142.38/21.25 | | | CLOSE: (16) is inconsistent.
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (17) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.38/21.25 | | e2)
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (1), (3), (6), (7), (9), (17) are inconsistent by sub-proof #689.
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #598 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.25 (2) all_57_9 = e3
% 142.38/21.25 (3) ~ (e3 = e2)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (1) implies:
% 142.38/21.25 | (4) all_57_9 = e2
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.25 | (5) e3 = e2
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #599 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_9 = e1 & op(e3, e0) = e1
% 142.38/21.25 (2) all_57_9 = e3
% 142.38/21.25 (3) ~ (e3 = e1)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (1) implies:
% 142.38/21.25 | (4) all_57_9 = e1
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.25 | (5) e3 = e1
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #600 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_13 = e3 & op(e0, e2) = e3
% 142.38/21.25 (2) all_57_13 = e0
% 142.38/21.25 (3) ~ (e3 = e0)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (1) implies:
% 142.38/21.25 | (4) all_57_13 = e3
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.25 | (5) e3 = e0
% 142.38/21.25 |
% 142.38/21.25 | REDUCE: (3), (5) imply:
% 142.38/21.25 | (6) $false
% 142.38/21.25 |
% 142.38/21.25 | CLOSE: (6) is inconsistent.
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #601 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_6 = e3
% 142.38/21.25 (2) all_57_11 = e0
% 142.38/21.25 (3) ~ (e2 = e1)
% 142.38/21.25 (4) ~ (e3 = e0)
% 142.38/21.25 (5) op(e1, e1) = e1
% 142.38/21.25 (6) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.25 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.25 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.25 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.38/21.25 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.38/21.25 (9) ~ (e1 = e0)
% 142.38/21.25 (10) ~ (e2 = e0)
% 142.38/21.25 (11) ~ (e3 = e2)
% 142.38/21.25 (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.38/21.25 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.38/21.25 (13) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.38/21.25 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.38/21.25 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25 (15) ~ (e3 = e1)
% 142.38/21.25 (16) all_57_1 = e2
% 142.38/21.25 (17) all_57_0 = e0
% 142.38/21.25 (18) op(e3, e3) = e0
% 142.38/21.25 (19) all_57_2 = e2
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | ALPHA: (6) implies:
% 142.38/21.25 | (20) all_57_1 = e3
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (16), (20) imply:
% 142.38/21.25 | (21) e3 = e2
% 142.38/21.25 |
% 142.38/21.25 | SIMP: (21) implies:
% 142.38/21.25 | (22) e3 = e2
% 142.38/21.25 |
% 142.38/21.25 | COMBINE_EQS: (1), (22) imply:
% 142.38/21.25 | (23) all_57_6 = e2
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (12) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (24) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.38/21.25 | | e3)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (24) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (25) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (1), (11), (23) are inconsistent by sub-proof #1004.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (26) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.25 | | |
% 142.38/21.25 | | | ALPHA: (26) implies:
% 142.38/21.25 | | | (27) all_57_7 = e3
% 142.38/21.25 | | |
% 142.38/21.25 | | | BETA: splitting (8) gives:
% 142.38/21.25 | | |
% 142.38/21.25 | | | Case 1:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3)
% 142.38/21.25 | | | | = e1)
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | BETA: splitting (28) gives:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | Case 1:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (29) all_57_0 = e1 & op(e3, e3) = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | ALPHA: (29) implies:
% 142.38/21.25 | | | | | (30) op(e3, e3) = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | REF_CLOSE: (9), (14), (18), (30) are inconsistent by sub-proof #840.
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | Case 2:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (31) all_57_2 = e1 & op(e2, e3) = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | ALPHA: (31) implies:
% 142.38/21.25 | | | | | (32) all_57_2 = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | COMBINE_EQS: (19), (32) imply:
% 142.38/21.25 | | | | | (33) e2 = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | SIMP: (33) implies:
% 142.38/21.25 | | | | | (34) e2 = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | COMBINE_EQS: (23), (34) imply:
% 142.38/21.25 | | | | | (35) all_57_6 = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | REF_CLOSE: (2), (3), (5), (10), (11), (13), (14), (27), (35) are
% 142.38/21.25 | | | | | inconsistent by sub-proof #1081.
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | End of split
% 142.38/21.25 | | | |
% 142.38/21.25 | | | Case 2:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | (36) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3)
% 142.38/21.25 | | | | = e1)
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | BETA: splitting (36) gives:
% 142.38/21.25 | | | |
% 142.38/21.25 | | | | Case 1:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (37) all_57_6 = e1 & op(e1, e3) = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | ALPHA: (37) implies:
% 142.38/21.25 | | | | | (38) all_57_6 = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | REF_CLOSE: (2), (3), (5), (10), (11), (13), (14), (27), (38) are
% 142.38/21.25 | | | | | inconsistent by sub-proof #1081.
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | Case 2:
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | (39) all_57_12 = e1 & op(e0, e3) = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | ALPHA: (39) implies:
% 142.38/21.25 | | | | | (40) all_57_12 = e1
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | | REF_CLOSE: (4), (7), (11), (15), (17), (19), (23), (40) are
% 142.38/21.25 | | | | | inconsistent by sub-proof #614.
% 142.38/21.25 | | | | |
% 142.38/21.25 | | | | End of split
% 142.38/21.25 | | | |
% 142.38/21.25 | | | End of split
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (41) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.38/21.25 | | e3)
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (2), (4), (5), (14), (15), (41) are inconsistent by sub-proof
% 142.38/21.25 | | #956.
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #602 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.25 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.25 (2) ~ (e2 = e1)
% 142.38/21.25 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.25 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.25 (4) ~ (e3 = e0)
% 142.38/21.25 (5) op(e1, e1) = e1
% 142.38/21.25 (6) op(e3, e1) = all_52_8
% 142.38/21.25 (7) all_57_14 = e1
% 142.38/21.25 (8) ~ (e1 = e0)
% 142.38/21.25 (9) ~ (e2 = e0)
% 142.38/21.25 (10) ~ (e3 = e2)
% 142.38/21.25 (11) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.25 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.25 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.25 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.25 (13) ~ (all_52_8 = e0)
% 142.38/21.25 (14) ~ (e3 = e1)
% 142.38/21.25
% 142.38/21.25 Begin of proof
% 142.38/21.25 |
% 142.38/21.25 | BETA: splitting (3) gives:
% 142.38/21.25 |
% 142.38/21.25 | Case 1:
% 142.38/21.25 | |
% 142.38/21.25 | | (15) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 142.38/21.25 | | e0)
% 142.38/21.25 | |
% 142.38/21.25 | | BETA: splitting (15) gives:
% 142.38/21.25 | |
% 142.38/21.25 | | Case 1:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (16) all_57_4 = e0 & op(e3, e1) = e0
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (6), (12), (13), (16) are inconsistent by sub-proof #981.
% 142.38/21.25 | | |
% 142.38/21.25 | | Case 2:
% 142.38/21.25 | | |
% 142.38/21.25 | | | (17) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.25 | | |
% 142.38/21.25 | | | ALPHA: (17) implies:
% 142.38/21.25 | | | (18) all_57_5 = e0
% 142.38/21.25 | | |
% 142.38/21.25 | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12), (14), (18) are
% 142.38/21.25 | | | inconsistent by sub-proof #1040.
% 142.38/21.25 | | |
% 142.38/21.25 | | End of split
% 142.38/21.25 | |
% 142.38/21.25 | Case 2:
% 142.38/21.25 | |
% 142.38/21.25 | | (19) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.38/21.25 | | e0)
% 142.38/21.25 | |
% 142.38/21.25 | | REF_CLOSE: (5), (7), (8), (12), (19) are inconsistent by sub-proof #1039.
% 142.38/21.25 | |
% 142.38/21.25 | End of split
% 142.38/21.25 |
% 142.38/21.25 End of proof
% 142.38/21.25
% 142.38/21.25 Sub-proof #603 shows that the following formulas are inconsistent:
% 142.38/21.25 ----------------------------------------------------------------
% 142.38/21.25 (1) all_57_6 = e0 & op(e1, e3) = e0
% 142.38/21.25 (2) all_57_6 = e3
% 142.38/21.26 (3) ~ (e3 = e0)
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | ALPHA: (1) implies:
% 142.38/21.26 | (4) all_57_6 = e0
% 142.38/21.26 |
% 142.38/21.26 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.26 | (5) e3 = e0
% 142.38/21.26 |
% 142.38/21.26 | REDUCE: (3), (5) imply:
% 142.38/21.26 | (6) $false
% 142.38/21.26 |
% 142.38/21.26 | CLOSE: (6) is inconsistent.
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #604 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.26 (2) all_57_7 = e1
% 142.38/21.26 (3) ~ (e1 = e0)
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | ALPHA: (1) implies:
% 142.38/21.26 | (4) all_57_7 = e0
% 142.38/21.26 |
% 142.38/21.26 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.26 | (5) e1 = e0
% 142.38/21.26 |
% 142.38/21.26 | REDUCE: (3), (5) imply:
% 142.38/21.26 | (6) $false
% 142.38/21.26 |
% 142.38/21.26 | CLOSE: (6) is inconsistent.
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #605 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) op(e3, e0) = e1
% 142.38/21.26 (2) op(e1, e3) = all_52_2
% 142.38/21.26 (3) all_57_6 = e3
% 142.38/21.26 (4) ~ (e2 = e1)
% 142.38/21.26 (5) ~ (e3 = e0)
% 142.38/21.26 (6) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.38/21.26 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.38/21.26 all_14_1 & $i(all_14_1))
% 142.38/21.26 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.26 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.26 (8) all_57_3 = e1
% 142.38/21.26 (9) all_28_2 = e0
% 142.38/21.26 (10) ~ (e2 = e0)
% 142.38/21.26 (11) ~ (e3 = e2)
% 142.38/21.26 (12) op(e3, e0) = all_52_12
% 142.38/21.26 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.26 (14) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.26 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.26 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.26 (15) ~ (e3 = e1)
% 142.38/21.26 (16) all_57_0 = e0
% 142.38/21.26 (17) op(e3, e3) = e0
% 142.38/21.26 (18) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.26 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.26 (19) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.26 (20) all_57_12 = e1
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | ALPHA: (19) implies:
% 142.38/21.26 | (21) all_57_3 = e3
% 142.38/21.26 |
% 142.38/21.26 | COMBINE_EQS: (8), (21) imply:
% 142.38/21.26 | (22) e3 = e1
% 142.38/21.26 |
% 142.38/21.26 | COMBINE_EQS: (3), (22) imply:
% 142.38/21.26 | (23) all_57_6 = e1
% 142.38/21.26 |
% 142.38/21.26 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 142.38/21.26 | (15), (16), (17), (18), (20), (23) are inconsistent by sub-proof
% 142.38/21.26 | #606.
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #606 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) op(e3, e0) = e1
% 142.38/21.26 (2) op(e1, e3) = all_52_2
% 142.38/21.26 (3) ~ (e2 = e1)
% 142.38/21.26 (4) ~ (e3 = e0)
% 142.38/21.26 (5) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.38/21.26 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.38/21.26 all_14_1 & $i(all_14_1))
% 142.38/21.26 (6) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.26 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.26 (7) all_28_2 = e0
% 142.38/21.26 (8) ~ (e2 = e0)
% 142.38/21.26 (9) ~ (e3 = e2)
% 142.38/21.26 (10) op(e3, e0) = all_52_12
% 142.38/21.26 (11) all_57_6 = e1
% 142.38/21.26 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.26 (13) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.26 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.26 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.26 (14) ~ (e3 = e1)
% 142.38/21.26 (15) all_57_0 = e0
% 142.38/21.26 (16) op(e3, e3) = e0
% 142.38/21.26 (17) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.26 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.26 (18) all_57_12 = e1
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | BETA: splitting (6) gives:
% 142.38/21.26 |
% 142.38/21.26 | Case 1:
% 142.38/21.26 | |
% 142.38/21.26 | | (19) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 142.38/21.26 | | e3)
% 142.38/21.26 | |
% 142.38/21.26 | | BETA: splitting (19) gives:
% 142.38/21.26 | |
% 142.38/21.26 | | Case 1:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (20) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.26 | | |
% 142.38/21.26 | | | REF_CLOSE: (4), (15), (20) are inconsistent by sub-proof #1108.
% 142.38/21.26 | | |
% 142.38/21.26 | | Case 2:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (21) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.26 | | |
% 142.38/21.26 | | | ALPHA: (21) implies:
% 142.38/21.26 | | | (22) all_57_2 = e3
% 142.38/21.26 | | |
% 142.38/21.26 | | | BETA: splitting (17) gives:
% 142.38/21.26 | | |
% 142.38/21.26 | | | Case 1:
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | (23) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 142.38/21.26 | | | | = e2)
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | REF_CLOSE: (8), (9), (12), (16), (22), (23) are inconsistent by
% 142.38/21.26 | | | | sub-proof #634.
% 142.38/21.26 | | | |
% 142.38/21.26 | | | Case 2:
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | (24) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 142.38/21.26 | | | | = e2)
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | REF_CLOSE: (1), (2), (3), (5), (7), (10), (12), (13), (18), (24) are
% 142.38/21.26 | | | | inconsistent by sub-proof #633.
% 142.38/21.26 | | | |
% 142.38/21.26 | | | End of split
% 142.38/21.26 | | |
% 142.38/21.26 | | End of split
% 142.38/21.26 | |
% 142.38/21.26 | Case 2:
% 142.38/21.26 | |
% 142.38/21.26 | | (25) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.38/21.26 | | e3)
% 142.38/21.26 | |
% 142.38/21.26 | | BETA: splitting (25) gives:
% 142.38/21.26 | |
% 142.38/21.26 | | Case 1:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (26) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.26 | | |
% 142.38/21.26 | | | REF_CLOSE: (11), (14), (26) are inconsistent by sub-proof #1099.
% 142.38/21.26 | | |
% 142.38/21.26 | | Case 2:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (27) all_57_12 = e3 & op(e0, e3) = e3
% 142.38/21.26 | | |
% 142.38/21.26 | | | ALPHA: (27) implies:
% 142.38/21.26 | | | (28) all_57_12 = e3
% 142.38/21.26 | | |
% 142.38/21.26 | | | REF_CLOSE: (14), (18), (28) are inconsistent by sub-proof #834.
% 142.38/21.26 | | |
% 142.38/21.26 | | End of split
% 142.38/21.26 | |
% 142.38/21.26 | End of split
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #607 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) op(e3, e0) = e1
% 142.38/21.26 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.26 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.26 (3) ~ (all_52_13 = e0)
% 142.38/21.26 (4) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.26 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.26 (5) op(e1, e3) = all_52_2
% 142.38/21.26 (6) ~ (all_52_12 = e3)
% 142.38/21.26 (7) ~ (all_52_4 = e0)
% 142.38/21.26 (8) ~ (e2 = e1)
% 142.38/21.26 (9) op(e0, e0) = e3
% 142.38/21.26 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.26 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.26 (11) op(e2, e2) = e1
% 142.38/21.26 (12) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.26 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.26 (13) ~ (all_52_1 = e0)
% 142.38/21.26 (14) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.26 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.26 (15) ~ (e3 = e0)
% 142.38/21.26 (16) op(e1, e1) = e1
% 142.38/21.26 (17) op(e3, e1) = all_52_8
% 142.38/21.26 (18) op(e2, e3) = all_52_1
% 142.38/21.26 (19) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.26 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.26 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.26 (20) all_57_3 = e1
% 142.38/21.26 (21) all_28_2 = e0
% 142.38/21.26 (22) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.26 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.26 (23) ~ (e1 = e0)
% 142.38/21.26 (24) op(e3, e2) = all_52_4
% 142.38/21.26 (25) ~ (e2 = e0)
% 142.38/21.26 (26) ~ (e3 = e2)
% 142.38/21.26 (27) op(e3, e0) = all_52_12
% 142.38/21.26 (28) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.26 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.26 (29) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.26 (30) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.26 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.26 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.26 (31) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.26 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.26 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.26 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.26 (32) all_57_1 = e3
% 142.38/21.26 (33) ~ (all_52_8 = e0)
% 142.38/21.26 (34) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.26 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.26 (35) ~ (e3 = e1)
% 142.38/21.26 (36) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.26 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.26 (37) all_57_0 = e0
% 142.38/21.26 (38) op(e3, e3) = e0
% 142.38/21.26 (39) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.26 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.26 (40) op(e2, e0) = all_52_13
% 142.38/21.26 (41) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.26 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.26 (42) all_57_12 = e1
% 142.38/21.26 (43) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.26 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | SIMP: (23) implies:
% 142.38/21.26 | (44) ~ (e1 = e0)
% 142.38/21.26 |
% 142.38/21.26 | BETA: splitting (43) gives:
% 142.38/21.26 |
% 142.38/21.26 | Case 1:
% 142.38/21.26 | |
% 142.38/21.26 | | (45) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.38/21.26 | | e0)
% 142.38/21.26 | |
% 142.38/21.26 | | REF_CLOSE: (11), (13), (18), (29), (44), (45) are inconsistent by sub-proof
% 142.38/21.26 | | #640.
% 142.38/21.26 | |
% 142.38/21.26 | Case 2:
% 142.38/21.26 | |
% 142.38/21.26 | | (46) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.38/21.26 | | e0)
% 142.38/21.26 | |
% 142.38/21.26 | | BETA: splitting (46) gives:
% 142.38/21.26 | |
% 142.38/21.26 | | Case 1:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (47) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.26 | | |
% 142.38/21.26 | | | ALPHA: (47) implies:
% 142.38/21.26 | | | (48) all_57_5 = e0
% 142.38/21.26 | | |
% 142.38/21.26 | | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (14),
% 142.38/21.26 | | | (15), (16), (17), (19), (20), (21), (22), (24), (25), (26),
% 142.38/21.26 | | | (27), (28), (29), (30), (31), (32), (33), (34), (35), (36),
% 142.38/21.26 | | | (37), (38), (39), (41), (42), (44), (48) are inconsistent by
% 142.38/21.26 | | | sub-proof #617.
% 142.38/21.26 | | |
% 142.38/21.26 | | Case 2:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (49) all_57_10 = e0 & op(e2, e0) = e0
% 142.38/21.26 | | |
% 142.38/21.26 | | | REF_CLOSE: (3), (29), (40), (49) are inconsistent by sub-proof #1078.
% 142.38/21.26 | | |
% 142.38/21.26 | | End of split
% 142.38/21.26 | |
% 142.38/21.26 | End of split
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #608 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) op(e3, e0) = e1
% 142.38/21.26 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.26 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.26 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.26 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.26 (4) op(e1, e3) = all_52_2
% 142.38/21.26 (5) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.38/21.26 (6) ~ (all_52_12 = e3)
% 142.38/21.26 (7) op(e1, e2) = all_52_6
% 142.38/21.26 (8) ~ (all_52_4 = e0)
% 142.38/21.26 (9) ~ (e2 = e1)
% 142.38/21.26 (10) op(e0, e0) = e3
% 142.38/21.26 (11) ~ (all_42_0 = e2)
% 142.38/21.26 (12) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.26 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.26 (13) op(e2, e2) = e1
% 142.38/21.26 (14) ~ (all_52_6 = all_42_0)
% 142.38/21.26 (15) all_57_9 = e1
% 142.38/21.26 (16) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.26 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.26 (17) ~ (all_52_1 = e0)
% 142.38/21.26 (18) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.26 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.26 (19) ~ (e3 = e0)
% 142.38/21.26 (20) op(e1, e1) = e1
% 142.38/21.26 (21) op(e3, e1) = all_52_8
% 142.38/21.26 (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.38/21.26 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.38/21.26 (23) op(e2, e3) = all_52_1
% 142.38/21.26 (24) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.26 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.26 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.26 (25) all_54_11 = all_42_0
% 142.38/21.26 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.26 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.26 (27) all_57_3 = e1
% 142.38/21.26 (28) all_28_2 = e0
% 142.38/21.26 (29) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.26 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.26 (30) ~ (e1 = e0)
% 142.38/21.26 (31) op(e3, e2) = all_52_4
% 142.38/21.26 (32) ~ (e2 = e0)
% 142.38/21.26 (33) ~ (e3 = e2)
% 142.38/21.26 (34) op(e3, e0) = all_52_12
% 142.38/21.26 (35) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.26 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.26 (36) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.38/21.26 (37) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.26 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.26 (38) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.26 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.26 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.26 (39) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.26 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.26 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.26 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.26 (40) ~ (all_52_8 = e0)
% 142.38/21.26 (41) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.26 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.26 (42) ~ (e3 = e1)
% 142.38/21.26 (43) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.26 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.26 (44) all_57_0 = e0
% 142.38/21.26 (45) op(e3, e3) = e0
% 142.38/21.26 (46) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.26 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.26 (47) all_57_2 = e2
% 142.38/21.26 (48) ~ (all_42_0 = e1)
% 142.38/21.26 (49) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.26 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.26 (50) all_57_12 = e1
% 142.38/21.26 (51) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.26 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | BETA: splitting (36) gives:
% 142.38/21.26 |
% 142.38/21.26 | Case 1:
% 142.38/21.26 | |
% 142.38/21.26 | | (52) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.26 | |
% 142.38/21.26 | | REF_CLOSE: (9), (15), (52) are inconsistent by sub-proof #636.
% 142.38/21.26 | |
% 142.38/21.26 | Case 2:
% 142.38/21.26 | |
% 142.38/21.26 | | (53) all_57_10 = e2 & op(e2, e0) = e2
% 142.38/21.26 | |
% 142.38/21.26 | | ALPHA: (53) implies:
% 142.38/21.26 | | (54) all_57_10 = e2
% 142.38/21.26 | |
% 142.38/21.26 | | BETA: splitting (51) gives:
% 142.38/21.26 | |
% 142.38/21.26 | | Case 1:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (55) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.38/21.26 | | | e0)
% 142.38/21.26 | | |
% 142.38/21.26 | | | REF_CLOSE: (13), (17), (23), (30), (37), (55) are inconsistent by
% 142.38/21.26 | | | sub-proof #640.
% 142.38/21.26 | | |
% 142.38/21.26 | | Case 2:
% 142.38/21.26 | | |
% 142.38/21.26 | | | (56) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.38/21.26 | | | e0)
% 142.38/21.26 | | |
% 142.38/21.26 | | | BETA: splitting (56) gives:
% 142.38/21.26 | | |
% 142.38/21.26 | | | Case 1:
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | (57) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | ALPHA: (57) implies:
% 142.38/21.26 | | | | (58) all_57_5 = e0
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | BETA: splitting (43) gives:
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | Case 1:
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | | (59) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3,
% 142.38/21.26 | | | | | e2) = e3)
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (12), (13), (16),
% 142.38/21.26 | | | | | (18), (19), (20), (21), (24), (27), (28), (29), (30), (31),
% 142.38/21.26 | | | | | (32), (33), (34), (35), (37), (38), (39), (40), (41), (42),
% 142.38/21.26 | | | | | (43), (44), (45), (46), (49), (50), (58), (59) are
% 142.38/21.26 | | | | | inconsistent by sub-proof #616.
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | Case 2:
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | | (60) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3,
% 142.38/21.26 | | | | | e0) = e3)
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | | BETA: splitting (60) gives:
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | | Case 1:
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | (61) all_57_4 = e3 & op(e3, e1) = e3
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | ALPHA: (61) implies:
% 142.38/21.26 | | | | | | (62) all_57_4 = e3
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | BETA: splitting (26) gives:
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | Case 1:
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | | (63) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 &
% 142.38/21.26 | | | | | | | op(e2, e3) = e3)
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | | REF_CLOSE: (1), (4), (9), (19), (24), (28), (32), (33), (34),
% 142.38/21.26 | | | | | | | (37), (38), (44), (45), (46), (50), (63) are
% 142.38/21.26 | | | | | | | inconsistent by sub-proof #615.
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | Case 2:
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | | (64) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 &
% 142.38/21.26 | | | | | | | op(e0, e3) = e3)
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | | BETA: splitting (64) gives:
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | | (65) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | | ALPHA: (65) implies:
% 142.38/21.26 | | | | | | | | (66) all_57_6 = e3
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | | BETA: splitting (35) gives:
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | | (67) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 142.38/21.26 | | | | | | | | | op(e2, e1) = e2)
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | | BETA: splitting (67) gives:
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | (68) all_57_4 = e2 & op(e3, e1) = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | ALPHA: (68) implies:
% 142.38/21.26 | | | | | | | | | | (69) all_57_4 = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | COMBINE_EQS: (62), (69) imply:
% 142.38/21.26 | | | | | | | | | | (70) e3 = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | COMBINE_EQS: (66), (70) imply:
% 142.38/21.26 | | | | | | | | | | (71) all_57_6 = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | REF_CLOSE: (19), (26), (33), (42), (44), (47), (50), (71) are
% 142.38/21.26 | | | | | | | | | | inconsistent by sub-proof #614.
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | (72) all_57_5 = e2 & op(e2, e1) = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | ALPHA: (72) implies:
% 142.38/21.26 | | | | | | | | | | (73) all_57_5 = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | COMBINE_EQS: (58), (73) imply:
% 142.38/21.26 | | | | | | | | | | (74) e2 = e0
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | REDUCE: (32), (74) imply:
% 142.38/21.26 | | | | | | | | | | (75) $false
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | CLOSE: (75) is inconsistent.
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | | (76) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 142.38/21.26 | | | | | | | | | op(e0, e1) = e2)
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | | BETA: splitting (76) gives:
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | (77) all_57_8 = e2 & op(e1, e1) = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | ALPHA: (77) implies:
% 142.38/21.26 | | | | | | | | | | (78) op(e1, e1) = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | REF_CLOSE: (9), (20), (37), (78) are inconsistent by
% 142.38/21.26 | | | | | | | | | | sub-proof #1085.
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | (79) all_57_14 = e2 & op(e0, e1) = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | ALPHA: (79) implies:
% 142.38/21.26 | | | | | | | | | | (80) all_57_14 = e2
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | BETA: splitting (22) gives:
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | (81) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0
% 142.38/21.26 | | | | | | | | | | | & op(e1, e2) = e0)
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | BETA: splitting (81) gives:
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | (82) all_57_6 = e0 & op(e1, e3) = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | ALPHA: (82) implies:
% 142.38/21.26 | | | | | | | | | | | | (83) all_57_6 = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | REF_CLOSE: (19), (66), (83) are inconsistent by sub-proof
% 142.38/21.26 | | | | | | | | | | | | #873.
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | (84) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | REF_CLOSE: (5), (7), (11), (14), (25), (37), (48), (84) are
% 142.38/21.26 | | | | | | | | | | | | inconsistent by sub-proof #611.
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | (85) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 =
% 142.38/21.26 | | | | | | | | | | | e0 & op(e1, e0) = e0)
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | BETA: splitting (85) gives:
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | (86) all_57_8 = e0 & op(e1, e1) = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | ALPHA: (86) implies:
% 142.38/21.26 | | | | | | | | | | | | (87) op(e1, e1) = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | REF_CLOSE: (20), (30), (37), (87) are inconsistent by
% 142.38/21.26 | | | | | | | | | | | | sub-proof #1089.
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | (88) all_57_11 = e0 & op(e1, e0) = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | ALPHA: (88) implies:
% 142.38/21.26 | | | | | | | | | | | | (89) all_57_11 = e0
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | BETA: splitting (2) gives:
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | (90) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3
% 142.38/21.26 | | | | | | | | | | | | | & op(e2, e2) = e3)
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | BETA: splitting (90) gives:
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | (91) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | ALPHA: (91) implies:
% 142.38/21.26 | | | | | | | | | | | | | | (92) all_57_2 = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | REF_CLOSE: (1), (4), (9), (24), (28), (32), (33), (34), (37),
% 142.38/21.26 | | | | | | | | | | | | | | (38), (45), (46), (50), (92) are inconsistent by
% 142.38/21.26 | | | | | | | | | | | | | | sub-proof #632.
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | (93) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | REF_CLOSE: (3), (9), (12), (19), (20), (21), (27), (30),
% 142.38/21.26 | | | | | | | | | | | | | | (32), (33), (35), (37), (40), (42), (62), (93) are
% 142.38/21.26 | | | | | | | | | | | | | | inconsistent by sub-proof #622.
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | (94) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 =
% 142.38/21.26 | | | | | | | | | | | | | e3 & op(e2, e0) = e3)
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | BETA: splitting (94) gives:
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | Case 1:
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | (95) all_57_5 = e3 & op(e2, e1) = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | ALPHA: (95) implies:
% 142.38/21.26 | | | | | | | | | | | | | | (96) all_57_5 = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | REF_CLOSE: (12), (19), (20), (21), (30), (32), (37), (40),
% 142.38/21.26 | | | | | | | | | | | | | | (80), (96) are inconsistent by sub-proof #630.
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | (97) all_57_10 = e3 & op(e2, e0) = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | ALPHA: (97) implies:
% 142.38/21.26 | | | | | | | | | | | | | | (98) all_57_10 = e3
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | | REF_CLOSE: (9), (10), (16), (30), (32), (33), (37), (41),
% 142.38/21.26 | | | | | | | | | | | | | | (42), (89), (98) are inconsistent by sub-proof
% 142.38/21.26 | | | | | | | | | | | | | | #688.
% 142.38/21.26 | | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | | |
% 142.38/21.26 | | | | | | | | | End of split
% 142.38/21.26 | | | | | | | | |
% 142.38/21.26 | | | | | | | | End of split
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | Case 2:
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | | (99) all_57_12 = e3 & op(e0, e3) = e3
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | | REF_CLOSE: (3), (9), (12), (19), (20), (21), (30), (32), (33),
% 142.38/21.26 | | | | | | | | (35), (37), (40), (42), (50), (62), (99) are
% 142.38/21.26 | | | | | | | | inconsistent by sub-proof #610.
% 142.38/21.26 | | | | | | | |
% 142.38/21.26 | | | | | | | End of split
% 142.38/21.26 | | | | | | |
% 142.38/21.26 | | | | | | End of split
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | Case 2:
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | (100) all_57_9 = e3 & op(e3, e0) = e3
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | ALPHA: (100) implies:
% 142.38/21.26 | | | | | | (101) op(e3, e0) = e3
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | | REF_CLOSE: (6), (34), (37), (101) are inconsistent by sub-proof
% 142.38/21.26 | | | | | | #1105.
% 142.38/21.26 | | | | | |
% 142.38/21.26 | | | | | End of split
% 142.38/21.26 | | | | |
% 142.38/21.26 | | | | End of split
% 142.38/21.26 | | | |
% 142.38/21.26 | | | Case 2:
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | (102) all_57_10 = e0 & op(e2, e0) = e0
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | ALPHA: (102) implies:
% 142.38/21.26 | | | | (103) all_57_10 = e0
% 142.38/21.26 | | | |
% 142.38/21.26 | | | | REF_CLOSE: (32), (54), (103) are inconsistent by sub-proof #609.
% 142.38/21.26 | | | |
% 142.38/21.26 | | | End of split
% 142.38/21.26 | | |
% 142.38/21.26 | | End of split
% 142.38/21.26 | |
% 142.38/21.26 | End of split
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #609 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) all_57_10 = e2
% 142.38/21.26 (2) all_57_10 = e0
% 142.38/21.26 (3) ~ (e2 = e0)
% 142.38/21.26
% 142.38/21.26 Begin of proof
% 142.38/21.26 |
% 142.38/21.26 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.26 | (4) e2 = e0
% 142.38/21.26 |
% 142.38/21.26 | SIMP: (4) implies:
% 142.38/21.26 | (5) e2 = e0
% 142.38/21.26 |
% 142.38/21.26 | REDUCE: (3), (5) imply:
% 142.38/21.26 | (6) $false
% 142.38/21.26 |
% 142.38/21.26 | CLOSE: (6) is inconsistent.
% 142.38/21.26 |
% 142.38/21.26 End of proof
% 142.38/21.26
% 142.38/21.26 Sub-proof #610 shows that the following formulas are inconsistent:
% 142.38/21.26 ----------------------------------------------------------------
% 142.38/21.26 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.26 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.26 (2) ~ (e2 = e1)
% 142.38/21.26 (3) all_57_4 = e3
% 142.38/21.26 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.26 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.27 (5) all_57_12 = e3 & op(e0, e3) = e3
% 142.38/21.27 (6) ~ (e3 = e0)
% 142.38/21.27 (7) op(e1, e1) = e1
% 142.38/21.27 (8) op(e3, e1) = all_52_8
% 142.38/21.27 (9) ~ (e1 = e0)
% 142.38/21.27 (10) ~ (e2 = e0)
% 142.38/21.27 (11) ~ (e3 = e2)
% 142.38/21.27 (12) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.27 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.27 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (14) ~ (all_52_8 = e0)
% 142.38/21.27 (15) ~ (e3 = e1)
% 142.38/21.27 (16) all_57_12 = e1
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | ALPHA: (5) implies:
% 142.38/21.27 | (17) all_57_12 = e3
% 142.38/21.27 |
% 142.38/21.27 | COMBINE_EQS: (16), (17) imply:
% 142.38/21.27 | (18) e3 = e1
% 142.38/21.27 |
% 142.38/21.27 | COMBINE_EQS: (3), (18) imply:
% 142.38/21.27 | (19) all_57_4 = e1
% 142.38/21.27 |
% 142.38/21.27 | REF_CLOSE: (1), (2), (4), (6), (7), (8), (9), (10), (11), (12), (13), (14),
% 142.38/21.27 | (15), (19) are inconsistent by sub-proof #623.
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #611 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.38/21.27 (2) op(e1, e2) = all_52_6
% 142.38/21.27 (3) ~ (all_42_0 = e2)
% 142.38/21.27 (4) ~ (all_52_6 = all_42_0)
% 142.38/21.27 (5) all_54_11 = all_42_0
% 142.38/21.27 (6) all_57_7 = e0 & op(e1, e2) = e0
% 142.38/21.27 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (8) ~ (all_42_0 = e1)
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | ALPHA: (6) implies:
% 142.38/21.27 | (9) op(e1, e2) = e0
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (1) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (10) all_54_11 = e2
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #613.
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (11) all_54_11 = e1 | all_54_11 = e0
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (11) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (12) all_54_11 = e1
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (5), (8), (12) are inconsistent by sub-proof #612.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (13) all_54_11 = e0
% 142.38/21.27 | | |
% 142.38/21.27 | | | COMBINE_EQS: (5), (13) imply:
% 142.38/21.27 | | | (14) all_42_0 = e0
% 142.38/21.27 | | |
% 142.38/21.27 | | | SIMP: (14) implies:
% 142.38/21.27 | | | (15) all_42_0 = e0
% 142.38/21.27 | | |
% 142.38/21.27 | | | REDUCE: (4), (15) imply:
% 142.38/21.27 | | | (16) ~ (all_52_6 = e0)
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (2), (7), (9), (16) are inconsistent by sub-proof #999.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #612 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) all_54_11 = all_42_0
% 142.38/21.27 (2) all_54_11 = e1
% 142.38/21.27 (3) ~ (all_42_0 = e1)
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.27 | (4) all_42_0 = e1
% 142.38/21.27 |
% 142.38/21.27 | SIMP: (4) implies:
% 142.38/21.27 | (5) all_42_0 = e1
% 142.38/21.27 |
% 142.38/21.27 | REDUCE: (3), (5) imply:
% 142.38/21.27 | (6) $false
% 142.38/21.27 |
% 142.38/21.27 | CLOSE: (6) is inconsistent.
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #613 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) all_54_11 = all_42_0
% 142.38/21.27 (2) all_54_11 = e2
% 142.38/21.27 (3) ~ (all_42_0 = e2)
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.27 | (4) all_42_0 = e2
% 142.38/21.27 |
% 142.38/21.27 | SIMP: (4) implies:
% 142.38/21.27 | (5) all_42_0 = e2
% 142.38/21.27 |
% 142.38/21.27 | REDUCE: (3), (5) imply:
% 142.38/21.27 | (6) $false
% 142.38/21.27 |
% 142.38/21.27 | CLOSE: (6) is inconsistent.
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #614 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) ~ (e3 = e0)
% 142.38/21.27 (2) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.38/21.27 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.38/21.27 (3) all_57_6 = e2
% 142.38/21.27 (4) ~ (e3 = e2)
% 142.38/21.27 (5) ~ (e3 = e1)
% 142.38/21.27 (6) all_57_0 = e0
% 142.38/21.27 (7) all_57_2 = e2
% 142.38/21.27 (8) all_57_12 = e1
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (2) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (9) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (10) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (1), (6), (10) are inconsistent by sub-proof #1108.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (11) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (4), (7), (11) are inconsistent by sub-proof #781.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (12) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.38/21.27 | | e3)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (12) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (13) all_57_6 = e3 & op(e1, e3) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (13) implies:
% 142.38/21.27 | | | (14) all_57_6 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #1004.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (15) all_57_12 = e3 & op(e0, e3) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (15) implies:
% 142.38/21.27 | | | (16) all_57_12 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (5), (8), (16) are inconsistent by sub-proof #834.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #615 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) op(e3, e0) = e1
% 142.38/21.27 (2) op(e1, e3) = all_52_2
% 142.38/21.27 (3) ~ (e2 = e1)
% 142.38/21.27 (4) ~ (e3 = e0)
% 142.38/21.27 (5) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.38/21.27 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.38/21.27 all_14_1 & $i(all_14_1))
% 142.38/21.27 (6) all_28_2 = e0
% 142.38/21.27 (7) ~ (e2 = e0)
% 142.38/21.27 (8) ~ (e3 = e2)
% 142.38/21.27 (9) op(e3, e0) = all_52_12
% 142.38/21.27 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (11) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.27 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.27 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.27 (12) all_57_0 = e0
% 142.38/21.27 (13) op(e3, e3) = e0
% 142.38/21.27 (14) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.27 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.27 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 142.38/21.27 (16) all_57_12 = e1
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (15) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (17) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (4), (12), (17) are inconsistent by sub-proof #1108.
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (18) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.27 | |
% 142.38/21.27 | | ALPHA: (18) implies:
% 142.38/21.27 | | (19) all_57_2 = e3
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (10), (11), (13), (14),
% 142.38/21.27 | | (16), (19) are inconsistent by sub-proof #632.
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #616 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) op(e3, e0) = e1
% 142.38/21.27 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.27 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.27 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.27 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.27 (4) op(e1, e3) = all_52_2
% 142.38/21.27 (5) ~ (all_52_12 = e3)
% 142.38/21.27 (6) ~ (all_52_4 = e0)
% 142.38/21.27 (7) ~ (e2 = e1)
% 142.38/21.27 (8) op(e0, e0) = e3
% 142.38/21.27 (9) all_57_5 = e0
% 142.38/21.27 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.27 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.27 (11) op(e2, e2) = e1
% 142.38/21.27 (12) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.27 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.27 (13) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.27 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.27 (14) ~ (e3 = e0)
% 142.38/21.27 (15) op(e1, e1) = e1
% 142.38/21.27 (16) op(e3, e1) = all_52_8
% 142.38/21.27 (17) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.27 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.27 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.27 (18) all_57_3 = e1
% 142.38/21.27 (19) all_28_2 = e0
% 142.38/21.27 (20) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.27 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.27 (21) ~ (e1 = e0)
% 142.38/21.27 (22) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 142.38/21.27 (23) op(e3, e2) = all_52_4
% 142.38/21.27 (24) ~ (e2 = e0)
% 142.38/21.27 (25) ~ (e3 = e2)
% 142.38/21.27 (26) op(e3, e0) = all_52_12
% 142.38/21.27 (27) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.27 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.27 (28) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (29) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.27 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.27 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.27 (30) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.27 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.27 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.27 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.27 (31) ~ (all_52_8 = e0)
% 142.38/21.27 (32) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.27 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.27 (33) ~ (e3 = e1)
% 142.38/21.27 (34) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.27 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.27 (35) all_57_0 = e0
% 142.38/21.27 (36) op(e3, e3) = e0
% 142.38/21.27 (37) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.27 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.27 (38) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.27 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.27 (39) all_57_12 = e1
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (22) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (40) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (14), (35), (40) are inconsistent by sub-proof #1108.
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (41) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.27 | |
% 142.38/21.27 | | ALPHA: (41) implies:
% 142.38/21.27 | | (42) all_57_1 = e3
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.38/21.27 | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (23), (24),
% 142.38/21.27 | | (25), (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 142.38/21.27 | | (36), (37), (38), (39), (42) are inconsistent by sub-proof #617.
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #617 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) op(e3, e0) = e1
% 142.38/21.27 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.27 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.38/21.27 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.27 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.27 (4) op(e1, e3) = all_52_2
% 142.38/21.27 (5) ~ (all_52_12 = e3)
% 142.38/21.27 (6) ~ (all_52_4 = e0)
% 142.38/21.27 (7) ~ (e2 = e1)
% 142.38/21.27 (8) op(e0, e0) = e3
% 142.38/21.27 (9) all_57_5 = e0
% 142.38/21.27 (10) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.27 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.27 (11) op(e2, e2) = e1
% 142.38/21.27 (12) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.38/21.27 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.38/21.27 (13) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.27 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.27 (14) ~ (e3 = e0)
% 142.38/21.27 (15) op(e1, e1) = e1
% 142.38/21.27 (16) op(e3, e1) = all_52_8
% 142.38/21.27 (17) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.38/21.27 all_14_1 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3,
% 142.38/21.27 e0) = all_14_1 & $i(all_14_1))
% 142.38/21.27 (18) all_57_3 = e1
% 142.38/21.27 (19) all_28_2 = e0
% 142.38/21.27 (20) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.27 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.27 (21) ~ (e1 = e0)
% 142.38/21.27 (22) op(e3, e2) = all_52_4
% 142.38/21.27 (23) ~ (e2 = e0)
% 142.38/21.27 (24) ~ (e3 = e2)
% 142.38/21.27 (25) op(e3, e0) = all_52_12
% 142.38/21.27 (26) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.27 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.27 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (28) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.27 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.27 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.27 (29) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.38/21.27 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.38/21.27 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.38/21.27 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.38/21.27 (30) all_57_1 = e3
% 142.38/21.27 (31) ~ (all_52_8 = e0)
% 142.38/21.27 (32) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.38/21.27 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.38/21.27 (33) ~ (e3 = e1)
% 142.38/21.27 (34) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.27 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.27 (35) all_57_0 = e0
% 142.38/21.27 (36) op(e3, e3) = e0
% 142.38/21.27 (37) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.27 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.27 (38) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.27 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.27 (39) all_57_12 = e1
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (2) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (40) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 142.38/21.27 | | e3)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (40) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (41) all_57_2 = e3 & op(e2, e3) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (41) implies:
% 142.38/21.27 | | | (42) all_57_2 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (1), (4), (7), (17), (19), (23), (24), (25), (27), (28), (36),
% 142.38/21.27 | | | (37), (39), (42) are inconsistent by sub-proof #632.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (43) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (43) implies:
% 142.38/21.27 | | | (44) all_57_3 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | COMBINE_EQS: (18), (44) imply:
% 142.38/21.27 | | | (45) e3 = e1
% 142.38/21.27 | | |
% 142.38/21.27 | | | SIMP: (45) implies:
% 142.38/21.27 | | | (46) e3 = e1
% 142.38/21.27 | | |
% 142.38/21.27 | | | COMBINE_EQS: (30), (46) imply:
% 142.38/21.27 | | | (47) all_57_1 = e1
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (3), (5), (6), (7), (10), (11), (13), (14), (15), (16), (18),
% 142.38/21.27 | | | (20), (21), (22), (23), (24), (25), (26), (27), (31), (33),
% 142.38/21.27 | | | (34), (35), (38), (47) are inconsistent by sub-proof #618.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (48) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 142.38/21.27 | | e3)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (48) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (49) all_57_5 = e3 & op(e2, e1) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (49) implies:
% 142.38/21.27 | | | (50) all_57_5 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (9), (14), (50) are inconsistent by sub-proof #1041.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (51) all_57_10 = e3 & op(e2, e0) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (51) implies:
% 142.38/21.27 | | | (52) all_57_10 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (7), (8), (12), (14), (21), (23), (24), (27), (29), (32), (33),
% 142.38/21.27 | | | (52) are inconsistent by sub-proof #650.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #618 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.27 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.27 (2) ~ (all_52_12 = e3)
% 142.38/21.27 (3) ~ (all_52_4 = e0)
% 142.38/21.27 (4) ~ (e2 = e1)
% 142.38/21.27 (5) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.27 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.27 (6) op(e2, e2) = e1
% 142.38/21.27 (7) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.27 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.27 (8) ~ (e3 = e0)
% 142.38/21.27 (9) op(e1, e1) = e1
% 142.38/21.27 (10) op(e3, e1) = all_52_8
% 142.38/21.27 (11) all_57_3 = e1
% 142.38/21.27 (12) all_57_1 = e1
% 142.38/21.27 (13) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.27 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.27 (14) ~ (e1 = e0)
% 142.38/21.27 (15) op(e3, e2) = all_52_4
% 142.38/21.27 (16) ~ (e2 = e0)
% 142.38/21.27 (17) ~ (e3 = e2)
% 142.38/21.27 (18) op(e3, e0) = all_52_12
% 142.38/21.27 (19) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.27 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.27 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (21) ~ (all_52_8 = e0)
% 142.38/21.27 (22) ~ (e3 = e1)
% 142.38/21.27 (23) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.38/21.27 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.38/21.27 (24) all_57_0 = e0
% 142.38/21.27 (25) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.38/21.27 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (23) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) =
% 142.38/21.27 | | e3)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (26) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (27) all_57_0 = e3 & op(e3, e3) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (8), (24), (27) are inconsistent by sub-proof #1108.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (28) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (12), (22), (28) are inconsistent by sub-proof #724.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (29) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) =
% 142.38/21.27 | | e3)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (29) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (30) all_57_4 = e3 & op(e3, e1) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (30) implies:
% 142.38/21.27 | | | (31) all_57_4 = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | BETA: splitting (25) gives:
% 142.38/21.27 | | |
% 142.38/21.27 | | | Case 1:
% 142.38/21.27 | | | |
% 142.38/21.27 | | | | (32) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 142.38/21.27 | | | | = e3)
% 142.38/21.27 | | | |
% 142.38/21.27 | | | | REF_CLOSE: (1), (4), (5), (8), (9), (10), (11), (12), (14), (16), (17),
% 142.38/21.27 | | | | (19), (20), (21), (22), (31), (32) are inconsistent by
% 142.38/21.27 | | | | sub-proof #621.
% 142.38/21.27 | | | |
% 142.38/21.27 | | | Case 2:
% 142.38/21.27 | | | |
% 142.38/21.27 | | | | (33) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 142.38/21.27 | | | | = e3)
% 142.38/21.27 | | | |
% 142.38/21.27 | | | | BETA: splitting (33) gives:
% 142.38/21.27 | | | |
% 142.38/21.27 | | | | Case 1:
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | (34) all_57_7 = e3 & op(e1, e2) = e3
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | ALPHA: (34) implies:
% 142.38/21.27 | | | | | (35) all_57_7 = e3
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | REF_CLOSE: (3), (4), (6), (7), (8), (12), (13), (14), (15), (16),
% 142.38/21.27 | | | | | (17), (20), (35) are inconsistent by sub-proof #619.
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | Case 2:
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | (36) all_57_13 = e3 & op(e0, e2) = e3
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | ALPHA: (36) implies:
% 142.38/21.27 | | | | | (37) all_57_13 = e3
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | BETA: splitting (7) gives:
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | | Case 1:
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | | (38) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2,
% 142.38/21.27 | | | | | | e2) = e2)
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | | REF_CLOSE: (4), (6), (12), (20), (38) are inconsistent by sub-proof
% 142.38/21.27 | | | | | | #620.
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | Case 2:
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | | (39) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0,
% 142.38/21.27 | | | | | | e2) = e2)
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | | BETA: splitting (39) gives:
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | | Case 1:
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | | (40) all_57_7 = e2 & op(e1, e2) = e2
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | | ALPHA: (40) implies:
% 142.38/21.27 | | | | | | | (41) all_57_7 = e2
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | | REF_CLOSE: (3), (6), (8), (13), (14), (15), (16), (20), (37), (41)
% 142.38/21.27 | | | | | | | are inconsistent by sub-proof #1015.
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | Case 2:
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | | (42) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | | ALPHA: (42) implies:
% 142.38/21.27 | | | | | | | (43) all_57_13 = e2
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | | REF_CLOSE: (17), (37), (43) are inconsistent by sub-proof #1068.
% 142.38/21.27 | | | | | | |
% 142.38/21.27 | | | | | | End of split
% 142.38/21.27 | | | | | |
% 142.38/21.27 | | | | | End of split
% 142.38/21.27 | | | | |
% 142.38/21.27 | | | | End of split
% 142.38/21.27 | | | |
% 142.38/21.27 | | | End of split
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (44) all_57_9 = e3 & op(e3, e0) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (44) implies:
% 142.38/21.27 | | | (45) op(e3, e0) = e3
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (2), (18), (20), (45) are inconsistent by sub-proof #1105.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #619 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) ~ (all_52_4 = e0)
% 142.38/21.27 (2) ~ (e2 = e1)
% 142.38/21.27 (3) op(e2, e2) = e1
% 142.38/21.27 (4) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.38/21.27 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.38/21.27 (5) ~ (e3 = e0)
% 142.38/21.27 (6) all_57_1 = e1
% 142.38/21.27 (7) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.27 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.38/21.27 (8) ~ (e1 = e0)
% 142.38/21.27 (9) op(e3, e2) = all_52_4
% 142.38/21.27 (10) ~ (e2 = e0)
% 142.38/21.27 (11) ~ (e3 = e2)
% 142.38/21.27 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27 (13) all_57_7 = e3
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (4) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (14) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 142.38/21.27 | | e2)
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (2), (3), (6), (12), (14) are inconsistent by sub-proof #620.
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (15) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.38/21.27 | | e2)
% 142.38/21.27 | |
% 142.38/21.27 | | BETA: splitting (15) gives:
% 142.38/21.27 | |
% 142.38/21.27 | | Case 1:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (16) all_57_7 = e2 & op(e1, e2) = e2
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (11), (13), (16) are inconsistent by sub-proof #1084.
% 142.38/21.27 | | |
% 142.38/21.27 | | Case 2:
% 142.38/21.27 | | |
% 142.38/21.27 | | | (17) all_57_13 = e2 & op(e0, e2) = e2
% 142.38/21.27 | | |
% 142.38/21.27 | | | ALPHA: (17) implies:
% 142.38/21.27 | | | (18) all_57_13 = e2
% 142.38/21.27 | | |
% 142.38/21.27 | | | REF_CLOSE: (1), (3), (5), (7), (8), (9), (10), (12), (13), (18) are
% 142.38/21.27 | | | inconsistent by sub-proof #1059.
% 142.38/21.27 | | |
% 142.38/21.27 | | End of split
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #620 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) ~ (e2 = e1)
% 142.38/21.27 (2) op(e2, e2) = e1
% 142.38/21.27 (3) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 142.38/21.27 (4) all_57_1 = e1
% 142.38/21.27 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.27 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.27
% 142.38/21.27 Begin of proof
% 142.38/21.27 |
% 142.38/21.27 | BETA: splitting (3) gives:
% 142.38/21.27 |
% 142.38/21.27 | Case 1:
% 142.38/21.27 | |
% 142.38/21.27 | | (6) all_57_1 = e2 & op(e3, e2) = e2
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #1074.
% 142.38/21.27 | |
% 142.38/21.27 | Case 2:
% 142.38/21.27 | |
% 142.38/21.27 | | (7) all_57_3 = e2 & op(e2, e2) = e2
% 142.38/21.27 | |
% 142.38/21.27 | | ALPHA: (7) implies:
% 142.38/21.27 | | (8) op(e2, e2) = e2
% 142.38/21.27 | |
% 142.38/21.27 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #749.
% 142.38/21.27 | |
% 142.38/21.27 | End of split
% 142.38/21.27 |
% 142.38/21.27 End of proof
% 142.38/21.27
% 142.38/21.27 Sub-proof #621 shows that the following formulas are inconsistent:
% 142.38/21.27 ----------------------------------------------------------------
% 142.38/21.27 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.27 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.27 (2) ~ (e2 = e1)
% 142.38/21.27 (3) all_57_4 = e3
% 142.38/21.27 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.27 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (5) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.38/21.28 (6) ~ (e3 = e0)
% 142.38/21.28 (7) op(e1, e1) = e1
% 142.38/21.28 (8) op(e3, e1) = all_52_8
% 142.38/21.28 (9) all_57_3 = e1
% 142.38/21.28 (10) all_57_1 = e1
% 142.38/21.28 (11) ~ (e1 = e0)
% 142.38/21.28 (12) ~ (e2 = e0)
% 142.38/21.28 (13) ~ (e3 = e2)
% 142.38/21.28 (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.28 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.28 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (16) ~ (all_52_8 = e0)
% 142.38/21.28 (17) ~ (e3 = e1)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (5) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (18) all_57_1 = e3 & op(e3, e2) = e3
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (18) implies:
% 142.38/21.28 | | (19) all_57_1 = e3
% 142.38/21.28 | |
% 142.38/21.28 | | COMBINE_EQS: (10), (19) imply:
% 142.38/21.28 | | (20) e3 = e1
% 142.38/21.28 | |
% 142.38/21.28 | | SIMP: (20) implies:
% 142.38/21.28 | | (21) e3 = e1
% 142.38/21.28 | |
% 142.38/21.28 | | COMBINE_EQS: (3), (21) imply:
% 142.38/21.28 | | (22) all_57_4 = e1
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (2), (4), (6), (7), (8), (11), (12), (13), (14), (15), (16),
% 142.38/21.28 | | (17), (22) are inconsistent by sub-proof #623.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (23) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (11), (12), (13), (14),
% 142.38/21.28 | | (15), (16), (17), (23) are inconsistent by sub-proof #622.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #622 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.28 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.28 (2) ~ (e2 = e1)
% 142.38/21.28 (3) all_57_4 = e3
% 142.38/21.28 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.28 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (5) ~ (e3 = e0)
% 142.38/21.28 (6) op(e1, e1) = e1
% 142.38/21.28 (7) op(e3, e1) = all_52_8
% 142.38/21.28 (8) all_57_3 = e1
% 142.38/21.28 (9) ~ (e1 = e0)
% 142.38/21.28 (10) ~ (e2 = e0)
% 142.38/21.28 (11) ~ (e3 = e2)
% 142.38/21.28 (12) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.28 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.28 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (14) ~ (all_52_8 = e0)
% 142.38/21.28 (15) ~ (e3 = e1)
% 142.38/21.28 (16) all_57_3 = e3 & op(e2, e2) = e3
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | ALPHA: (16) implies:
% 142.38/21.28 | (17) all_57_3 = e3
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (8), (17) imply:
% 142.38/21.28 | (18) e3 = e1
% 142.38/21.28 |
% 142.38/21.28 | SIMP: (18) implies:
% 142.38/21.28 | (19) e3 = e1
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (3), (19) imply:
% 142.38/21.28 | (20) all_57_4 = e1
% 142.38/21.28 |
% 142.38/21.28 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (10), (11), (12), (13), (14),
% 142.38/21.28 | (15), (20) are inconsistent by sub-proof #623.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #623 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.38/21.28 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.38/21.28 (2) ~ (e2 = e1)
% 142.38/21.28 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.28 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (4) ~ (e3 = e0)
% 142.38/21.28 (5) op(e1, e1) = e1
% 142.38/21.28 (6) op(e3, e1) = all_52_8
% 142.38/21.28 (7) ~ (e1 = e0)
% 142.38/21.28 (8) ~ (e2 = e0)
% 142.38/21.28 (9) ~ (e3 = e2)
% 142.38/21.28 (10) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.28 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.28 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (12) ~ (all_52_8 = e0)
% 142.38/21.28 (13) all_57_4 = e1
% 142.38/21.28 (14) ~ (e3 = e1)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (1) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (15) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 142.38/21.28 | | e3)
% 142.38/21.28 | |
% 142.38/21.28 | | BETA: splitting (15) gives:
% 142.38/21.28 | |
% 142.38/21.28 | | Case 1:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (16) all_57_4 = e3 & op(e3, e1) = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (16) implies:
% 142.38/21.28 | | | (17) all_57_4 = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (13), (14), (17) are inconsistent by sub-proof #631.
% 142.38/21.28 | | |
% 142.38/21.28 | | Case 2:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (18) all_57_5 = e3 & op(e2, e1) = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (18) implies:
% 142.38/21.28 | | | (19) all_57_5 = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.38/21.28 | | | (19) are inconsistent by sub-proof #628.
% 142.38/21.28 | | |
% 142.38/21.28 | | End of split
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (20) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 142.38/21.28 | | e3)
% 142.38/21.28 | |
% 142.38/21.28 | | BETA: splitting (20) gives:
% 142.38/21.28 | |
% 142.38/21.28 | | Case 1:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (21) all_57_8 = e3 & op(e1, e1) = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (21) implies:
% 142.38/21.28 | | | (22) op(e1, e1) = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (5), (11), (14), (22) are inconsistent by sub-proof #1096.
% 142.38/21.28 | | |
% 142.38/21.28 | | Case 2:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (23) all_57_14 = e3 & op(e0, e1) = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (23) implies:
% 142.38/21.28 | | | (24) all_57_14 = e3
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.38/21.28 | | | (24) are inconsistent by sub-proof #624.
% 142.38/21.28 | | |
% 142.38/21.28 | | End of split
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #624 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) ~ (e2 = e1)
% 142.38/21.28 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.28 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (3) ~ (e3 = e0)
% 142.38/21.28 (4) op(e1, e1) = e1
% 142.38/21.28 (5) all_57_14 = e3
% 142.38/21.28 (6) op(e3, e1) = all_52_8
% 142.38/21.28 (7) ~ (e1 = e0)
% 142.38/21.28 (8) ~ (e2 = e0)
% 142.38/21.28 (9) ~ (e3 = e2)
% 142.38/21.28 (10) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.28 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.28 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (12) ~ (all_52_8 = e0)
% 142.38/21.28 (13) all_57_4 = e1
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (10) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 142.38/21.28 | | e2)
% 142.38/21.28 | |
% 142.38/21.28 | | BETA: splitting (14) gives:
% 142.38/21.28 | |
% 142.38/21.28 | | Case 1:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (15) all_57_4 = e2 & op(e3, e1) = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (15) implies:
% 142.38/21.28 | | | (16) all_57_4 = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (1), (13), (16) are inconsistent by sub-proof #1088.
% 142.38/21.28 | | |
% 142.38/21.28 | | Case 2:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (17) all_57_5 = e2 & op(e2, e1) = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (17) implies:
% 142.38/21.28 | | | (18) all_57_5 = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | BETA: splitting (2) gives:
% 142.38/21.28 | | |
% 142.38/21.28 | | | Case 1:
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | (19) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1)
% 142.38/21.28 | | | | = e0)
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | BETA: splitting (19) gives:
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | Case 1:
% 142.38/21.28 | | | | |
% 142.38/21.28 | | | | | (20) all_57_4 = e0 & op(e3, e1) = e0
% 142.38/21.28 | | | | |
% 142.38/21.28 | | | | | REF_CLOSE: (6), (11), (12), (20) are inconsistent by sub-proof #981.
% 142.38/21.28 | | | | |
% 142.38/21.28 | | | | Case 2:
% 142.38/21.28 | | | | |
% 142.38/21.28 | | | | | (21) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.28 | | | | |
% 142.38/21.28 | | | | | REF_CLOSE: (8), (18), (21) are inconsistent by sub-proof #627.
% 142.38/21.28 | | | | |
% 142.38/21.28 | | | | End of split
% 142.38/21.28 | | | |
% 142.38/21.28 | | | Case 2:
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | (22) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1)
% 142.38/21.28 | | | | = e0)
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | REF_CLOSE: (3), (4), (5), (7), (11), (22) are inconsistent by sub-proof
% 142.38/21.28 | | | | #625.
% 142.38/21.28 | | | |
% 142.38/21.28 | | | End of split
% 142.38/21.28 | | |
% 142.38/21.28 | | End of split
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (23) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.38/21.28 | | e2)
% 142.38/21.28 | |
% 142.38/21.28 | | BETA: splitting (23) gives:
% 142.38/21.28 | |
% 142.38/21.28 | | Case 1:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (24) all_57_8 = e2 & op(e1, e1) = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (24) implies:
% 142.38/21.28 | | | (25) op(e1, e1) = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (1), (4), (11), (25) are inconsistent by sub-proof #1085.
% 142.38/21.28 | | |
% 142.38/21.28 | | Case 2:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (26) all_57_14 = e2 & op(e0, e1) = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (26) implies:
% 142.38/21.28 | | | (27) all_57_14 = e2
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (5), (9), (27) are inconsistent by sub-proof #1011.
% 142.38/21.28 | | |
% 142.38/21.28 | | End of split
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #625 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) ~ (e3 = e0)
% 142.38/21.28 (2) op(e1, e1) = e1
% 142.38/21.28 (3) all_57_14 = e3
% 142.38/21.28 (4) ~ (e1 = e0)
% 142.38/21.28 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (6) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (6) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (7) implies:
% 142.38/21.28 | | (8) op(e1, e1) = e0
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #1089.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (9) all_57_14 = e0 & op(e0, e1) = e0
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (3), (9) are inconsistent by sub-proof #626.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #626 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_57_14 = e0 & op(e0, e1) = e0
% 142.38/21.28 (2) all_57_14 = e3
% 142.38/21.28 (3) ~ (e3 = e0)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | ALPHA: (1) implies:
% 142.38/21.28 | (4) all_57_14 = e0
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.28 | (5) e3 = e0
% 142.38/21.28 |
% 142.38/21.28 | REDUCE: (3), (5) imply:
% 142.38/21.28 | (6) $false
% 142.38/21.28 |
% 142.38/21.28 | CLOSE: (6) is inconsistent.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #627 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.28 (2) all_57_5 = e2
% 142.38/21.28 (3) ~ (e2 = e0)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | ALPHA: (1) implies:
% 142.38/21.28 | (4) all_57_5 = e0
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.28 | (5) e2 = e0
% 142.38/21.28 |
% 142.38/21.28 | REDUCE: (3), (5) imply:
% 142.38/21.28 | (6) $false
% 142.38/21.28 |
% 142.38/21.28 | CLOSE: (6) is inconsistent.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #628 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) ~ (e2 = e1)
% 142.38/21.28 (2) all_57_5 = e3
% 142.38/21.28 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.28 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (4) ~ (e3 = e0)
% 142.38/21.28 (5) op(e1, e1) = e1
% 142.38/21.28 (6) op(e3, e1) = all_52_8
% 142.38/21.28 (7) ~ (e1 = e0)
% 142.38/21.28 (8) ~ (e2 = e0)
% 142.38/21.28 (9) ~ (e3 = e2)
% 142.38/21.28 (10) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.38/21.28 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.28 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (12) ~ (all_52_8 = e0)
% 142.38/21.28 (13) all_57_4 = e1
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (10) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (14) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 142.38/21.28 | | e2)
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (2), (9), (13), (14) are inconsistent by sub-proof #1086.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (15) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.38/21.28 | | e2)
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (11), (12), (15) are
% 142.38/21.28 | | inconsistent by sub-proof #629.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #629 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.38/21.28 (2) ~ (e2 = e1)
% 142.38/21.28 (3) all_57_5 = e3
% 142.38/21.28 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.28 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (5) ~ (e3 = e0)
% 142.38/21.28 (6) op(e1, e1) = e1
% 142.38/21.28 (7) op(e3, e1) = all_52_8
% 142.38/21.28 (8) ~ (e1 = e0)
% 142.38/21.28 (9) ~ (e2 = e0)
% 142.38/21.28 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (11) ~ (all_52_8 = e0)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (1) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (12) all_57_8 = e2 & op(e1, e1) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (12) implies:
% 142.38/21.28 | | (13) op(e1, e1) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (2), (6), (10), (13) are inconsistent by sub-proof #1085.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (14) all_57_14 = e2 & op(e0, e1) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (14) implies:
% 142.38/21.28 | | (15) all_57_14 = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (10), (11), (15) are
% 142.38/21.28 | | inconsistent by sub-proof #630.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #630 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_57_5 = e3
% 142.38/21.28 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.38/21.28 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.38/21.28 (3) all_57_14 = e2
% 142.38/21.28 (4) ~ (e3 = e0)
% 142.38/21.28 (5) op(e1, e1) = e1
% 142.38/21.28 (6) op(e3, e1) = all_52_8
% 142.38/21.28 (7) ~ (e1 = e0)
% 142.38/21.28 (8) ~ (e2 = e0)
% 142.38/21.28 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (10) ~ (all_52_8 = e0)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (2) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (11) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 142.38/21.28 | | e0)
% 142.38/21.28 | |
% 142.38/21.28 | | BETA: splitting (11) gives:
% 142.38/21.28 | |
% 142.38/21.28 | | Case 1:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (12) all_57_4 = e0 & op(e3, e1) = e0
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (6), (9), (10), (12) are inconsistent by sub-proof #981.
% 142.38/21.28 | | |
% 142.38/21.28 | | Case 2:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (13) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.28 | | |
% 142.38/21.28 | | | REF_CLOSE: (1), (4), (13) are inconsistent by sub-proof #729.
% 142.38/21.28 | | |
% 142.38/21.28 | | End of split
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (14) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.38/21.28 | | e0)
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (3), (5), (7), (8), (9), (14) are inconsistent by sub-proof #919.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #631 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_57_4 = e3
% 142.38/21.28 (2) all_57_4 = e1
% 142.38/21.28 (3) ~ (e3 = e1)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.28 | (4) e3 = e1
% 142.38/21.28 |
% 142.38/21.28 | SIMP: (4) implies:
% 142.38/21.28 | (5) e3 = e1
% 142.38/21.28 |
% 142.38/21.28 | REDUCE: (3), (5) imply:
% 142.38/21.28 | (6) $false
% 142.38/21.28 |
% 142.38/21.28 | CLOSE: (6) is inconsistent.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #632 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) op(e3, e0) = e1
% 142.38/21.28 (2) op(e1, e3) = all_52_2
% 142.38/21.28 (3) ~ (e2 = e1)
% 142.38/21.28 (4) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.38/21.28 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.38/21.28 all_14_1 & $i(all_14_1))
% 142.38/21.28 (5) all_28_2 = e0
% 142.38/21.28 (6) ~ (e2 = e0)
% 142.38/21.28 (7) ~ (e3 = e2)
% 142.38/21.28 (8) op(e3, e0) = all_52_12
% 142.38/21.28 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (10) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.28 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.28 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.28 (11) op(e3, e3) = e0
% 142.38/21.28 (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.38/21.28 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.28 (13) all_57_2 = e3
% 142.38/21.28 (14) all_57_12 = e1
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (12) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (15) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) =
% 142.38/21.28 | | e2)
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (6), (7), (9), (11), (13), (15) are inconsistent by sub-proof
% 142.38/21.28 | | #634.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (16) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) =
% 142.38/21.28 | | e2)
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (2), (3), (4), (5), (8), (9), (10), (14), (16) are
% 142.38/21.28 | | inconsistent by sub-proof #633.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #633 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) op(e3, e0) = e1
% 142.38/21.28 (2) op(e1, e3) = all_52_2
% 142.38/21.28 (3) ~ (e2 = e1)
% 142.38/21.28 (4) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.38/21.28 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.38/21.28 all_14_1 & $i(all_14_1))
% 142.38/21.28 (5) all_28_2 = e0
% 142.38/21.28 (6) op(e3, e0) = all_52_12
% 142.38/21.28 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (8) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.38/21.28 (9) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.38/21.28 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.38/21.28 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.38/21.28 (10) all_57_12 = e1
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (8) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (11) all_57_6 = e2 & op(e1, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (11) implies:
% 142.38/21.28 | | (12) op(e1, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (12) are inconsistent by
% 142.38/21.28 | | sub-proof #654.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (13) all_57_12 = e2 & op(e0, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (3), (10), (13) are inconsistent by sub-proof #674.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #634 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 142.38/21.28 (2) ~ (e2 = e0)
% 142.38/21.28 (3) ~ (e3 = e2)
% 142.38/21.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (5) op(e3, e3) = e0
% 142.38/21.28 (6) all_57_2 = e3
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (1) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (7) implies:
% 142.38/21.28 | | (8) op(e3, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #880.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (9) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #635.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #635 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.28 (2) all_57_2 = e3
% 142.38/21.28 (3) ~ (e3 = e2)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | ALPHA: (1) implies:
% 142.38/21.28 | (4) all_57_2 = e2
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.28 | (5) e3 = e2
% 142.38/21.28 |
% 142.38/21.28 | REDUCE: (3), (5) imply:
% 142.38/21.28 | (6) $false
% 142.38/21.28 |
% 142.38/21.28 | CLOSE: (6) is inconsistent.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #636 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_57_9 = e2 & op(e3, e0) = e2
% 142.38/21.28 (2) all_57_9 = e1
% 142.38/21.28 (3) ~ (e2 = e1)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | ALPHA: (1) implies:
% 142.38/21.28 | (4) all_57_9 = e2
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (2), (4) imply:
% 142.38/21.28 | (5) e2 = e1
% 142.38/21.28 |
% 142.38/21.28 | REDUCE: (3), (5) imply:
% 142.38/21.28 | (6) $false
% 142.38/21.28 |
% 142.38/21.28 | CLOSE: (6) is inconsistent.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #637 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) all_54_11 = all_42_0
% 142.38/21.28 (2) all_54_11 = e3
% 142.38/21.28 (3) ~ (all_42_0 = e3)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | COMBINE_EQS: (1), (2) imply:
% 142.38/21.28 | (4) all_42_0 = e3
% 142.38/21.28 |
% 142.38/21.28 | SIMP: (4) implies:
% 142.38/21.28 | (5) all_42_0 = e3
% 142.38/21.28 |
% 142.38/21.28 | REDUCE: (3), (5) imply:
% 142.38/21.28 | (6) $false
% 142.38/21.28 |
% 142.38/21.28 | CLOSE: (6) is inconsistent.
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #638 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) ~ (e2 = e1)
% 142.38/21.28 (2) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 142.38/21.28 (3) ~ (e2 = e0)
% 142.38/21.28 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (5) all_57_2 = e1
% 142.38/21.28 (6) op(e3, e3) = e0
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (2) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (7) implies:
% 142.38/21.28 | | (8) op(e3, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (3), (4), (6), (8) are inconsistent by sub-proof #880.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (9) all_57_2 = e2 & op(e2, e3) = e2
% 142.38/21.28 | |
% 142.38/21.28 | | ALPHA: (9) implies:
% 142.38/21.28 | | (10) all_57_2 = e2
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (1), (5), (10) are inconsistent by sub-proof #943.
% 142.38/21.28 | |
% 142.38/21.28 | End of split
% 142.38/21.28 |
% 142.38/21.28 End of proof
% 142.38/21.28
% 142.38/21.28 Sub-proof #639 shows that the following formulas are inconsistent:
% 142.38/21.28 ----------------------------------------------------------------
% 142.38/21.28 (1) ~ (all_52_13 = e0)
% 142.38/21.28 (2) op(e0, e0) = e0
% 142.38/21.28 (3) op(e2, e2) = e1
% 142.38/21.28 (4) ~ (all_52_1 = e0)
% 142.38/21.28 (5) ~ (e3 = e0)
% 142.38/21.28 (6) op(e1, e1) = all_4_2
% 142.38/21.28 (7) op(e2, e3) = all_52_1
% 142.38/21.28 (8) ~ (all_4_2 = e3)
% 142.38/21.28 (9) ~ (e1 = e0)
% 142.38/21.28 (10) ~ (e2 = e0)
% 142.38/21.28 (11) ~ (all_4_2 = e2)
% 142.38/21.28 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.28 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.28 (13) ~ (all_52_9 = e1)
% 142.38/21.28 (14) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.38/21.28 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.38/21.28 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.38/21.28 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.38/21.28 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.38/21.28 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.38/21.28 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.38/21.28 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.38/21.28 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.38/21.28 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.38/21.28 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.38/21.28 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.38/21.28 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.38/21.28 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.38/21.28 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.38/21.28 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.38/21.28 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.38/21.28 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.38/21.28 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.38/21.28 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.28 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.38/21.28 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.38/21.28 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.38/21.28 $i(all_56_14))))
% 142.38/21.28 (15) op(e3, e3) = e0
% 142.38/21.28 (16) op(e2, e1) = all_52_9
% 142.38/21.28 (17) op(e2, e0) = all_52_13
% 142.38/21.28 (18) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.38/21.28 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.38/21.28
% 142.38/21.28 Begin of proof
% 142.38/21.28 |
% 142.38/21.28 | BETA: splitting (18) gives:
% 142.38/21.28 |
% 142.38/21.28 | Case 1:
% 142.38/21.28 | |
% 142.38/21.28 | | (19) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.38/21.28 | | e0)
% 142.38/21.28 | |
% 142.38/21.28 | | REF_CLOSE: (3), (4), (7), (9), (12), (19) are inconsistent by sub-proof
% 142.38/21.28 | | #640.
% 142.38/21.28 | |
% 142.38/21.28 | Case 2:
% 142.38/21.28 | |
% 142.38/21.28 | | (20) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.38/21.28 | | e0)
% 142.38/21.28 | |
% 142.38/21.28 | | BETA: splitting (20) gives:
% 142.38/21.28 | |
% 142.38/21.28 | | Case 1:
% 142.38/21.28 | | |
% 142.38/21.28 | | | (21) all_57_5 = e0 & op(e2, e1) = e0
% 142.38/21.28 | | |
% 142.38/21.28 | | | ALPHA: (21) implies:
% 142.38/21.28 | | | (22) op(e2, e1) = e0
% 142.38/21.28 | | |
% 142.38/21.28 | | | BETA: splitting (14) gives:
% 142.38/21.28 | | |
% 142.38/21.28 | | | Case 1:
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | (23) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3,
% 142.38/21.28 | | | | e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 &
% 142.38/21.28 | | | | $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3
% 142.38/21.28 | | | | = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2, e2)
% 142.38/21.28 | | | | = e3 & $i(all_56_3)) | (all_56_9 = e1 & all_56_13 = e3 & ~
% 142.38/21.28 | | | | (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) = all_56_1 &
% 142.38/21.28 | | | | op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13 =
% 142.38/21.28 | | | | e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.38/21.28 | | | | all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.38/21.28 | | | |
% 142.38/21.28 | | | | REF_CLOSE: (9), (10), (12), (15), (23) are inconsistent by sub-proof
% 142.38/21.28 | | | | #752.
% 142.38/21.28 | | | |
% 142.38/21.28 | | | Case 2:
% 142.38/21.28 | | | |
% 142.38/21.29 | | | | (24) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.38/21.29 | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.38/21.29 | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 142.38/21.29 | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 142.38/21.29 | | | | op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 & all_56_13
% 142.38/21.29 | | | | = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.38/21.29 | | | | all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.38/21.29 | | | | all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2,
% 142.38/21.29 | | | | e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0,
% 142.38/21.29 | | | | e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.38/21.29 | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0
% 142.38/21.29 | | | | & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.38/21.29 | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0
% 142.38/21.29 | | | | & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.38/21.29 | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.38/21.29 | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.38/21.29 | | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | BETA: splitting (24) gives:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | Case 1:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | (25) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.38/21.29 | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.38/21.29 | | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 142.38/21.29 | | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 142.38/21.29 | | | | | op(e1, e1) = e2 & $i(all_56_4))
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | BETA: splitting (25) gives:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | Case 1:
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | (26) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.38/21.29 | | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.38/21.29 | | | | | | $i(all_56_2)
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | ALPHA: (26) implies:
% 142.38/21.29 | | | | | | (27) op(e0, e0) = e3
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | REF_CLOSE: (2), (5), (12), (27) are inconsistent by sub-proof #751.
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | Case 2:
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | (28) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) &
% 142.38/21.29 | | | | | | op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.38/21.29 | | | | | | $i(all_56_4)
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | ALPHA: (28) implies:
% 142.38/21.29 | | | | | | (29) op(e1, e1) = e2
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | REF_CLOSE: (6), (11), (12), (29) are inconsistent by sub-proof
% 142.38/21.29 | | | | | | #1124.
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | End of split
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | Case 2:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | (30) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.38/21.29 | | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.38/21.29 | | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.38/21.29 | | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 142.38/21.29 | | | | | op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.38/21.29 | | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 142.38/21.29 | | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 142.38/21.29 | | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15
% 142.38/21.29 | | | | | = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 142.38/21.29 | | | | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.29 | | | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.38/21.29 | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0
% 142.38/21.29 | | | | | & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0
% 142.38/21.29 | | | | | & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | BETA: splitting (30) gives:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | Case 1:
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | (31) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 142.38/21.29 | | | | | | op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.38/21.29 | | | | | | $i(all_56_7)
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | ALPHA: (31) implies:
% 142.38/21.29 | | | | | | (32) op(e1, e1) = e2
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | REF_CLOSE: (6), (11), (12), (32) are inconsistent by sub-proof
% 142.38/21.29 | | | | | | #1124.
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | Case 2:
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | (33) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 142.38/21.29 | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2
% 142.38/21.29 | | | | | | & $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15)
% 142.38/21.29 | | | | | | & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.38/21.29 | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.38/21.29 | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.38/21.29 | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.38/21.29 | | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.29 | | | | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0
% 142.38/21.29 | | | | | | & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 =
% 142.38/21.29 | | | | | | e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1)
% 142.38/21.29 | | | | | | = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | BETA: splitting (33) gives:
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | | Case 1:
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | (34) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 142.38/21.29 | | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2
% 142.38/21.29 | | | | | | | & $i(all_56_5)
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | ALPHA: (34) implies:
% 142.38/21.29 | | | | | | | (35) op(e0, e0) = e2
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | REF_CLOSE: (2), (10), (12), (35) are inconsistent by sub-proof
% 142.38/21.29 | | | | | | | #1094.
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | Case 2:
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | (36) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.38/21.29 | | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0
% 142.38/21.29 | | | | | | | & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11
% 142.38/21.29 | | | | | | | = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2,
% 142.38/21.29 | | | | | | | e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 142.38/21.29 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.38/21.29 | | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 142.38/21.29 | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.38/21.29 | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.38/21.29 | | | | | | | all_56_14 & $i(all_56_14)))
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | ALPHA: (36) implies:
% 142.38/21.29 | | | | | | | (37) op(e0, e0) = all_56_15
% 142.38/21.29 | | | | | | | (38) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.38/21.29 | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.38/21.29 | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.38/21.29 | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.38/21.29 | | | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 142.38/21.29 | | | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.38/21.29 | | | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.38/21.29 | | | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.38/21.29 | | | | | | | e1) = all_56_14 & $i(all_56_14))
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | GROUND_INST: instantiating (12) with e0, all_56_15, e0, e0,
% 142.38/21.29 | | | | | | | simplifying with (2), (37) gives:
% 142.38/21.29 | | | | | | | (39) all_56_15 = e0
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | GROUND_INST: instantiating (12) with all_52_9, e0, e1, e2,
% 142.38/21.29 | | | | | | | simplifying with (16), (22) gives:
% 142.38/21.29 | | | | | | | (40) all_52_9 = e0
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | REDUCE: (13), (40) imply:
% 142.38/21.29 | | | | | | | (41) ~ (e1 = e0)
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | BETA: splitting (38) gives:
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | | Case 1:
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | | (42) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.38/21.29 | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.38/21.29 | | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.38/21.29 | | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.38/21.29 | | | | | | | | all_56_12 & $i(all_56_12))
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | | BETA: splitting (42) gives:
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | | Case 1:
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | | (43) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.38/21.29 | | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.38/21.29 | | | | | | | | | $i(all_56_10)
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | | REF_CLOSE: (5), (39), (43) are inconsistent by sub-proof #747.
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | Case 2:
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | | (44) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0)
% 142.38/21.29 | | | | | | | | | & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.38/21.29 | | | | | | | | | $i(all_56_12)
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | | ALPHA: (44) implies:
% 142.38/21.29 | | | | | | | | | (45) op(e2, e2) = e0
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | | REF_CLOSE: (3), (9), (12), (45) are inconsistent by sub-proof
% 142.38/21.29 | | | | | | | | | #1117.
% 142.38/21.29 | | | | | | | | |
% 142.38/21.29 | | | | | | | | End of split
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | Case 2:
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | | (46) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.38/21.29 | | | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 142.38/21.29 | | | | | | | | $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.38/21.29 | | | | | | | | (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.38/21.29 | | | | | | | | all_56_14 & $i(all_56_14))
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | | REF_CLOSE: (2), (6), (8), (9), (11), (12), (37), (38), (46) are
% 142.38/21.29 | | | | | | | | inconsistent by sub-proof #744.
% 142.38/21.29 | | | | | | | |
% 142.38/21.29 | | | | | | | End of split
% 142.38/21.29 | | | | | | |
% 142.38/21.29 | | | | | | End of split
% 142.38/21.29 | | | | | |
% 142.38/21.29 | | | | | End of split
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | End of split
% 142.38/21.29 | | | |
% 142.38/21.29 | | | End of split
% 142.38/21.29 | | |
% 142.38/21.29 | | Case 2:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (47) all_57_10 = e0 & op(e2, e0) = e0
% 142.38/21.29 | | |
% 142.38/21.29 | | | REF_CLOSE: (1), (12), (17), (47) are inconsistent by sub-proof #1078.
% 142.38/21.29 | | |
% 142.38/21.29 | | End of split
% 142.38/21.29 | |
% 142.38/21.29 | End of split
% 142.38/21.29 |
% 142.38/21.29 End of proof
% 142.38/21.29
% 142.38/21.29 Sub-proof #640 shows that the following formulas are inconsistent:
% 142.38/21.29 ----------------------------------------------------------------
% 142.38/21.29 (1) op(e2, e2) = e1
% 142.38/21.29 (2) ~ (all_52_1 = e0)
% 142.38/21.29 (3) op(e2, e3) = all_52_1
% 142.38/21.29 (4) ~ (e1 = e0)
% 142.38/21.29 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.29 (6) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 142.38/21.29
% 142.38/21.29 Begin of proof
% 142.38/21.29 |
% 142.38/21.29 | BETA: splitting (6) gives:
% 142.38/21.29 |
% 142.38/21.29 | Case 1:
% 142.38/21.29 | |
% 142.38/21.29 | | (7) all_57_2 = e0 & op(e2, e3) = e0
% 142.38/21.29 | |
% 142.38/21.29 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #1028.
% 142.38/21.29 | |
% 142.38/21.29 | Case 2:
% 142.38/21.29 | |
% 142.38/21.29 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 142.38/21.29 | |
% 142.38/21.29 | | ALPHA: (8) implies:
% 142.38/21.29 | | (9) op(e2, e2) = e0
% 142.38/21.29 | |
% 142.38/21.29 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1117.
% 142.38/21.29 | |
% 142.38/21.29 | End of split
% 142.38/21.29 |
% 142.38/21.29 End of proof
% 142.38/21.29
% 142.38/21.29 Sub-proof #641 shows that the following formulas are inconsistent:
% 142.38/21.29 ----------------------------------------------------------------
% 142.38/21.29 (1) all_54_5 = e1 | all_54_5 = e0
% 142.38/21.29 (2) all_54_5 = all_6_2
% 142.38/21.29 (3) ~ (all_6_2 = e1)
% 142.38/21.29 (4) ~ (all_6_2 = e0)
% 142.38/21.29
% 142.38/21.29 Begin of proof
% 142.38/21.29 |
% 142.38/21.29 | BETA: splitting (1) gives:
% 142.38/21.29 |
% 142.38/21.29 | Case 1:
% 142.38/21.29 | |
% 142.38/21.29 | | (5) all_54_5 = e1
% 142.38/21.29 | |
% 142.38/21.29 | | COMBINE_EQS: (2), (5) imply:
% 142.38/21.29 | | (6) all_6_2 = e1
% 142.38/21.29 | |
% 142.38/21.29 | | REDUCE: (3), (6) imply:
% 142.38/21.29 | | (7) $false
% 142.38/21.29 | |
% 142.38/21.29 | | CLOSE: (7) is inconsistent.
% 142.38/21.29 | |
% 142.38/21.29 | Case 2:
% 142.38/21.29 | |
% 142.38/21.29 | | (8) all_54_5 = e0
% 142.38/21.29 | |
% 142.38/21.29 | | COMBINE_EQS: (2), (8) imply:
% 142.38/21.29 | | (9) all_6_2 = e0
% 142.38/21.29 | |
% 142.38/21.29 | | REDUCE: (4), (9) imply:
% 142.38/21.29 | | (10) $false
% 142.38/21.29 | |
% 142.38/21.29 | | CLOSE: (10) is inconsistent.
% 142.38/21.29 | |
% 142.38/21.29 | End of split
% 142.38/21.29 |
% 142.38/21.29 End of proof
% 142.38/21.29
% 142.38/21.29 Sub-proof #642 shows that the following formulas are inconsistent:
% 142.38/21.29 ----------------------------------------------------------------
% 142.38/21.29 (1) ~ (e2 = e1)
% 142.38/21.29 (2) ~ (e1 = e0)
% 142.38/21.29 (3) op(e2, e2) = e2
% 142.38/21.29 (4) ~ (e2 = e0)
% 142.38/21.29 (5) ~ (e3 = e2)
% 142.38/21.29 (6) op(e0, e0) = e2
% 142.38/21.29 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.29 (8) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.38/21.29 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.38/21.29 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 142.38/21.29 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.38/21.29 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.38/21.29 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 142.38/21.29 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 142.38/21.29 op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 & all_56_15 = e3 & ~
% 142.38/21.29 (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0)
% 142.38/21.29 = e3 & $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4
% 142.38/21.29 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.38/21.29 $i(all_56_4)) | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) &
% 142.38/21.29 op(e2, e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.38/21.29 $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 142.38/21.29 op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.38/21.29 $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 =
% 142.38/21.29 e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.38/21.29 all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 142.38/21.29 = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 &
% 142.38/21.29 ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 &
% 142.38/21.29 $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 =
% 142.38/21.29 e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.38/21.29 (9) op(e3, e3) = e0
% 142.38/21.29
% 142.38/21.29 Begin of proof
% 142.38/21.29 |
% 142.38/21.29 | BETA: splitting (8) gives:
% 142.38/21.29 |
% 142.38/21.29 | Case 1:
% 142.38/21.29 | |
% 142.38/21.29 | | (10) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 142.38/21.29 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.38/21.29 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 142.38/21.29 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 142.38/21.29 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 142.38/21.29 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.38/21.29 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 142.38/21.29 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.38/21.29 | |
% 142.38/21.29 | | REF_CLOSE: (2), (4), (7), (9), (10) are inconsistent by sub-proof #752.
% 142.38/21.29 | |
% 142.38/21.29 | Case 2:
% 142.38/21.29 | |
% 142.38/21.29 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) =
% 142.38/21.29 | | e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.38/21.29 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) =
% 142.38/21.29 | | e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 142.38/21.29 | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) =
% 142.38/21.29 | | e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.38/21.29 | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 142.38/21.29 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.38/21.29 | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.38/21.29 | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.38/21.29 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.38/21.29 | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.29 | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1,
% 142.38/21.29 | | e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.38/21.29 | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.38/21.29 | | all_56_14 & $i(all_56_14))))
% 142.38/21.29 | |
% 142.38/21.29 | | BETA: splitting (11) gives:
% 142.38/21.29 | |
% 142.38/21.29 | | Case 1:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (12) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.38/21.29 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.38/21.29 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 142.38/21.29 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4))
% 142.38/21.29 | | |
% 142.38/21.29 | | | BETA: splitting (12) gives:
% 142.38/21.29 | | |
% 142.38/21.29 | | | Case 1:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | (13) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.38/21.29 | | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | ALPHA: (13) implies:
% 142.38/21.29 | | | | (14) op(e0, e0) = e3
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | REF_CLOSE: (5), (6), (7), (14) are inconsistent by sub-proof #1066.
% 142.38/21.29 | | | |
% 142.38/21.29 | | | Case 2:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | (15) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2,
% 142.38/21.29 | | | | e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.38/21.29 | | | | $i(all_56_4)
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | ALPHA: (15) implies:
% 142.38/21.29 | | | | (16) op(e2, e2) = e1
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | REF_CLOSE: (1), (3), (7), (16) are inconsistent by sub-proof #749.
% 142.38/21.29 | | | |
% 142.38/21.29 | | | End of split
% 142.38/21.29 | | |
% 142.38/21.29 | | Case 2:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (17) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 142.38/21.29 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.38/21.29 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 142.38/21.29 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.38/21.29 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.38/21.29 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.38/21.29 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.38/21.29 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.29 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.38/21.29 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.38/21.29 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.38/21.29 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.38/21.29 | | |
% 142.38/21.29 | | | BETA: splitting (17) gives:
% 142.38/21.29 | | |
% 142.38/21.29 | | | Case 1:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | (18) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.38/21.29 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.38/21.29 | | | | $i(all_56_7)
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | ALPHA: (18) implies:
% 142.38/21.29 | | | | (19) op(e2, e2) = e1
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | REF_CLOSE: (1), (3), (7), (19) are inconsistent by sub-proof #749.
% 142.38/21.29 | | | |
% 142.38/21.29 | | | Case 2:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | (20) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.38/21.29 | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.38/21.29 | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.38/21.29 | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.38/21.29 | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 142.38/21.29 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.38/21.29 | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 142.38/21.29 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.38/21.29 | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.38/21.29 | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.38/21.29 | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.38/21.29 | | | | $i(all_56_14))))
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | BETA: splitting (20) gives:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | Case 1:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | (21) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.38/21.29 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.38/21.29 | | | | | $i(all_56_5)
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | ALPHA: (21) implies:
% 142.38/21.29 | | | | | (22) op(e2, e2) = e0
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | REF_CLOSE: (3), (4), (7), (22) are inconsistent by sub-proof #1076.
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | Case 2:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | (23) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.38/21.29 | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0
% 142.38/21.29 | | | | | & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.38/21.29 | | | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0
% 142.38/21.29 | | | | | & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.38/21.29 | | | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.38/21.29 | | | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.38/21.29 | | | | | op(e0, e1) = all_56_14 & $i(all_56_14)))
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | ALPHA: (23) implies:
% 142.38/21.29 | | | | | (24) op(e0, e0) = all_56_15
% 142.38/21.29 | | | | | (25) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3,
% 142.38/21.29 | | | | | e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.38/21.29 | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.38/21.29 | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 142.38/21.29 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1,
% 142.38/21.29 | | | | | e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.38/21.29 | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.38/21.29 | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (24), (25) are inconsistent
% 142.38/21.29 | | | | | by sub-proof #643.
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | End of split
% 142.38/21.29 | | | |
% 142.38/21.29 | | | End of split
% 142.38/21.29 | | |
% 142.38/21.29 | | End of split
% 142.38/21.29 | |
% 142.38/21.29 | End of split
% 142.38/21.29 |
% 142.38/21.29 End of proof
% 142.38/21.29
% 142.38/21.29 Sub-proof #643 shows that the following formulas are inconsistent:
% 142.38/21.29 ----------------------------------------------------------------
% 142.38/21.29 (1) ~ (e2 = e1)
% 142.38/21.29 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.38/21.29 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.38/21.29 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.38/21.29 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.38/21.29 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.38/21.29 e1) = all_56_14 & $i(all_56_14))
% 142.38/21.29 (3) op(e2, e2) = e2
% 142.38/21.29 (4) ~ (e2 = e0)
% 142.38/21.29 (5) ~ (e3 = e2)
% 142.38/21.29 (6) op(e0, e0) = e2
% 142.38/21.29 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.29 (8) op(e0, e0) = all_56_15
% 142.38/21.29
% 142.38/21.29 Begin of proof
% 142.38/21.29 |
% 142.38/21.29 | BETA: splitting (2) gives:
% 142.38/21.29 |
% 142.38/21.29 | Case 1:
% 142.38/21.29 | |
% 142.38/21.29 | | (9) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.38/21.29 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.38/21.29 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 142.38/21.29 | | = all_56_12 & $i(all_56_12))
% 142.38/21.29 | |
% 142.38/21.29 | | BETA: splitting (9) gives:
% 142.38/21.29 | |
% 142.38/21.29 | | Case 1:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (10) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 142.38/21.29 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.38/21.29 | | |
% 142.38/21.29 | | | ALPHA: (10) implies:
% 142.38/21.29 | | | (11) all_56_15 = e3
% 142.38/21.29 | | |
% 142.38/21.29 | | | REDUCE: (8), (11) imply:
% 142.38/21.29 | | | (12) op(e0, e0) = e3
% 142.38/21.29 | | |
% 142.38/21.29 | | | REF_CLOSE: (5), (6), (7), (12) are inconsistent by sub-proof #1066.
% 142.38/21.29 | | |
% 142.38/21.29 | | Case 2:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (13) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.38/21.29 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.38/21.29 | | |
% 142.38/21.29 | | | ALPHA: (13) implies:
% 142.38/21.29 | | | (14) op(e2, e2) = e0
% 142.38/21.29 | | |
% 142.38/21.29 | | | REF_CLOSE: (3), (4), (7), (14) are inconsistent by sub-proof #1076.
% 142.38/21.29 | | |
% 142.38/21.29 | | End of split
% 142.38/21.29 | |
% 142.38/21.29 | Case 2:
% 142.38/21.29 | |
% 142.38/21.29 | | (15) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.38/21.29 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.38/21.29 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.38/21.29 | | e1) = all_56_14 & $i(all_56_14))
% 142.38/21.29 | |
% 142.38/21.29 | | BETA: splitting (15) gives:
% 142.38/21.29 | |
% 142.38/21.29 | | Case 1:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (16) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1)
% 142.38/21.29 | | | = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 142.38/21.29 | | |
% 142.38/21.29 | | | ALPHA: (16) implies:
% 142.38/21.29 | | | (17) all_56_15 = e1
% 142.38/21.29 | | |
% 142.38/21.29 | | | REDUCE: (8), (17) imply:
% 142.38/21.29 | | | (18) op(e0, e0) = e1
% 142.38/21.29 | | |
% 142.38/21.29 | | | REF_CLOSE: (1), (6), (7), (18) are inconsistent by sub-proof #1070.
% 142.38/21.29 | | |
% 142.38/21.29 | | Case 2:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (19) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1)
% 142.38/21.29 | | | = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.38/21.29 | | |
% 142.38/21.29 | | | ALPHA: (19) implies:
% 142.38/21.29 | | | (20) all_56_15 = e1
% 142.38/21.29 | | |
% 142.38/21.29 | | | REDUCE: (8), (20) imply:
% 142.38/21.29 | | | (21) op(e0, e0) = e1
% 142.38/21.29 | | |
% 142.38/21.29 | | | REF_CLOSE: (1), (6), (7), (21) are inconsistent by sub-proof #1070.
% 142.38/21.29 | | |
% 142.38/21.29 | | End of split
% 142.38/21.29 | |
% 142.38/21.29 | End of split
% 142.38/21.29 |
% 142.38/21.29 End of proof
% 142.38/21.29
% 142.38/21.29 Sub-proof #644 shows that the following formulas are inconsistent:
% 142.38/21.29 ----------------------------------------------------------------
% 142.38/21.29 (1) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.38/21.29 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 142.38/21.29 ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 142.38/21.29 all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | (
% 142.38/21.29 ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.38/21.29 ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 142.38/21.29 all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 142.38/21.29 (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 142.38/21.29 ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 142.38/21.29 all_56_8 & $i(all_56_8)))
% 142.38/21.29 (2) ~ (all_52_12 = e3)
% 142.38/21.29 (3) ~ (e2 = e1)
% 142.38/21.29 (4) op(e0, e0) = e3
% 142.38/21.29 (5) ~ (e1 = e0)
% 142.38/21.29 (6) op(e2, e2) = e2
% 142.38/21.29 (7) ~ (e2 = e0)
% 142.38/21.29 (8) ~ (e3 = e2)
% 142.38/21.29 (9) op(e3, e0) = all_52_12
% 142.38/21.29 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.38/21.29 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.38/21.29 (11) ~ (e3 = e1)
% 142.38/21.29 (12) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.38/21.29 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.38/21.29 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.38/21.29 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.38/21.29 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.38/21.29 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.38/21.29 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.38/21.29 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.38/21.29 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.38/21.29 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.38/21.29 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.38/21.29 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.38/21.29 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.38/21.29 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.38/21.29 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.38/21.29 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.38/21.29 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.38/21.29 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.38/21.29 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.38/21.29 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.29 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.38/21.29 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.38/21.29 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.38/21.29 $i(all_56_14))))
% 142.38/21.29 (13) op(e3, e3) = e0
% 142.38/21.29
% 142.38/21.29 Begin of proof
% 142.38/21.29 |
% 142.38/21.29 | ALPHA: (1) implies:
% 142.38/21.29 | (14) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 142.38/21.29 | all_56_9 & $i(all_56_9))
% 142.38/21.29 |
% 142.38/21.29 | BETA: splitting (14) gives:
% 142.38/21.29 |
% 142.38/21.29 | Case 1:
% 142.38/21.29 | |
% 142.38/21.29 | | (15) all_56_2 = e3 & op(e3, e0) = e3
% 142.38/21.29 | |
% 142.38/21.29 | | ALPHA: (15) implies:
% 142.38/21.29 | | (16) op(e3, e0) = e3
% 142.38/21.29 | |
% 142.38/21.29 | | REF_CLOSE: (2), (9), (10), (16) are inconsistent by sub-proof #1105.
% 142.38/21.29 | |
% 142.38/21.29 | Case 2:
% 142.38/21.29 | |
% 142.38/21.29 | | (17) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 142.38/21.29 | |
% 142.38/21.29 | | ALPHA: (17) implies:
% 142.38/21.29 | | (18) ~ (all_56_9 = e0)
% 142.38/21.29 | |
% 142.38/21.29 | | BETA: splitting (12) gives:
% 142.38/21.29 | |
% 142.38/21.29 | | Case 1:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (19) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 142.38/21.29 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.38/21.29 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 142.38/21.29 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 142.38/21.29 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 142.38/21.29 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.38/21.29 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 142.38/21.29 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.38/21.29 | | |
% 142.38/21.29 | | | REF_CLOSE: (5), (7), (10), (13), (19) are inconsistent by sub-proof #752.
% 142.38/21.29 | | |
% 142.38/21.29 | | Case 2:
% 142.38/21.29 | | |
% 142.38/21.29 | | | (20) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.38/21.29 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.38/21.29 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 142.38/21.29 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 142.38/21.29 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 142.38/21.29 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.38/21.29 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 142.38/21.29 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.38/21.29 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.38/21.29 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.38/21.29 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.38/21.29 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.38/21.29 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.38/21.29 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.38/21.29 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.38/21.29 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.38/21.29 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.38/21.29 | | |
% 142.38/21.29 | | | BETA: splitting (20) gives:
% 142.38/21.29 | | |
% 142.38/21.29 | | | Case 1:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | (21) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.38/21.29 | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.38/21.29 | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 142.38/21.29 | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 142.38/21.29 | | | | op(e1, e1) = e2 & $i(all_56_4))
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | BETA: splitting (21) gives:
% 142.38/21.29 | | | |
% 142.38/21.29 | | | | Case 1:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | (22) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.38/21.29 | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.38/21.29 | | | | | $i(all_56_2)
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | ALPHA: (22) implies:
% 142.38/21.29 | | | | | (23) all_56_9 = e0
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | REDUCE: (18), (23) imply:
% 142.38/21.29 | | | | | (24) $false
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | CLOSE: (24) is inconsistent.
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | Case 2:
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | (25) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2,
% 142.38/21.29 | | | | | e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.38/21.29 | | | | | $i(all_56_4)
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | ALPHA: (25) implies:
% 142.38/21.29 | | | | | (26) op(e2, e2) = e1
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | | REF_CLOSE: (3), (6), (10), (26) are inconsistent by sub-proof #749.
% 142.38/21.29 | | | | |
% 142.38/21.29 | | | | End of split
% 142.38/21.29 | | | |
% 142.38/21.29 | | | Case 2:
% 142.38/21.29 | | | |
% 142.38/21.30 | | | | (27) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.38/21.30 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.38/21.30 | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.38/21.30 | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 142.38/21.30 | | | | op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.38/21.30 | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 142.38/21.30 | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 142.38/21.30 | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.38/21.30 | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.38/21.30 | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 142.38/21.30 | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 142.38/21.30 | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 142.38/21.30 | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.38/21.30 | | | | all_56_14 & $i(all_56_14))))
% 142.38/21.30 | | | |
% 142.38/21.30 | | | | BETA: splitting (27) gives:
% 142.38/21.30 | | | |
% 142.38/21.30 | | | | Case 1:
% 142.38/21.30 | | | | |
% 142.38/21.30 | | | | | (28) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.38/21.30 | | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.38/21.30 | | | | | $i(all_56_7)
% 142.38/21.30 | | | | |
% 142.38/21.30 | | | | | ALPHA: (28) implies:
% 142.38/21.30 | | | | | (29) op(e2, e2) = e1
% 142.38/21.30 | | | | |
% 142.38/21.30 | | | | | REF_CLOSE: (3), (6), (10), (29) are inconsistent by sub-proof #749.
% 142.38/21.30 | | | | |
% 142.38/21.30 | | | | Case 2:
% 142.38/21.30 | | | | |
% 142.58/21.30 | | | | | (30) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.58/21.30 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.58/21.30 | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.58/21.30 | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.30 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.58/21.30 | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.58/21.30 | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.58/21.30 | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 142.58/21.30 | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.30 | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.58/21.30 | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.30 | | | | | e1) = all_56_14 & $i(all_56_14))))
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REF_CLOSE: (4), (8), (10), (11), (18), (30) are inconsistent by
% 142.58/21.30 | | | | | sub-proof #645.
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | End of split
% 142.58/21.30 | | | |
% 142.58/21.30 | | | End of split
% 142.58/21.30 | | |
% 142.58/21.30 | | End of split
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #645 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) op(e0, e0) = e3
% 142.58/21.30 (2) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 &
% 142.58/21.30 op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) =
% 142.58/21.30 all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 142.58/21.30 (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.58/21.30 $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 =
% 142.58/21.30 e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 142.58/21.30 (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.58/21.30 e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.58/21.30 all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1)
% 142.58/21.30 = all_56_14 & $i(all_56_14))))
% 142.58/21.30 (3) ~ (e3 = e2)
% 142.58/21.30 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (5) ~ (e3 = e1)
% 142.58/21.30 (6) ~ (all_56_9 = e0)
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (2) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (7) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) =
% 142.58/21.30 | | e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (7) implies:
% 142.58/21.30 | | (8) op(e0, e0) = e2
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1066.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (9) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 & all_56_15
% 142.58/21.30 | | = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 142.58/21.30 | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 &
% 142.58/21.30 | | ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.58/21.30 | | $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8
% 142.58/21.30 | | = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8))
% 142.58/21.30 | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1,
% 142.58/21.30 | | e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)))
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (9) implies:
% 142.58/21.30 | | (10) op(e0, e0) = all_56_15
% 142.58/21.30 | | (11) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.58/21.30 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.58/21.30 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 142.58/21.30 | | e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 142.58/21.30 | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) = all_56_8
% 142.58/21.30 | | & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14
% 142.58/21.30 | | = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.30 | | $i(all_56_14))
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (3), (4), (5), (6), (10), (11) are inconsistent by sub-proof
% 142.58/21.30 | | #731.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #646 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) (all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.58/21.30 all_56_11 & $i(all_56_11))
% 142.58/21.30 (2) ~ (all_56_4 = e2)
% 142.58/21.30 (3) all_56_11 = e1
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (1) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (4) all_56_4 = e2 & op(e2, e1) = e2
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (4) implies:
% 142.58/21.30 | | (5) all_56_4 = e2
% 142.58/21.30 | |
% 142.58/21.30 | | REDUCE: (2), (5) imply:
% 142.58/21.30 | | (6) $false
% 142.58/21.30 | |
% 142.58/21.30 | | CLOSE: (6) is inconsistent.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (7) ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (7) implies:
% 142.58/21.30 | | (8) ~ (all_56_11 = e1)
% 142.58/21.30 | |
% 142.58/21.30 | | REDUCE: (3), (8) imply:
% 142.58/21.30 | | (9) $false
% 142.58/21.30 | |
% 142.58/21.30 | | CLOSE: (9) is inconsistent.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #647 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.30 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.30 (2) op(e2, e1) = e3
% 142.58/21.30 (3) ~ (all_52_4 = e0)
% 142.58/21.30 (4) ~ (e2 = e1)
% 142.58/21.30 (5) op(e0, e0) = e3
% 142.58/21.30 (6) all_57_8 = e0
% 142.58/21.30 (7) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.30 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.30 (8) all_57_13 = e0
% 142.58/21.30 (9) ~ (e3 = e0)
% 142.58/21.30 (10) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.58/21.30 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.30 e2)
% 142.58/21.30 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.30 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.30 (12) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.30 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.30 (13) ~ (e1 = e0)
% 142.58/21.30 (14) op(e2, e2) = e2
% 142.58/21.30 (15) op(e3, e2) = all_52_4
% 142.58/21.30 (16) ~ (e2 = e0)
% 142.58/21.30 (17) ~ (e3 = e2)
% 142.58/21.30 (18) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.58/21.30 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.58/21.30 (19) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (20) ~ (e3 = e1)
% 142.58/21.30 (21) all_57_2 = e1
% 142.58/21.30 (22) all_57_0 = e0
% 142.58/21.30 (23) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.30 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.30 (24) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 142.58/21.30 all_48_1 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1,
% 142.58/21.30 e0) = all_48_1 & $i(all_48_1))
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (11) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 142.58/21.30 | | e3)
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (9), (20), (21), (22), (25) are inconsistent by sub-proof #649.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (26) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.58/21.30 | | e3)
% 142.58/21.30 | |
% 142.58/21.30 | | BETA: splitting (26) gives:
% 142.58/21.30 | |
% 142.58/21.30 | | Case 1:
% 142.58/21.30 | | |
% 142.58/21.30 | | | (27) all_57_6 = e3 & op(e1, e3) = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | ALPHA: (27) implies:
% 142.58/21.30 | | | (28) all_57_6 = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | BETA: splitting (18) gives:
% 142.58/21.30 | | |
% 142.58/21.30 | | | Case 1:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | (29) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 142.58/21.30 | | | | = e2)
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | BETA: splitting (29) gives:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | Case 1:
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | (30) all_57_6 = e2 & op(e1, e3) = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | ALPHA: (30) implies:
% 142.58/21.30 | | | | | (31) all_57_6 = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REF_CLOSE: (17), (28), (31) are inconsistent by sub-proof #1004.
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | Case 2:
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | (32) all_57_7 = e2 & op(e1, e2) = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | ALPHA: (32) implies:
% 142.58/21.30 | | | | | (33) all_57_7 = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REF_CLOSE: (1), (4), (8), (9), (13), (14), (17), (19), (20), (23),
% 142.58/21.30 | | | | | (33) are inconsistent by sub-proof #720.
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | End of split
% 142.58/21.30 | | | |
% 142.58/21.30 | | | Case 2:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | (34) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 142.58/21.30 | | | | = e2)
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | BETA: splitting (34) gives:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | Case 1:
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | (35) all_57_8 = e2 & op(e1, e1) = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REF_CLOSE: (6), (16), (35) are inconsistent by sub-proof #718.
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | Case 2:
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | (36) all_57_11 = e2 & op(e1, e0) = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | ALPHA: (36) implies:
% 142.58/21.30 | | | | | (37) op(e1, e0) = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REF_CLOSE: (2), (19), (24), (37) are inconsistent by sub-proof #648.
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | End of split
% 142.58/21.30 | | | |
% 142.58/21.30 | | | End of split
% 142.58/21.30 | | |
% 142.58/21.30 | | Case 2:
% 142.58/21.30 | | |
% 142.58/21.30 | | | (38) all_57_12 = e3 & op(e0, e3) = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | ALPHA: (38) implies:
% 142.58/21.30 | | | (39) all_57_12 = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (12), (13), (14),
% 142.58/21.30 | | | (15), (16), (17), (19), (20), (23), (39) are inconsistent by
% 142.58/21.30 | | | sub-proof #708.
% 142.58/21.30 | | |
% 142.58/21.30 | | End of split
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #648 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) = all_48_1
% 142.58/21.30 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0) =
% 142.58/21.30 all_48_1 & $i(all_48_1))
% 142.58/21.30 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (3) op(e1, e0) = e2
% 142.58/21.30 (4) op(e2, e1) = e3
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (1) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (5) ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 142.58/21.30 | | all_48_1 & $i(all_48_0) & $i(all_48_1)
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (5) implies:
% 142.58/21.30 | | (6) ~ (all_48_0 = e3)
% 142.58/21.30 | | (7) op(e1, e0) = all_48_1
% 142.58/21.30 | | (8) op(all_48_1, e1) = all_48_0
% 142.58/21.30 | |
% 142.58/21.30 | | GROUND_INST: instantiating (2) with e2, all_48_1, e0, e1, simplifying with
% 142.58/21.30 | | (3), (7) gives:
% 142.58/21.30 | | (9) all_48_1 = e2
% 142.58/21.30 | |
% 142.58/21.30 | | REDUCE: (8), (9) imply:
% 142.58/21.30 | | (10) op(e2, e1) = all_48_0
% 142.58/21.30 | |
% 142.58/21.30 | | GROUND_INST: instantiating (2) with e3, all_48_0, e1, e2, simplifying with
% 142.58/21.30 | | (4), (10) gives:
% 142.58/21.30 | | (11) all_48_0 = e3
% 142.58/21.30 | |
% 142.58/21.30 | | REDUCE: (6), (11) imply:
% 142.58/21.30 | | (12) $false
% 142.58/21.30 | |
% 142.58/21.30 | | CLOSE: (12) is inconsistent.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (13) ~ (all_48_1 = e2) & op(e1, e0) = all_48_1 & $i(all_48_1)
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (13) implies:
% 142.58/21.30 | | (14) ~ (all_48_1 = e2)
% 142.58/21.30 | | (15) op(e1, e0) = all_48_1
% 142.58/21.30 | |
% 142.58/21.30 | | GROUND_INST: instantiating (2) with e2, all_48_1, e0, e1, simplifying with
% 142.58/21.30 | | (3), (15) gives:
% 142.58/21.30 | | (16) all_48_1 = e2
% 142.58/21.30 | |
% 142.58/21.30 | | REDUCE: (14), (16) imply:
% 142.58/21.30 | | (17) $false
% 142.58/21.30 | |
% 142.58/21.30 | | CLOSE: (17) is inconsistent.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #649 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) ~ (e3 = e0)
% 142.58/21.30 (2) ~ (e3 = e1)
% 142.58/21.30 (3) all_57_2 = e1
% 142.58/21.30 (4) all_57_0 = e0
% 142.58/21.30 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (5) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (6) all_57_0 = e3 & op(e3, e3) = e3
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (4), (6) are inconsistent by sub-proof #1108.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (7) all_57_2 = e3 & op(e2, e3) = e3
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (7) implies:
% 142.58/21.30 | | (8) all_57_2 = e3
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (2), (3), (8) are inconsistent by sub-proof #701.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #650 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) ~ (e2 = e1)
% 142.58/21.30 (2) op(e0, e0) = e3
% 142.58/21.30 (3) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.58/21.30 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.30 (4) ~ (e3 = e0)
% 142.58/21.30 (5) ~ (e1 = e0)
% 142.58/21.30 (6) ~ (e2 = e0)
% 142.58/21.30 (7) ~ (e3 = e2)
% 142.58/21.30 (8) all_57_10 = e3
% 142.58/21.30 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.30 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.30 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.30 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.30 (11) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.58/21.30 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.30 (12) ~ (e3 = e1)
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (10) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (13) all_57_15 = e0 & op(e0, e0) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (13) implies:
% 142.58/21.30 | | (14) op(e0, e0) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (2), (4), (9), (14) are inconsistent by sub-proof #751.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (15) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.58/21.30 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.58/21.30 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.30 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (15) implies:
% 142.58/21.30 | | (16) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.58/21.30 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (11), (12), (16) are
% 142.58/21.30 | | inconsistent by sub-proof #687.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #651 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) ~ (all_52_1 = e2)
% 142.58/21.30 (2) ~ (e2 = e1)
% 142.58/21.30 (3) ~ (e3 = e0)
% 142.58/21.30 (4) op(e1, e1) = e1
% 142.58/21.30 (5) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.58/21.30 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.30 (6) op(e2, e3) = all_52_1
% 142.58/21.30 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.30 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.30 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.30 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.30 (9) all_57_11 = e2
% 142.58/21.30 (10) ~ (e1 = e0)
% 142.58/21.30 (11) ~ (e2 = e0)
% 142.58/21.30 (12) all_57_6 = e2
% 142.58/21.30 (13) ~ (e3 = e2)
% 142.58/21.30 (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.58/21.30 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.58/21.30 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (16) ~ (e3 = e1)
% 142.58/21.30 (17) all_57_0 = e0
% 142.58/21.30 (18) op(e3, e3) = e0
% 142.58/21.30 (19) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.58/21.30 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (14) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (20) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.58/21.30 | | e3)
% 142.58/21.30 | |
% 142.58/21.30 | | BETA: splitting (20) gives:
% 142.58/21.30 | |
% 142.58/21.30 | | Case 1:
% 142.58/21.30 | | |
% 142.58/21.30 | | | (21) all_57_6 = e3 & op(e1, e3) = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | ALPHA: (21) implies:
% 142.58/21.30 | | | (22) all_57_6 = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | REF_CLOSE: (12), (13), (22) are inconsistent by sub-proof #1004.
% 142.58/21.30 | | |
% 142.58/21.30 | | Case 2:
% 142.58/21.30 | | |
% 142.58/21.30 | | | (23) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.30 | | |
% 142.58/21.30 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 142.58/21.30 | | | (15), (16), (17), (18), (19), (23) are inconsistent by
% 142.58/21.30 | | | sub-proof #679.
% 142.58/21.30 | | |
% 142.58/21.30 | | End of split
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (24) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.58/21.30 | | e3)
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (4), (9), (13), (15), (16), (24) are inconsistent by sub-proof
% 142.58/21.30 | | #1054.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #652 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) ~ (all_52_7 = e0)
% 142.58/21.30 (2) op(e0, e3) = all_52_3
% 142.58/21.30 (3) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.30 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.30 (4) ~ (e2 = e0)
% 142.58/21.30 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (6) ~ (all_52_3 = e0)
% 142.58/21.30 (7) op(e0, e2) = all_52_7
% 142.58/21.30 (8) all_57_14 = e2 & op(e0, e1) = e2
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | ALPHA: (8) implies:
% 142.58/21.30 | (9) all_57_14 = e2
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (3) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (10) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (10) implies:
% 142.58/21.30 | | (11) op(e0, e3) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (2), (5), (6), (11) are inconsistent by sub-proof #986.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (12) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.58/21.30 | | e0)
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (4), (5), (7), (9), (12) are inconsistent by sub-proof #653.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #653 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.30 (2) ~ (all_52_7 = e0)
% 142.58/21.30 (3) all_57_14 = e2
% 142.58/21.30 (4) ~ (e2 = e0)
% 142.58/21.30 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (6) op(e0, e2) = all_52_7
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (1) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (7) all_57_13 = e0 & op(e0, e2) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | ALPHA: (7) implies:
% 142.58/21.30 | | (8) op(e0, e2) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #977.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (9) all_57_14 = e0 & op(e0, e1) = e0
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #920.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #654 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) op(e3, e0) = e1
% 142.58/21.30 (2) op(e1, e3) = all_52_2
% 142.58/21.30 (3) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.58/21.30 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.58/21.30 all_14_1 & $i(all_14_1))
% 142.58/21.30 (4) op(e1, e3) = e2
% 142.58/21.30 (5) all_28_2 = e0
% 142.58/21.30 (6) op(e3, e0) = all_52_12
% 142.58/21.30 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (8) ~ (all_28_2 = e0) | ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 &
% 142.58/21.30 op(e3, e0) = all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 =
% 142.58/21.30 e1) & op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | GROUND_INST: instantiating (7) with all_52_2, e2, e3, e1, simplifying with
% 142.58/21.30 | (2), (4) gives:
% 142.58/21.30 | (9) all_52_2 = e2
% 142.58/21.30 |
% 142.58/21.30 | GROUND_INST: instantiating (7) with all_52_12, e1, e0, e3, simplifying with
% 142.58/21.30 | (1), (6) gives:
% 142.58/21.30 | (10) all_52_12 = e1
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (8) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (11) ~ (all_28_2 = e0)
% 142.58/21.30 | |
% 142.58/21.30 | | REDUCE: (5), (11) imply:
% 142.58/21.30 | | (12) $false
% 142.58/21.30 | |
% 142.58/21.30 | | CLOSE: (12) is inconsistent.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (13) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.58/21.30 | | all_28_1 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) &
% 142.58/21.30 | | op(e3, e0) = all_28_1 & $i(all_28_1))
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (3), (4), (7), (13) are inconsistent by sub-proof #683.
% 142.58/21.30 | |
% 142.58/21.30 | End of split
% 142.58/21.30 |
% 142.58/21.30 End of proof
% 142.58/21.30
% 142.58/21.30 Sub-proof #655 shows that the following formulas are inconsistent:
% 142.58/21.30 ----------------------------------------------------------------
% 142.58/21.30 (1) ~ (all_52_1 = e2)
% 142.58/21.30 (2) ~ (all_52_1 = all_52_3)
% 142.58/21.30 (3) op(e0, e0) = e3
% 142.58/21.30 (4) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 142.58/21.30 (5) ~ (all_52_11 = e1)
% 142.58/21.30 (6) ~ (all_52_11 = e3)
% 142.58/21.30 (7) ~ (all_52_1 = e3)
% 142.58/21.30 (8) all_57_12 = e3
% 142.58/21.30 (9) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.30 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.30 (10) all_54_12 = all_52_3
% 142.58/21.30 (11) ~ (all_52_1 = e0)
% 142.58/21.30 (12) ~ (e3 = e0)
% 142.58/21.30 (13) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.58/21.30 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.30 e2)
% 142.58/21.30 (14) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.58/21.30 (15) ~ (all_52_3 = all_52_11)
% 142.58/21.30 (16) ~ (all_52_7 = all_52_11)
% 142.58/21.30 (17) all_54_14 = all_52_11
% 142.58/21.30 (18) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.30 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.30 (19) ~ (all_52_3 = e0)
% 142.58/21.30 (20) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.30 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.30 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.30 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.30 (21) op(e0, e2) = all_52_7
% 142.58/21.30 (22) all_54_4 = all_52_1
% 142.58/21.30 (23) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 142.58/21.30 (24) ~ (all_52_3 = e3)
% 142.58/21.30
% 142.58/21.30 Begin of proof
% 142.58/21.30 |
% 142.58/21.30 | BETA: splitting (23) gives:
% 142.58/21.30 |
% 142.58/21.30 | Case 1:
% 142.58/21.30 | |
% 142.58/21.30 | | (25) all_54_4 = e2
% 142.58/21.30 | |
% 142.58/21.30 | | REF_CLOSE: (1), (22), (25) are inconsistent by sub-proof #677.
% 142.58/21.30 | |
% 142.58/21.30 | Case 2:
% 142.58/21.30 | |
% 142.58/21.30 | | (26) all_54_4 = e1 | all_54_4 = e0
% 142.58/21.30 | |
% 142.58/21.30 | | BETA: splitting (26) gives:
% 142.58/21.30 | |
% 142.58/21.30 | | Case 1:
% 142.58/21.30 | | |
% 142.58/21.30 | | | (27) all_54_4 = e1
% 142.58/21.30 | | |
% 142.58/21.30 | | | COMBINE_EQS: (22), (27) imply:
% 142.58/21.30 | | | (28) all_52_1 = e1
% 142.58/21.30 | | |
% 142.58/21.30 | | | SIMP: (28) implies:
% 142.58/21.30 | | | (29) all_52_1 = e1
% 142.58/21.30 | | |
% 142.58/21.30 | | | REDUCE: (2), (29) imply:
% 142.58/21.30 | | | (30) ~ (all_52_3 = e1)
% 142.58/21.30 | | |
% 142.58/21.30 | | | SIMP: (30) implies:
% 142.58/21.30 | | | (31) ~ (all_52_3 = e1)
% 142.58/21.30 | | |
% 142.58/21.30 | | | REDUCE: (7), (29) imply:
% 142.58/21.30 | | | (32) ~ (e3 = e1)
% 142.58/21.30 | | |
% 142.58/21.30 | | | SIMP: (32) implies:
% 142.58/21.30 | | | (33) ~ (e3 = e1)
% 142.58/21.30 | | |
% 142.58/21.30 | | | BETA: splitting (4) gives:
% 142.58/21.30 | | |
% 142.58/21.30 | | | Case 1:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | (34) all_54_12 = e3
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | COMBINE_EQS: (10), (34) imply:
% 142.58/21.30 | | | | (35) all_52_3 = e3
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | REDUCE: (24), (35) imply:
% 142.58/21.30 | | | | (36) $false
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | CLOSE: (36) is inconsistent.
% 142.58/21.30 | | | |
% 142.58/21.30 | | | Case 2:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | (37) ~ (all_54_12 = e3)
% 142.58/21.30 | | | | (38) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | BETA: splitting (38) gives:
% 142.58/21.30 | | | |
% 142.58/21.30 | | | | Case 1:
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | (39) all_54_12 = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | COMBINE_EQS: (10), (39) imply:
% 142.58/21.30 | | | | | (40) all_52_3 = e2
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REDUCE: (15), (40) imply:
% 142.58/21.30 | | | | | (41) ~ (all_52_11 = e2)
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | SIMP: (41) implies:
% 142.58/21.30 | | | | | (42) ~ (all_52_11 = e2)
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REDUCE: (24), (40) imply:
% 142.58/21.30 | | | | | (43) ~ (e3 = e2)
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | SIMP: (43) implies:
% 142.58/21.30 | | | | | (44) ~ (e3 = e2)
% 142.58/21.30 | | | | |
% 142.58/21.30 | | | | | REDUCE: (31), (40) imply:
% 142.58/21.30 | | | | | (45) ~ (e2 = e1)
% 142.58/21.30 | | | | |
% 142.58/21.31 | | | | | BETA: splitting (14) gives:
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | Case 1:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | (46) all_54_14 = e3
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | COMBINE_EQS: (17), (46) imply:
% 142.58/21.31 | | | | | | (47) all_52_11 = e3
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | REDUCE: (6), (47) imply:
% 142.58/21.31 | | | | | | (48) $false
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | CLOSE: (48) is inconsistent.
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | Case 2:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | (49) ~ (all_54_14 = e3)
% 142.58/21.31 | | | | | | (50) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | BETA: splitting (50) gives:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | Case 1:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | (51) all_54_14 = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | COMBINE_EQS: (17), (51) imply:
% 142.58/21.31 | | | | | | | (52) all_52_11 = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | REDUCE: (42), (52) imply:
% 142.58/21.31 | | | | | | | (53) $false
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | CLOSE: (53) is inconsistent.
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | Case 2:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | (54) ~ (all_54_14 = e2)
% 142.58/21.31 | | | | | | | (55) all_54_14 = e1 | all_54_14 = e0
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | BETA: splitting (20) gives:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | Case 1:
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | (56) all_57_15 = e0 & op(e0, e0) = e0
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | ALPHA: (56) implies:
% 142.58/21.31 | | | | | | | | (57) op(e0, e0) = e0
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | REF_CLOSE: (3), (12), (18), (57) are inconsistent by sub-proof
% 142.58/21.31 | | | | | | | | #751.
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | Case 2:
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | (58) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 &
% 142.58/21.31 | | | | | | | | op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.58/21.31 | | | | | | | | e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) |
% 142.58/21.31 | | | | | | | | (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 &
% 142.58/21.31 | | | | | | | | op(e0, e1) = e0))
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | ALPHA: (58) implies:
% 142.58/21.31 | | | | | | | | (59) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.31 | | | | | | | | op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | BETA: splitting (55) gives:
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | | Case 1:
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | (60) all_54_14 = e1
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | REF_CLOSE: (5), (17), (60) are inconsistent by sub-proof #673.
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | Case 2:
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | (61) all_54_14 = e0
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | COMBINE_EQS: (17), (61) imply:
% 142.58/21.31 | | | | | | | | | (62) all_52_11 = e0
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | SIMP: (62) implies:
% 142.58/21.31 | | | | | | | | | (63) all_52_11 = e0
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | REDUCE: (16), (63) imply:
% 142.58/21.31 | | | | | | | | | (64) ~ (all_52_7 = e0)
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | REDUCE: (6), (63) imply:
% 142.58/21.31 | | | | | | | | | (65) ~ (e3 = e0)
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | REDUCE: (42), (63) imply:
% 142.58/21.31 | | | | | | | | | (66) ~ (e2 = e0)
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | SIMP: (66) implies:
% 142.58/21.31 | | | | | | | | | (67) ~ (e2 = e0)
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | REDUCE: (5), (63) imply:
% 142.58/21.31 | | | | | | | | | (68) ~ (e1 = e0)
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | SIMP: (68) implies:
% 142.58/21.31 | | | | | | | | | (69) ~ (e1 = e0)
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | | REF_CLOSE: (3), (8), (9), (12), (13), (18), (21), (33), (44),
% 142.58/21.31 | | | | | | | | | (45), (59), (64), (67), (69) are inconsistent by
% 142.58/21.31 | | | | | | | | | sub-proof #656.
% 142.58/21.31 | | | | | | | | |
% 142.58/21.31 | | | | | | | | End of split
% 142.58/21.31 | | | | | | | |
% 142.58/21.31 | | | | | | | End of split
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | End of split
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | End of split
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | Case 2:
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | (70) all_54_12 = e1 | all_54_12 = e0
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | REF_CLOSE: (10), (19), (31), (70) are inconsistent by sub-proof #661.
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | End of split
% 142.58/21.31 | | | |
% 142.58/21.31 | | | End of split
% 142.58/21.31 | | |
% 142.58/21.31 | | Case 2:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (71) all_54_4 = e0
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (11), (22), (71) are inconsistent by sub-proof #794.
% 142.58/21.31 | | |
% 142.58/21.31 | | End of split
% 142.58/21.31 | |
% 142.58/21.31 | End of split
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #656 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) ~ (e2 = e1)
% 142.58/21.31 (2) op(e0, e0) = e3
% 142.58/21.31 (3) ~ (all_52_7 = e0)
% 142.58/21.31 (4) all_57_12 = e3
% 142.58/21.31 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.31 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.31 (6) ~ (e3 = e0)
% 142.58/21.31 (7) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.31 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.31 (8) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.31 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.31 (9) ~ (e1 = e0)
% 142.58/21.31 (10) ~ (e2 = e0)
% 142.58/21.31 (11) ~ (e3 = e2)
% 142.58/21.31 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.31 (13) ~ (e3 = e1)
% 142.58/21.31 (14) op(e0, e2) = all_52_7
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | BETA: splitting (8) gives:
% 142.58/21.31 |
% 142.58/21.31 | Case 1:
% 142.58/21.31 | |
% 142.58/21.31 | | (15) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.31 | |
% 142.58/21.31 | | ALPHA: (15) implies:
% 142.58/21.31 | | (16) all_57_12 = e0
% 142.58/21.31 | |
% 142.58/21.31 | | REF_CLOSE: (4), (6), (16) are inconsistent by sub-proof #828.
% 142.58/21.31 | |
% 142.58/21.31 | Case 2:
% 142.58/21.31 | |
% 142.58/21.31 | | (17) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.58/21.31 | | e0)
% 142.58/21.31 | |
% 142.58/21.31 | | BETA: splitting (17) gives:
% 142.58/21.31 | |
% 142.58/21.31 | | Case 1:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (18) all_57_13 = e0 & op(e0, e2) = e0
% 142.58/21.31 | | |
% 142.58/21.31 | | | ALPHA: (18) implies:
% 142.58/21.31 | | | (19) op(e0, e2) = e0
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (3), (12), (14), (19) are inconsistent by sub-proof #977.
% 142.58/21.31 | | |
% 142.58/21.31 | | Case 2:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (20) all_57_14 = e0 & op(e0, e1) = e0
% 142.58/21.31 | | |
% 142.58/21.31 | | | ALPHA: (20) implies:
% 142.58/21.31 | | | (21) all_57_14 = e0
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (1), (2), (4), (5), (7), (9), (10), (11), (12), (13), (21) are
% 142.58/21.31 | | | inconsistent by sub-proof #657.
% 142.58/21.31 | | |
% 142.58/21.31 | | End of split
% 142.58/21.31 | |
% 142.58/21.31 | End of split
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #657 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) all_57_14 = e0
% 142.58/21.31 (2) ~ (e2 = e1)
% 142.58/21.31 (3) op(e0, e0) = e3
% 142.58/21.31 (4) all_57_12 = e3
% 142.58/21.31 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.31 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.31 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.31 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.31 (7) ~ (e1 = e0)
% 142.58/21.31 (8) ~ (e2 = e0)
% 142.58/21.31 (9) ~ (e3 = e2)
% 142.58/21.31 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.31 (11) ~ (e3 = e1)
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | BETA: splitting (5) gives:
% 142.58/21.31 |
% 142.58/21.31 | Case 1:
% 142.58/21.31 | |
% 142.58/21.31 | | (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.58/21.31 | | e1)
% 142.58/21.31 | |
% 142.58/21.31 | | BETA: splitting (12) gives:
% 142.58/21.31 | |
% 142.58/21.31 | | Case 1:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (13) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (4), (11), (13) are inconsistent by sub-proof #1073.
% 142.58/21.31 | | |
% 142.58/21.31 | | Case 2:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (14) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.31 | | |
% 142.58/21.31 | | | ALPHA: (14) implies:
% 142.58/21.31 | | | (15) all_57_13 = e1
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (1), (2), (3), (4), (6), (8), (9), (10), (15) are inconsistent
% 142.58/21.31 | | | by sub-proof #658.
% 142.58/21.31 | | |
% 142.58/21.31 | | End of split
% 142.58/21.31 | |
% 142.58/21.31 | Case 2:
% 142.58/21.31 | |
% 142.58/21.31 | | (16) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.58/21.31 | | e1)
% 142.58/21.31 | |
% 142.58/21.31 | | REF_CLOSE: (1), (3), (7), (10), (11), (16) are inconsistent by sub-proof
% 142.58/21.31 | | #667.
% 142.58/21.31 | |
% 142.58/21.31 | End of split
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #658 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) all_57_14 = e0
% 142.58/21.31 (2) ~ (e2 = e1)
% 142.58/21.31 (3) op(e0, e0) = e3
% 142.58/21.31 (4) all_57_12 = e3
% 142.58/21.31 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.31 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.31 (6) all_57_13 = e1
% 142.58/21.31 (7) ~ (e2 = e0)
% 142.58/21.31 (8) ~ (e3 = e2)
% 142.58/21.31 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | BETA: splitting (5) gives:
% 142.58/21.31 |
% 142.58/21.31 | Case 1:
% 142.58/21.31 | |
% 142.58/21.31 | | (10) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.58/21.31 | | e2)
% 142.58/21.31 | |
% 142.58/21.31 | | BETA: splitting (10) gives:
% 142.58/21.31 | |
% 142.58/21.31 | | Case 1:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (11) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (4), (8), (11) are inconsistent by sub-proof #659.
% 142.58/21.31 | | |
% 142.58/21.31 | | Case 2:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (12) all_57_13 = e2 & op(e0, e2) = e2
% 142.58/21.31 | | |
% 142.58/21.31 | | | ALPHA: (12) implies:
% 142.58/21.31 | | | (13) all_57_13 = e2
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (2), (6), (13) are inconsistent by sub-proof #1057.
% 142.58/21.31 | | |
% 142.58/21.31 | | End of split
% 142.58/21.31 | |
% 142.58/21.31 | Case 2:
% 142.58/21.31 | |
% 142.58/21.31 | | (14) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.31 | | e2)
% 142.58/21.31 | |
% 142.58/21.31 | | REF_CLOSE: (1), (3), (7), (8), (9), (14) are inconsistent by sub-proof #967.
% 142.58/21.31 | |
% 142.58/21.31 | End of split
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #659 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.31 (2) all_57_12 = e3
% 142.58/21.31 (3) ~ (e3 = e2)
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | ALPHA: (1) implies:
% 142.58/21.31 | (4) all_57_12 = e2
% 142.58/21.31 |
% 142.58/21.31 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.31 | (5) e3 = e2
% 142.58/21.31 |
% 142.58/21.31 | REDUCE: (3), (5) imply:
% 142.58/21.31 | (6) $false
% 142.58/21.31 |
% 142.58/21.31 | CLOSE: (6) is inconsistent.
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #660 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) ~ (all_52_1 = e2)
% 142.58/21.31 (2) ~ (all_52_1 = all_52_3)
% 142.58/21.31 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.31 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.31 (4) ~ (all_4_2 = e0)
% 142.58/21.31 (5) all_57_6 = e3
% 142.58/21.31 (6) ~ (all_52_12 = e3)
% 142.58/21.31 (7) ~ (all_52_4 = e0)
% 142.58/21.31 (8) op(e0, e0) = e3
% 142.58/21.31 (9) all_54_12 = e3 | all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 142.58/21.31 (10) ~ (all_52_11 = e1)
% 142.58/21.31 (11) ~ (all_52_11 = e3)
% 142.58/21.31 (12) op(e0, e3) = all_52_3
% 142.58/21.31 (13) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.58/21.31 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.58/21.31 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.58/21.31 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.58/21.31 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.58/21.31 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.58/21.31 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.58/21.31 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.58/21.31 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.58/21.31 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.58/21.31 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.58/21.31 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.58/21.31 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.58/21.31 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.58/21.31 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.58/21.31 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.58/21.31 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.58/21.31 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.58/21.31 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.58/21.31 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.58/21.31 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.58/21.31 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.58/21.31 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.58/21.31 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.58/21.31 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.58/21.31 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.58/21.31 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.58/21.31 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.58/21.31 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.58/21.31 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.58/21.31 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.58/21.31 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.58/21.31 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.58/21.31 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.58/21.31 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.58/21.31 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.58/21.31 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.58/21.31 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.58/21.31 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.58/21.31 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.58/21.31 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.58/21.31 (14) ~ (all_52_1 = e3)
% 142.58/21.31 (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.31 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.58/21.31 e1)
% 142.58/21.31 (16) all_54_12 = all_52_3
% 142.58/21.31 (17) all_54_10 = e1 | all_54_10 = e0
% 142.58/21.31 (18) ~ (all_52_1 = e0)
% 142.58/21.31 (19) ~ (e3 = e0)
% 142.58/21.31 (20) op(e1, e1) = e1
% 142.58/21.31 (21) op(e1, e1) = all_4_2
% 142.58/21.31 (22) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.58/21.31 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.31 (23) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.58/21.31 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.31 e2)
% 142.58/21.31 (24) op(e2, e3) = all_52_1
% 142.58/21.31 (25) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.58/21.31 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.31 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.31 (27) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.31 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.31 (28) ~ (all_52_3 = all_52_11)
% 142.58/21.31 (29) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.31 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.31 (30) op(e2, e2) = e2
% 142.58/21.31 (31) op(e3, e2) = all_52_4
% 142.58/21.31 (32) ~ (all_52_7 = all_52_11)
% 142.58/21.31 (33) op(e0, e1) = all_52_11
% 142.58/21.31 (34) op(e3, e0) = all_52_12
% 142.58/21.31 (35) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.58/21.31 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.58/21.31 (36) ~ (all_4_2 = e2)
% 142.58/21.31 (37) all_54_10 = all_4_2
% 142.58/21.31 (38) all_54_14 = all_52_11
% 142.58/21.31 (39) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.31 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.31 (40) ~ (all_52_3 = e0)
% 142.58/21.31 (41) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.31 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.31 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.31 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.31 (42) op(e0, e2) = all_52_7
% 142.58/21.31 (43) all_54_4 = all_52_1
% 142.58/21.31 (44) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.31 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.31 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.58/21.31 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.58/21.31 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.58/21.31 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.58/21.31 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.58/21.31 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.58/21.31 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.58/21.31 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.58/21.31 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.58/21.31 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.58/21.31 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.58/21.31 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.58/21.31 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.58/21.31 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.31 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.58/21.31 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.58/21.31 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.31 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.31 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.31 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.58/21.31 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.31 $i(all_56_14))))
% 142.58/21.31 (45) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 142.58/21.31 (46) all_57_0 = e0
% 142.58/21.31 (47) op(e3, e3) = e0
% 142.58/21.31 (48) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.58/21.31 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.58/21.31 (49) ~ (all_52_3 = e3)
% 142.58/21.31 (50) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.31 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | BETA: splitting (45) gives:
% 142.58/21.31 |
% 142.58/21.31 | Case 1:
% 142.58/21.31 | |
% 142.58/21.31 | | (51) all_54_4 = e2
% 142.58/21.31 | |
% 142.58/21.31 | | REF_CLOSE: (1), (43), (51) are inconsistent by sub-proof #677.
% 142.58/21.31 | |
% 142.58/21.31 | Case 2:
% 142.58/21.31 | |
% 142.58/21.31 | | (52) ~ (all_54_4 = e2)
% 142.58/21.31 | | (53) all_54_4 = e1 | all_54_4 = e0
% 142.58/21.31 | |
% 142.58/21.31 | | BETA: splitting (53) gives:
% 142.58/21.31 | |
% 142.58/21.31 | | Case 1:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (54) all_54_4 = e1
% 142.58/21.31 | | |
% 142.58/21.31 | | | COMBINE_EQS: (43), (54) imply:
% 142.58/21.31 | | | (55) all_52_1 = e1
% 142.58/21.31 | | |
% 142.58/21.31 | | | SIMP: (55) implies:
% 142.58/21.31 | | | (56) all_52_1 = e1
% 142.58/21.31 | | |
% 142.58/21.31 | | | REDUCE: (2), (56) imply:
% 142.58/21.31 | | | (57) ~ (all_52_3 = e1)
% 142.58/21.31 | | |
% 142.58/21.31 | | | SIMP: (57) implies:
% 142.58/21.31 | | | (58) ~ (all_52_3 = e1)
% 142.58/21.31 | | |
% 142.58/21.31 | | | REDUCE: (14), (56) imply:
% 142.58/21.31 | | | (59) ~ (e3 = e1)
% 142.58/21.31 | | |
% 142.58/21.31 | | | SIMP: (59) implies:
% 142.58/21.31 | | | (60) ~ (e3 = e1)
% 142.58/21.31 | | |
% 142.58/21.31 | | | REDUCE: (18), (56) imply:
% 142.58/21.31 | | | (61) ~ (e1 = e0)
% 142.58/21.31 | | |
% 142.58/21.31 | | | BETA: splitting (9) gives:
% 142.58/21.31 | | |
% 142.58/21.31 | | | Case 1:
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | (62) all_54_12 = e3
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | COMBINE_EQS: (16), (62) imply:
% 142.58/21.31 | | | | (63) all_52_3 = e3
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | REDUCE: (49), (63) imply:
% 142.58/21.31 | | | | (64) $false
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | CLOSE: (64) is inconsistent.
% 142.58/21.31 | | | |
% 142.58/21.31 | | | Case 2:
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | (65) ~ (all_54_12 = e3)
% 142.58/21.31 | | | | (66) all_54_12 = e2 | all_54_12 = e1 | all_54_12 = e0
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | BETA: splitting (66) gives:
% 142.58/21.31 | | | |
% 142.58/21.31 | | | | Case 1:
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | (67) all_54_12 = e2
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | COMBINE_EQS: (16), (67) imply:
% 142.58/21.31 | | | | | (68) all_52_3 = e2
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | REDUCE: (28), (68) imply:
% 142.58/21.31 | | | | | (69) ~ (all_52_11 = e2)
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | SIMP: (69) implies:
% 142.58/21.31 | | | | | (70) ~ (all_52_11 = e2)
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | REDUCE: (49), (68) imply:
% 142.58/21.31 | | | | | (71) ~ (e3 = e2)
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | SIMP: (71) implies:
% 142.58/21.31 | | | | | (72) ~ (e3 = e2)
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | REDUCE: (58), (68) imply:
% 142.58/21.31 | | | | | (73) ~ (e2 = e1)
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | REDUCE: (40), (68) imply:
% 142.58/21.31 | | | | | (74) ~ (e2 = e0)
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | BETA: splitting (35) gives:
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | Case 1:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | (75) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 142.58/21.31 | | | | | | e2) = e2)
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | BETA: splitting (75) gives:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | Case 1:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | (76) all_57_6 = e2 & op(e1, e3) = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | REF_CLOSE: (5), (72), (76) are inconsistent by sub-proof #998.
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | Case 2:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | (77) all_57_7 = e2 & op(e1, e2) = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | REF_CLOSE: (3), (7), (19), (29), (30), (31), (39), (50), (60),
% 142.58/21.31 | | | | | | | (61), (72), (73), (74), (77) are inconsistent by
% 142.58/21.31 | | | | | | | sub-proof #681.
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | End of split
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | Case 2:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | (78) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 142.58/21.31 | | | | | | e0) = e2)
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | BETA: splitting (78) gives:
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | | Case 1:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | (79) all_57_8 = e2 & op(e1, e1) = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | ALPHA: (79) implies:
% 142.58/21.31 | | | | | | | (80) op(e1, e1) = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | REF_CLOSE: (20), (39), (73), (80) are inconsistent by sub-proof
% 142.58/21.31 | | | | | | | #1085.
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | Case 2:
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | (81) all_57_11 = e2 & op(e1, e0) = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | ALPHA: (81) implies:
% 142.58/21.31 | | | | | | | (82) all_57_11 = e2
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | | REF_CLOSE: (1), (4), (6), (8), (10), (11), (12), (13), (15), (17),
% 142.58/21.31 | | | | | | | (19), (20), (21), (22), (23), (24), (25), (26), (27),
% 142.58/21.31 | | | | | | | (30), (32), (33), (34), (36), (37), (38), (39), (40),
% 142.58/21.31 | | | | | | | (41), (42), (44), (46), (47), (48), (50), (60), (70),
% 142.58/21.31 | | | | | | | (72), (73), (82) are inconsistent by sub-proof #663.
% 142.58/21.31 | | | | | | |
% 142.58/21.31 | | | | | | End of split
% 142.58/21.31 | | | | | |
% 142.58/21.31 | | | | | End of split
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | Case 2:
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | (83) all_54_12 = e1 | all_54_12 = e0
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | | REF_CLOSE: (16), (40), (58), (83) are inconsistent by sub-proof #661.
% 142.58/21.31 | | | | |
% 142.58/21.31 | | | | End of split
% 142.58/21.31 | | | |
% 142.58/21.31 | | | End of split
% 142.58/21.31 | | |
% 142.58/21.31 | | Case 2:
% 142.58/21.31 | | |
% 142.58/21.31 | | | (84) all_54_4 = e0
% 142.58/21.31 | | |
% 142.58/21.31 | | | REF_CLOSE: (18), (43), (84) are inconsistent by sub-proof #794.
% 142.58/21.31 | | |
% 142.58/21.31 | | End of split
% 142.58/21.31 | |
% 142.58/21.31 | End of split
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #661 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) all_54_12 = e1 | all_54_12 = e0
% 142.58/21.31 (2) all_54_12 = all_52_3
% 142.58/21.31 (3) ~ (all_52_3 = e1)
% 142.58/21.31 (4) ~ (all_52_3 = e0)
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | BETA: splitting (1) gives:
% 142.58/21.31 |
% 142.58/21.31 | Case 1:
% 142.58/21.31 | |
% 142.58/21.31 | | (5) all_54_12 = e1
% 142.58/21.31 | |
% 142.58/21.31 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #662.
% 142.58/21.31 | |
% 142.58/21.31 | Case 2:
% 142.58/21.31 | |
% 142.58/21.31 | | (6) all_54_12 = e0
% 142.58/21.31 | |
% 142.58/21.31 | | COMBINE_EQS: (2), (6) imply:
% 142.58/21.31 | | (7) all_52_3 = e0
% 142.58/21.31 | |
% 142.58/21.31 | | SIMP: (7) implies:
% 142.58/21.31 | | (8) all_52_3 = e0
% 142.58/21.31 | |
% 142.58/21.31 | | REDUCE: (4), (8) imply:
% 142.58/21.31 | | (9) $false
% 142.58/21.31 | |
% 142.58/21.31 | | CLOSE: (9) is inconsistent.
% 142.58/21.31 | |
% 142.58/21.31 | End of split
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #662 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) all_54_12 = all_52_3
% 142.58/21.31 (2) all_54_12 = e1
% 142.58/21.31 (3) ~ (all_52_3 = e1)
% 142.58/21.31
% 142.58/21.31 Begin of proof
% 142.58/21.31 |
% 142.58/21.31 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.31 | (4) all_52_3 = e1
% 142.58/21.31 |
% 142.58/21.31 | SIMP: (4) implies:
% 142.58/21.31 | (5) all_52_3 = e1
% 142.58/21.31 |
% 142.58/21.31 | REDUCE: (3), (5) imply:
% 142.58/21.31 | (6) $false
% 142.58/21.31 |
% 142.58/21.31 | CLOSE: (6) is inconsistent.
% 142.58/21.31 |
% 142.58/21.31 End of proof
% 142.58/21.31
% 142.58/21.31 Sub-proof #663 shows that the following formulas are inconsistent:
% 142.58/21.31 ----------------------------------------------------------------
% 142.58/21.31 (1) ~ (all_52_1 = e2)
% 142.58/21.31 (2) ~ (all_4_2 = e0)
% 142.58/21.31 (3) ~ (all_52_12 = e3)
% 142.58/21.31 (4) ~ (e2 = e1)
% 142.58/21.31 (5) op(e0, e0) = e3
% 142.58/21.31 (6) ~ (all_52_11 = e1)
% 142.58/21.31 (7) ~ (all_52_11 = e3)
% 142.58/21.31 (8) op(e0, e3) = all_52_3
% 142.58/21.31 (9) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.58/21.31 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.58/21.31 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.58/21.31 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.58/21.31 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.58/21.31 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 142.58/21.31 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 142.58/21.31 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 142.58/21.31 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 142.58/21.31 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 142.58/21.31 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 142.58/21.31 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.58/21.31 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 142.58/21.31 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 142.58/21.31 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.58/21.31 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 142.58/21.31 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 142.58/21.31 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 142.58/21.31 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 142.58/21.31 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.58/21.31 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.58/21.31 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.58/21.31 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.58/21.31 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.58/21.31 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.58/21.31 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.58/21.31 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.58/21.31 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 142.58/21.31 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 142.58/21.31 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 142.58/21.31 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.58/21.31 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.58/21.31 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.58/21.31 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 142.58/21.31 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.58/21.31 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.58/21.31 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.58/21.31 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.58/21.31 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.58/21.31 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.58/21.31 (10) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.31 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.58/21.31 e1)
% 142.58/21.31 (11) ~ (all_52_11 = e2)
% 142.58/21.31 (12) all_54_10 = e1 | all_54_10 = e0
% 142.58/21.31 (13) ~ (e3 = e0)
% 142.58/21.31 (14) op(e1, e1) = e1
% 142.58/21.31 (15) op(e1, e1) = all_4_2
% 142.58/21.31 (16) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.58/21.31 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.31 (17) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.58/21.31 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.31 e2)
% 142.58/21.31 (18) op(e2, e3) = all_52_1
% 142.58/21.32 (19) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.58/21.32 (20) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.32 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.32 (21) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.32 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.32 (22) all_57_11 = e2
% 142.58/21.32 (23) op(e2, e2) = e2
% 142.58/21.32 (24) ~ (all_52_7 = all_52_11)
% 142.58/21.32 (25) ~ (e3 = e2)
% 142.58/21.32 (26) op(e0, e1) = all_52_11
% 142.58/21.32 (27) op(e3, e0) = all_52_12
% 142.58/21.32 (28) ~ (all_4_2 = e2)
% 142.58/21.32 (29) all_54_10 = all_4_2
% 142.58/21.32 (30) all_54_14 = all_52_11
% 142.58/21.32 (31) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (32) ~ (all_52_3 = e0)
% 142.58/21.32 (33) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.32 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.32 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.32 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.32 (34) ~ (e3 = e1)
% 142.58/21.32 (35) op(e0, e2) = all_52_7
% 142.58/21.32 (36) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.32 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.32 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.58/21.32 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.58/21.32 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.58/21.32 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.58/21.32 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.58/21.32 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.58/21.32 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.58/21.32 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.58/21.32 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.58/21.32 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.58/21.32 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.58/21.32 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.58/21.32 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.58/21.32 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.32 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.58/21.32 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.58/21.32 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.32 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.32 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.32 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.58/21.32 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.32 $i(all_56_14))))
% 142.58/21.32 (37) all_57_0 = e0
% 142.58/21.32 (38) op(e3, e3) = e0
% 142.58/21.32 (39) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.58/21.32 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.58/21.32 (40) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.32 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | BETA: splitting (19) gives:
% 142.58/21.32 |
% 142.58/21.32 | Case 1:
% 142.58/21.32 | |
% 142.58/21.32 | | (41) all_54_14 = e3
% 142.58/21.32 | |
% 142.58/21.32 | | COMBINE_EQS: (30), (41) imply:
% 142.58/21.32 | | (42) all_52_11 = e3
% 142.58/21.32 | |
% 142.58/21.32 | | REDUCE: (7), (42) imply:
% 142.58/21.32 | | (43) $false
% 142.58/21.32 | |
% 142.58/21.32 | | CLOSE: (43) is inconsistent.
% 142.58/21.32 | |
% 142.58/21.32 | Case 2:
% 142.58/21.32 | |
% 142.58/21.32 | | (44) ~ (all_54_14 = e3)
% 142.58/21.32 | | (45) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.58/21.32 | |
% 142.58/21.32 | | BETA: splitting (45) gives:
% 142.58/21.32 | |
% 142.58/21.32 | | Case 1:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (46) all_54_14 = e2
% 142.58/21.32 | | |
% 142.58/21.32 | | | COMBINE_EQS: (30), (46) imply:
% 142.58/21.32 | | | (47) all_52_11 = e2
% 142.58/21.32 | | |
% 142.58/21.32 | | | REDUCE: (11), (47) imply:
% 142.58/21.32 | | | (48) $false
% 142.58/21.32 | | |
% 142.58/21.32 | | | CLOSE: (48) is inconsistent.
% 142.58/21.32 | | |
% 142.58/21.32 | | Case 2:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (49) ~ (all_54_14 = e2)
% 142.58/21.32 | | | (50) all_54_14 = e1 | all_54_14 = e0
% 142.58/21.32 | | |
% 142.58/21.32 | | | BETA: splitting (33) gives:
% 142.58/21.32 | | |
% 142.58/21.32 | | | Case 1:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | (51) all_57_15 = e0 & op(e0, e0) = e0
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | ALPHA: (51) implies:
% 142.58/21.32 | | | | (52) op(e0, e0) = e0
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | REF_CLOSE: (5), (13), (31), (52) are inconsistent by sub-proof #751.
% 142.58/21.32 | | | |
% 142.58/21.32 | | | Case 2:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | (53) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 142.58/21.32 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.58/21.32 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.58/21.32 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | ALPHA: (53) implies:
% 142.58/21.32 | | | | (54) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.58/21.32 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | BETA: splitting (50) gives:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | Case 1:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | (55) all_54_14 = e1
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REF_CLOSE: (6), (30), (55) are inconsistent by sub-proof #673.
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | Case 2:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | (56) all_54_14 = e0
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | COMBINE_EQS: (30), (56) imply:
% 142.58/21.32 | | | | | (57) all_52_11 = e0
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | SIMP: (57) implies:
% 142.58/21.32 | | | | | (58) all_52_11 = e0
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REDUCE: (24), (58) imply:
% 142.58/21.32 | | | | | (59) ~ (all_52_7 = e0)
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REDUCE: (7), (58) imply:
% 142.58/21.32 | | | | | (60) ~ (e3 = e0)
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REDUCE: (11), (58) imply:
% 142.58/21.32 | | | | | (61) ~ (e2 = e0)
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | SIMP: (61) implies:
% 142.58/21.32 | | | | | (62) ~ (e2 = e0)
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REDUCE: (6), (58) imply:
% 142.58/21.32 | | | | | (63) ~ (e1 = e0)
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | SIMP: (63) implies:
% 142.58/21.32 | | | | | (64) ~ (e1 = e0)
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REDUCE: (26), (58) imply:
% 142.58/21.32 | | | | | (65) op(e0, e1) = e0
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | BETA: splitting (9) gives:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | Case 1:
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | | (66) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 142.58/21.32 | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 142.58/21.32 | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 142.58/21.32 | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 142.58/21.32 | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 142.58/21.32 | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 142.58/21.32 | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 142.58/21.32 | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 142.58/21.32 | | | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1,
% 142.58/21.32 | | | | | | e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 142.58/21.32 | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 142.58/21.32 | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 142.58/21.32 | | | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11
% 142.58/21.32 | | | | | | & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 142.58/21.32 | | | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 &
% 142.58/21.32 | | | | | | $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) = e1) |
% 142.58/21.32 | | | | | | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.58/21.32 | | | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) |
% 142.58/21.32 | | | | | | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.58/21.32 | | | | | | $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) |
% 142.58/21.32 | | | | | | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 142.58/21.32 | | | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2)
% 142.58/21.32 | | | | | | | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.58/21.32 | | | | | | $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 142.58/21.32 | | | | | | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 142.58/21.32 | | | | | | $i(all_56_12))))
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | | BETA: splitting (66) gives:
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | | Case 1:
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | (67) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 142.58/21.32 | | | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 142.58/21.32 | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1,
% 142.58/21.32 | | | | | | | e3) = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) =
% 142.58/21.32 | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_10 = e0 &
% 142.58/21.32 | | | | | | | op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 142.58/21.32 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 &
% 142.58/21.32 | | | | | | | op(e2, e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) =
% 142.58/21.32 | | | | | | | all_56_3 & $i(all_56_3))) & ((all_56_13 = e3 & op(e1,
% 142.58/21.32 | | | | | | | e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 142.58/21.32 | | | | | | | all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0,
% 142.58/21.32 | | | | | | | e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 142.58/21.32 | | | | | | | all_56_10 & $i(all_56_10)))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | REF_CLOSE: (2), (5), (8), (12), (15), (25), (28), (29), (31),
% 142.58/21.32 | | | | | | | (32), (36), (38), (62), (65), (67) are inconsistent by
% 142.58/21.32 | | | | | | | sub-proof #671.
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | Case 2:
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | (68) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 142.58/21.32 | | | | | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 142.58/21.32 | | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1,
% 142.58/21.32 | | | | | | | e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) =
% 142.58/21.32 | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3,
% 142.58/21.32 | | | | | | | e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 142.58/21.32 | | | | | | | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0,
% 142.58/21.32 | | | | | | | e2) = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) =
% 142.58/21.32 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 &
% 142.58/21.32 | | | | | | | op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 142.58/21.32 | | | | | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0,
% 142.58/21.32 | | | | | | | e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 142.58/21.32 | | | | | | | all_56_12 & $i(all_56_12)))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | ALPHA: (68) implies:
% 142.58/21.32 | | | | | | | (69) (all_56_9 = e2 & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) &
% 142.58/21.32 | | | | | | | op(e3, e2) = all_56_0 & $i(all_56_0))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | BETA: splitting (69) gives:
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | Case 1:
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | (70) all_56_9 = e2 & op(e3, e3) = e2
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | ALPHA: (70) implies:
% 142.58/21.32 | | | | | | | | (71) op(e3, e3) = e2
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | REF_CLOSE: (31), (38), (62), (71) are inconsistent by sub-proof
% 142.58/21.32 | | | | | | | | #880.
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | Case 2:
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | (72) ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.58/21.32 | | | | | | | | $i(all_56_0)
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | ALPHA: (72) implies:
% 142.58/21.32 | | | | | | | | (73) ~ (all_56_0 = e3)
% 142.58/21.32 | | | | | | | | (74) op(e3, e2) = all_56_0
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | BETA: splitting (40) gives:
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | | Case 1:
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | | (75) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 &
% 142.58/21.32 | | | | | | | | | op(e2, e2) = e3)
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | | BETA: splitting (75) gives:
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | | Case 1:
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | (76) all_57_1 = e3 & op(e3, e2) = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | ALPHA: (76) implies:
% 142.58/21.32 | | | | | | | | | | (77) op(e3, e2) = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | REF_CLOSE: (31), (73), (74), (77) are inconsistent by
% 142.58/21.32 | | | | | | | | | | sub-proof #670.
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | Case 2:
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | (78) all_57_3 = e3 & op(e2, e2) = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | ALPHA: (78) implies:
% 142.58/21.32 | | | | | | | | | | (79) op(e2, e2) = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | REF_CLOSE: (23), (25), (31), (79) are inconsistent by
% 142.58/21.32 | | | | | | | | | | sub-proof #728.
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | End of split
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | Case 2:
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | | (80) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 &
% 142.58/21.32 | | | | | | | | | op(e0, e2) = e3)
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | | BETA: splitting (80) gives:
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | | Case 1:
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | (81) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | REF_CLOSE: (1), (4), (13), (14), (16), (18), (20), (21),
% 142.58/21.32 | | | | | | | | | | (22), (25), (31), (34), (37), (38), (39), (62),
% 142.58/21.32 | | | | | | | | | | (64), (81) are inconsistent by sub-proof #679.
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | Case 2:
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | (82) all_57_13 = e3 & op(e0, e2) = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | ALPHA: (82) implies:
% 142.58/21.32 | | | | | | | | | | (83) all_57_13 = e3
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | | REF_CLOSE: (4), (5), (10), (17), (25), (31), (34), (35),
% 142.58/21.32 | | | | | | | | | | (54), (59), (62), (64), (83) are inconsistent by
% 142.58/21.32 | | | | | | | | | | sub-proof #665.
% 142.58/21.32 | | | | | | | | | |
% 142.58/21.32 | | | | | | | | | End of split
% 142.58/21.32 | | | | | | | | |
% 142.58/21.32 | | | | | | | | End of split
% 142.58/21.32 | | | | | | | |
% 142.58/21.32 | | | | | | | End of split
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | End of split
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | Case 2:
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | | (84) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 142.58/21.32 | | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.58/21.32 | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 142.58/21.32 | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.58/21.32 | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3,
% 142.58/21.32 | | | | | | e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 142.58/21.32 | | | | | | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 142.58/21.32 | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.58/21.32 | | | | | | all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 142.58/21.32 | | | | | | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.58/21.32 | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 &
% 142.58/21.32 | | | | | | op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.58/21.32 | | | | | | all_56_14 & $i(all_56_14)))) | (op(e0, e0) = all_56_15
% 142.58/21.32 | | | | | | & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 142.58/21.32 | | | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 142.58/21.32 | | | | | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.58/21.32 | | | | | | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 142.58/21.32 | | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) |
% 142.58/21.32 | | | | | | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.58/21.32 | | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) |
% 142.58/21.32 | | | | | | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 142.58/21.32 | | | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) |
% 142.58/21.32 | | | | | | ( ~ (all_56_5 = e2) & op(e2, e0) = all_56_5 &
% 142.58/21.32 | | | | | | $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.58/21.32 | | | | | | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 &
% 142.58/21.32 | | | | | | $i(all_56_8))))
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | | BETA: splitting (84) gives:
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | | Case 1:
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | (85) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 142.58/21.32 | | | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.58/21.32 | | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2,
% 142.58/21.32 | | | | | | | e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.58/21.32 | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3,
% 142.58/21.32 | | | | | | | e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 142.58/21.32 | | | | | | | all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2,
% 142.58/21.32 | | | | | | | e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.58/21.32 | | | | | | | all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0,
% 142.58/21.32 | | | | | | | e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.58/21.32 | | | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 &
% 142.58/21.32 | | | | | | | op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.58/21.32 | | | | | | | all_56_14 & $i(all_56_14)))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | ALPHA: (85) implies:
% 142.58/21.32 | | | | | | | (86) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0)
% 142.58/21.32 | | | | | | | & op(e0, e1) = all_56_14 & $i(all_56_14))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | REF_CLOSE: (5), (31), (34), (65), (86) are inconsistent by
% 142.58/21.32 | | | | | | | sub-proof #664.
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | Case 2:
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | (87) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 142.58/21.32 | | | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 142.58/21.32 | | | | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2,
% 142.58/21.32 | | | | | | | e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 142.58/21.32 | | | | | | | all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1,
% 142.58/21.32 | | | | | | | e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 142.58/21.32 | | | | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 142.58/21.32 | | | | | | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) =
% 142.58/21.32 | | | | | | | all_56_2 & $i(all_56_2))) & ((all_56_11 = e0 & op(e2,
% 142.58/21.32 | | | | | | | e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0) =
% 142.58/21.32 | | | | | | | all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1,
% 142.58/21.32 | | | | | | | e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 142.58/21.32 | | | | | | | all_56_8 & $i(all_56_8)))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | ALPHA: (87) implies:
% 142.58/21.32 | | | | | | | (88) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) &
% 142.58/21.32 | | | | | | | op(e3, e3) = all_56_9 & $i(all_56_9))
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | | REF_CLOSE: (3), (4), (5), (14), (25), (27), (31), (34), (36),
% 142.58/21.32 | | | | | | | (38), (62), (64), (88) are inconsistent by sub-proof
% 142.58/21.32 | | | | | | | #730.
% 142.58/21.32 | | | | | | |
% 142.58/21.32 | | | | | | End of split
% 142.58/21.32 | | | | | |
% 142.58/21.32 | | | | | End of split
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | End of split
% 142.58/21.32 | | | |
% 142.58/21.32 | | | End of split
% 142.58/21.32 | | |
% 142.58/21.32 | | End of split
% 142.58/21.32 | |
% 142.58/21.32 | End of split
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #664 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) op(e0, e0) = e3
% 142.58/21.32 (2) op(e0, e1) = e0
% 142.58/21.32 (3) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.58/21.32 all_56_14 & $i(all_56_14))
% 142.58/21.32 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (5) ~ (e3 = e1)
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | BETA: splitting (3) gives:
% 142.58/21.32 |
% 142.58/21.32 | Case 1:
% 142.58/21.32 | |
% 142.58/21.32 | | (6) all_56_15 = e1 & op(e0, e0) = e1
% 142.58/21.32 | |
% 142.58/21.32 | | ALPHA: (6) implies:
% 142.58/21.32 | | (7) op(e0, e0) = e1
% 142.58/21.32 | |
% 142.58/21.32 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #732.
% 142.58/21.32 | |
% 142.58/21.32 | Case 2:
% 142.58/21.32 | |
% 142.58/21.32 | | (8) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.58/21.32 | |
% 142.58/21.32 | | ALPHA: (8) implies:
% 142.58/21.32 | | (9) ~ (all_56_14 = e0)
% 142.58/21.32 | | (10) op(e0, e1) = all_56_14
% 142.58/21.32 | |
% 142.58/21.32 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #973.
% 142.58/21.32 | |
% 142.58/21.32 | End of split
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #665 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) ~ (e2 = e1)
% 142.58/21.32 (2) op(e0, e0) = e3
% 142.58/21.32 (3) ~ (all_52_7 = e0)
% 142.58/21.32 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.32 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.32 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.32 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.32 (6) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.32 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.32 (7) ~ (e1 = e0)
% 142.58/21.32 (8) ~ (e2 = e0)
% 142.58/21.32 (9) ~ (e3 = e2)
% 142.58/21.32 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (11) ~ (e3 = e1)
% 142.58/21.32 (12) all_57_13 = e3
% 142.58/21.32 (13) op(e0, e2) = all_52_7
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | BETA: splitting (6) gives:
% 142.58/21.32 |
% 142.58/21.32 | Case 1:
% 142.58/21.32 | |
% 142.58/21.32 | | (14) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.32 | |
% 142.58/21.32 | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (14) are
% 142.58/21.32 | | inconsistent by sub-proof #669.
% 142.58/21.32 | |
% 142.58/21.32 | Case 2:
% 142.58/21.32 | |
% 142.58/21.32 | | (15) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.58/21.32 | | e0)
% 142.58/21.32 | |
% 142.58/21.32 | | BETA: splitting (15) gives:
% 142.58/21.32 | |
% 142.58/21.32 | | Case 1:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (16) all_57_13 = e0 & op(e0, e2) = e0
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (16) implies:
% 142.58/21.32 | | | (17) op(e0, e2) = e0
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (3), (10), (13), (17) are inconsistent by sub-proof #977.
% 142.58/21.32 | | |
% 142.58/21.32 | | Case 2:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (18) all_57_14 = e0 & op(e0, e1) = e0
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (18) implies:
% 142.58/21.32 | | | (19) all_57_14 = e0
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (1), (2), (4), (5), (7), (8), (9), (10), (11), (12), (19) are
% 142.58/21.32 | | | inconsistent by sub-proof #666.
% 142.58/21.32 | | |
% 142.58/21.32 | | End of split
% 142.58/21.32 | |
% 142.58/21.32 | End of split
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #666 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) all_57_14 = e0
% 142.58/21.32 (2) ~ (e2 = e1)
% 142.58/21.32 (3) op(e0, e0) = e3
% 142.58/21.32 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.32 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.32 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.32 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.32 (6) ~ (e1 = e0)
% 142.58/21.32 (7) ~ (e2 = e0)
% 142.58/21.32 (8) ~ (e3 = e2)
% 142.58/21.32 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (10) ~ (e3 = e1)
% 142.58/21.32 (11) all_57_13 = e3
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | BETA: splitting (4) gives:
% 142.58/21.32 |
% 142.58/21.32 | Case 1:
% 142.58/21.32 | |
% 142.58/21.32 | | (12) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.58/21.32 | | e1)
% 142.58/21.32 | |
% 142.58/21.32 | | BETA: splitting (12) gives:
% 142.58/21.32 | |
% 142.58/21.32 | | Case 1:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (13) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (13) implies:
% 142.58/21.32 | | | (14) all_57_12 = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (1), (2), (3), (5), (7), (8), (9), (11), (14) are inconsistent
% 142.58/21.32 | | | by sub-proof #966.
% 142.58/21.32 | | |
% 142.58/21.32 | | Case 2:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (15) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (10), (11), (15) are inconsistent by sub-proof #1014.
% 142.58/21.32 | | |
% 142.58/21.32 | | End of split
% 142.58/21.32 | |
% 142.58/21.32 | Case 2:
% 142.58/21.32 | |
% 142.58/21.32 | | (16) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.58/21.32 | | e1)
% 142.58/21.32 | |
% 142.58/21.32 | | REF_CLOSE: (1), (3), (6), (9), (10), (16) are inconsistent by sub-proof
% 142.58/21.32 | | #667.
% 142.58/21.32 | |
% 142.58/21.32 | End of split
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #667 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) all_57_14 = e0
% 142.58/21.32 (2) op(e0, e0) = e3
% 142.58/21.32 (3) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.32 (4) ~ (e1 = e0)
% 142.58/21.32 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (6) ~ (e3 = e1)
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | BETA: splitting (3) gives:
% 142.58/21.32 |
% 142.58/21.32 | Case 1:
% 142.58/21.32 | |
% 142.58/21.32 | | (7) all_57_14 = e1 & op(e0, e1) = e1
% 142.58/21.32 | |
% 142.58/21.32 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #668.
% 142.58/21.32 | |
% 142.58/21.32 | Case 2:
% 142.58/21.32 | |
% 142.58/21.32 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 142.58/21.32 | |
% 142.58/21.32 | | ALPHA: (8) implies:
% 142.58/21.32 | | (9) op(e0, e0) = e1
% 142.58/21.32 | |
% 142.58/21.32 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #732.
% 142.58/21.32 | |
% 142.58/21.32 | End of split
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #668 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) all_57_14 = e1 & op(e0, e1) = e1
% 142.58/21.32 (2) all_57_14 = e0
% 142.58/21.32 (3) ~ (e1 = e0)
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | ALPHA: (1) implies:
% 142.58/21.32 | (4) all_57_14 = e1
% 142.58/21.32 |
% 142.58/21.32 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.32 | (5) e1 = e0
% 142.58/21.32 |
% 142.58/21.32 | REDUCE: (3), (5) imply:
% 142.58/21.32 | (6) $false
% 142.58/21.32 |
% 142.58/21.32 | CLOSE: (6) is inconsistent.
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #669 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.32 (2) ~ (e2 = e1)
% 142.58/21.32 (3) op(e0, e0) = e3
% 142.58/21.32 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.32 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.32 (5) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.32 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.32 (6) ~ (e1 = e0)
% 142.58/21.32 (7) ~ (e2 = e0)
% 142.58/21.32 (8) ~ (e3 = e2)
% 142.58/21.32 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (10) ~ (e3 = e1)
% 142.58/21.32 (11) all_57_13 = e3
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | ALPHA: (1) implies:
% 142.58/21.32 | (12) all_57_12 = e0
% 142.58/21.32 |
% 142.58/21.32 | BETA: splitting (4) gives:
% 142.58/21.32 |
% 142.58/21.32 | Case 1:
% 142.58/21.32 | |
% 142.58/21.32 | | (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.58/21.32 | | e1)
% 142.58/21.32 | |
% 142.58/21.32 | | BETA: splitting (13) gives:
% 142.58/21.32 | |
% 142.58/21.32 | | Case 1:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (14) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (14) implies:
% 142.58/21.32 | | | (15) all_57_12 = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (6), (12), (15) are inconsistent by sub-proof #1002.
% 142.58/21.32 | | |
% 142.58/21.32 | | Case 2:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (16) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (16) implies:
% 142.58/21.32 | | | (17) all_57_13 = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (10), (11), (17) are inconsistent by sub-proof #1001.
% 142.58/21.32 | | |
% 142.58/21.32 | | End of split
% 142.58/21.32 | |
% 142.58/21.32 | Case 2:
% 142.58/21.32 | |
% 142.58/21.32 | | (18) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.58/21.32 | | e1)
% 142.58/21.32 | |
% 142.58/21.32 | | BETA: splitting (18) gives:
% 142.58/21.32 | |
% 142.58/21.32 | | Case 1:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (19) all_57_14 = e1 & op(e0, e1) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (19) implies:
% 142.58/21.32 | | | (20) all_57_14 = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | BETA: splitting (5) gives:
% 142.58/21.32 | | |
% 142.58/21.32 | | | Case 1:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | (21) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0,
% 142.58/21.32 | | | | e2) = e2)
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | BETA: splitting (21) gives:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | Case 1:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | (22) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | ALPHA: (22) implies:
% 142.58/21.32 | | | | | (23) all_57_12 = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REF_CLOSE: (7), (12), (23) are inconsistent by sub-proof #1025.
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | Case 2:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | (24) all_57_13 = e2 & op(e0, e2) = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REF_CLOSE: (8), (11), (24) are inconsistent by sub-proof #969.
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | End of split
% 142.58/21.32 | | | |
% 142.58/21.32 | | | Case 2:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | (25) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0,
% 142.58/21.32 | | | | e0) = e2)
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | BETA: splitting (25) gives:
% 142.58/21.32 | | | |
% 142.58/21.32 | | | | Case 1:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | (26) all_57_14 = e2 & op(e0, e1) = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | ALPHA: (26) implies:
% 142.58/21.32 | | | | | (27) all_57_14 = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REF_CLOSE: (2), (20), (27) are inconsistent by sub-proof #1048.
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | Case 2:
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | (28) all_57_15 = e2 & op(e0, e0) = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | ALPHA: (28) implies:
% 142.58/21.32 | | | | | (29) op(e0, e0) = e2
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | | REF_CLOSE: (3), (8), (9), (29) are inconsistent by sub-proof #1066.
% 142.58/21.32 | | | | |
% 142.58/21.32 | | | | End of split
% 142.58/21.32 | | | |
% 142.58/21.32 | | | End of split
% 142.58/21.32 | | |
% 142.58/21.32 | | Case 2:
% 142.58/21.32 | | |
% 142.58/21.32 | | | (30) all_57_15 = e1 & op(e0, e0) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | ALPHA: (30) implies:
% 142.58/21.32 | | | (31) op(e0, e0) = e1
% 142.58/21.32 | | |
% 142.58/21.32 | | | REF_CLOSE: (3), (9), (10), (31) are inconsistent by sub-proof #732.
% 142.58/21.32 | | |
% 142.58/21.32 | | End of split
% 142.58/21.32 | |
% 142.58/21.32 | End of split
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #670 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.32 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.32 (2) op(e3, e2) = all_56_0
% 142.58/21.32 (3) op(e3, e2) = e3
% 142.58/21.32 (4) ~ (all_56_0 = e3)
% 142.58/21.32
% 142.58/21.32 Begin of proof
% 142.58/21.32 |
% 142.58/21.32 | GROUND_INST: instantiating (1) with e3, all_56_0, e2, e3, simplifying with
% 142.58/21.32 | (2), (3) gives:
% 142.58/21.32 | (5) all_56_0 = e3
% 142.58/21.32 |
% 142.58/21.32 | REDUCE: (4), (5) imply:
% 142.58/21.32 | (6) $false
% 142.58/21.32 |
% 142.58/21.32 | CLOSE: (6) is inconsistent.
% 142.58/21.32 |
% 142.58/21.32 End of proof
% 142.58/21.32
% 142.58/21.32 Sub-proof #671 shows that the following formulas are inconsistent:
% 142.58/21.32 ----------------------------------------------------------------
% 142.58/21.32 (1) ~ (all_4_2 = e0)
% 142.58/21.32 (2) op(e0, e0) = e3
% 142.58/21.32 (3) op(e0, e3) = all_52_3
% 142.58/21.32 (4) op(e0, e1) = e0
% 142.58/21.32 (5) all_54_10 = e1 | all_54_10 = e0
% 142.58/21.32 (6) op(e1, e1) = all_4_2
% 142.58/21.33 (7) ~ (e2 = e0)
% 142.58/21.33 (8) ~ (e3 = e2)
% 142.58/21.33 (9) ~ (all_4_2 = e2)
% 142.58/21.33 (10) all_54_10 = all_4_2
% 142.58/21.33 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.33 (12) ~ (all_52_3 = e0)
% 142.58/21.33 (13) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.58/21.33 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.58/21.33 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.58/21.33 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.58/21.33 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.58/21.33 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 142.58/21.33 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 142.58/21.33 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3) =
% 142.58/21.33 all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) | (
% 142.58/21.33 ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))
% 142.58/21.33 (14) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.33 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.33 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.58/21.33 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.58/21.33 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.58/21.33 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.58/21.33 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.58/21.33 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.58/21.33 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.58/21.33 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.58/21.33 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.58/21.33 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.58/21.33 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.58/21.33 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.58/21.33 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.58/21.33 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.33 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.58/21.33 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.58/21.33 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.33 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.33 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.33 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.58/21.33 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.33 $i(all_56_14))))
% 142.58/21.33 (15) op(e3, e3) = e0
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | ALPHA: (13) implies:
% 142.58/21.33 | (16) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.58/21.33 | = all_56_15 & $i(all_56_15))
% 142.58/21.33 |
% 142.58/21.33 | BETA: splitting (5) gives:
% 142.58/21.33 |
% 142.58/21.33 | Case 1:
% 142.58/21.33 | |
% 142.58/21.33 | | (17) all_54_10 = e1
% 142.58/21.33 | |
% 142.58/21.33 | | COMBINE_EQS: (10), (17) imply:
% 142.58/21.33 | | (18) all_4_2 = e1
% 142.58/21.33 | |
% 142.58/21.33 | | SIMP: (18) implies:
% 142.58/21.33 | | (19) all_4_2 = e1
% 142.58/21.33 | |
% 142.58/21.33 | | REDUCE: (9), (19) imply:
% 142.58/21.33 | | (20) ~ (e2 = e1)
% 142.58/21.33 | |
% 142.58/21.33 | | SIMP: (20) implies:
% 142.58/21.33 | | (21) ~ (e2 = e1)
% 142.58/21.33 | |
% 142.58/21.33 | | REDUCE: (1), (19) imply:
% 142.58/21.33 | | (22) ~ (e1 = e0)
% 142.58/21.33 | |
% 142.58/21.33 | | REDUCE: (6), (19) imply:
% 142.58/21.33 | | (23) op(e1, e1) = e1
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (2), (3), (4), (7), (8), (11), (12), (14), (15), (16), (21),
% 142.58/21.33 | | (22), (23) are inconsistent by sub-proof #672.
% 142.58/21.33 | |
% 142.58/21.33 | Case 2:
% 142.58/21.33 | |
% 142.58/21.33 | | (24) all_54_10 = e0
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (1), (10), (24) are inconsistent by sub-proof #899.
% 142.58/21.33 | |
% 142.58/21.33 | End of split
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #672 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) ~ (e2 = e1)
% 142.58/21.33 (2) op(e0, e0) = e3
% 142.58/21.33 (3) op(e0, e3) = all_52_3
% 142.58/21.33 (4) op(e0, e1) = e0
% 142.58/21.33 (5) op(e1, e1) = e1
% 142.58/21.33 (6) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 142.58/21.33 all_56_15 & $i(all_56_15))
% 142.58/21.33 (7) ~ (e1 = e0)
% 142.58/21.33 (8) ~ (e2 = e0)
% 142.58/21.33 (9) ~ (e3 = e2)
% 142.58/21.33 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.33 (11) ~ (all_52_3 = e0)
% 142.58/21.33 (12) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.33 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.33 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.58/21.33 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.58/21.33 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.58/21.33 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.58/21.33 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.58/21.33 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.58/21.33 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.58/21.33 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.58/21.33 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.58/21.33 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.58/21.33 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.58/21.33 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.58/21.33 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.58/21.33 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.33 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.58/21.33 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.58/21.33 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.33 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.33 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.33 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.58/21.33 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.33 $i(all_56_14))))
% 142.58/21.33 (13) op(e3, e3) = e0
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | BETA: splitting (6) gives:
% 142.58/21.33 |
% 142.58/21.33 | Case 1:
% 142.58/21.33 | |
% 142.58/21.33 | | (14) all_56_10 = e0 & op(e0, e3) = e0
% 142.58/21.33 | |
% 142.58/21.33 | | ALPHA: (14) implies:
% 142.58/21.33 | | (15) op(e0, e3) = e0
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (3), (10), (11), (15) are inconsistent by sub-proof #986.
% 142.58/21.33 | |
% 142.58/21.33 | Case 2:
% 142.58/21.33 | |
% 142.58/21.33 | | (16) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 142.58/21.33 | |
% 142.58/21.33 | | ALPHA: (16) implies:
% 142.58/21.33 | | (17) ~ (all_56_15 = e3)
% 142.58/21.33 | |
% 142.58/21.33 | | BETA: splitting (12) gives:
% 142.58/21.33 | |
% 142.58/21.33 | | Case 1:
% 142.58/21.33 | | |
% 142.58/21.33 | | | (18) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 142.58/21.33 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.58/21.33 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 142.58/21.33 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 142.58/21.33 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 142.58/21.33 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.58/21.33 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 142.58/21.33 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.58/21.33 | | |
% 142.58/21.33 | | | REF_CLOSE: (7), (8), (10), (13), (18) are inconsistent by sub-proof #752.
% 142.58/21.33 | | |
% 142.58/21.33 | | Case 2:
% 142.58/21.33 | | |
% 142.58/21.33 | | | (19) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.58/21.33 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.58/21.33 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 142.58/21.33 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 142.58/21.33 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 142.58/21.33 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.58/21.33 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 142.58/21.33 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.58/21.33 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.58/21.33 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.33 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.58/21.33 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.58/21.33 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.33 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.58/21.33 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.58/21.33 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.58/21.33 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.58/21.33 | | |
% 142.58/21.33 | | | BETA: splitting (19) gives:
% 142.58/21.33 | | |
% 142.58/21.33 | | | Case 1:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | (20) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.58/21.33 | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.58/21.33 | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 142.58/21.33 | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 142.58/21.33 | | | | op(e1, e1) = e2 & $i(all_56_4))
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | BETA: splitting (20) gives:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | Case 1:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | (21) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.58/21.33 | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.58/21.33 | | | | | $i(all_56_2)
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | ALPHA: (21) implies:
% 142.58/21.33 | | | | | (22) all_56_15 = e3
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | REDUCE: (17), (22) imply:
% 142.58/21.33 | | | | | (23) $false
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | CLOSE: (23) is inconsistent.
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | Case 2:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | (24) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2,
% 142.58/21.33 | | | | | e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.58/21.33 | | | | | $i(all_56_4)
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | ALPHA: (24) implies:
% 142.58/21.33 | | | | | (25) op(e1, e1) = e2
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | REF_CLOSE: (1), (5), (10), (25) are inconsistent by sub-proof #1085.
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | End of split
% 142.58/21.33 | | | |
% 142.58/21.33 | | | Case 2:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | (26) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.58/21.33 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.58/21.33 | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.58/21.33 | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 142.58/21.33 | | | | op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.33 | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 142.58/21.33 | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 142.58/21.33 | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.58/21.33 | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.58/21.33 | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 142.58/21.33 | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 142.58/21.33 | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 142.58/21.33 | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.58/21.33 | | | | all_56_14 & $i(all_56_14))))
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | BETA: splitting (26) gives:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | Case 1:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | (27) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.58/21.33 | | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.58/21.33 | | | | | $i(all_56_7)
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | ALPHA: (27) implies:
% 142.58/21.33 | | | | | (28) op(e1, e1) = e2
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | REF_CLOSE: (1), (5), (10), (28) are inconsistent by sub-proof #1085.
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | Case 2:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | (29) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.58/21.33 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.58/21.33 | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.58/21.33 | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.33 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.58/21.33 | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.58/21.33 | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.58/21.33 | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 142.58/21.33 | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.33 | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.58/21.33 | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.33 | | | | | e1) = all_56_14 & $i(all_56_14))))
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | BETA: splitting (29) gives:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | Case 1:
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | (30) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 142.58/21.33 | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.58/21.33 | | | | | | $i(all_56_5)
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | ALPHA: (30) implies:
% 142.58/21.33 | | | | | | (31) op(e0, e0) = e2
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | REF_CLOSE: (2), (9), (10), (31) are inconsistent by sub-proof #1066.
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | Case 2:
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | (32) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.58/21.33 | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.33 | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 =
% 142.58/21.33 | | | | | | e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 142.58/21.33 | | | | | | e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 142.58/21.33 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.58/21.33 | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8))
% 142.58/21.33 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.58/21.33 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.33 | | | | | | $i(all_56_14)))
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | ALPHA: (32) implies:
% 142.58/21.33 | | | | | | (33) op(e0, e0) = all_56_15
% 142.58/21.33 | | | | | | (34) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.33 | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 142.58/21.33 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.58/21.33 | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 142.58/21.33 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.58/21.33 | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.58/21.33 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.58/21.33 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | BETA: splitting (34) gives:
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | Case 1:
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | (35) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.33 | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.58/21.33 | | | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.58/21.33 | | | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.58/21.33 | | | | | | | all_56_12 & $i(all_56_12))
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | BETA: splitting (35) gives:
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | Case 1:
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | (36) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.33 | | | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | ALPHA: (36) implies:
% 142.58/21.33 | | | | | | | | (37) all_56_15 = e3
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REDUCE: (17), (37) imply:
% 142.58/21.33 | | | | | | | | (38) $false
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | CLOSE: (38) is inconsistent.
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | Case 2:
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | (39) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.58/21.33 | | | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | ALPHA: (39) implies:
% 142.58/21.33 | | | | | | | | (40) all_56_15 = e2
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REDUCE: (17), (40) imply:
% 142.58/21.33 | | | | | | | | (41) ~ (e3 = e2)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REDUCE: (33), (40) imply:
% 142.58/21.33 | | | | | | | | (42) op(e0, e0) = e2
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REF_CLOSE: (2), (9), (10), (42) are inconsistent by sub-proof
% 142.58/21.33 | | | | | | | | #1066.
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | End of split
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | Case 2:
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | (43) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.58/21.33 | | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8))
% 142.58/21.33 | | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.58/21.33 | | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.33 | | | | | | | $i(all_56_14))
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | BETA: splitting (43) gives:
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | Case 1:
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | (44) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.58/21.33 | | | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | ALPHA: (44) implies:
% 142.58/21.33 | | | | | | | | (45) all_56_15 = e1
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REDUCE: (17), (45) imply:
% 142.58/21.33 | | | | | | | | (46) ~ (e3 = e1)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | SIMP: (46) implies:
% 142.58/21.33 | | | | | | | | (47) ~ (e3 = e1)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REDUCE: (33), (45) imply:
% 142.58/21.33 | | | | | | | | (48) op(e0, e0) = e1
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REF_CLOSE: (2), (10), (47), (48) are inconsistent by sub-proof
% 142.58/21.33 | | | | | | | | #732.
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | Case 2:
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | (49) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.58/21.33 | | | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | ALPHA: (49) implies:
% 142.58/21.33 | | | | | | | | (50) ~ (all_56_14 = e0)
% 142.58/21.33 | | | | | | | | (51) op(e0, e1) = all_56_14
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | | REF_CLOSE: (4), (10), (50), (51) are inconsistent by sub-proof
% 142.58/21.33 | | | | | | | | #973.
% 142.58/21.33 | | | | | | | |
% 142.58/21.33 | | | | | | | End of split
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | End of split
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | End of split
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | End of split
% 142.58/21.33 | | | |
% 142.58/21.33 | | | End of split
% 142.58/21.33 | | |
% 142.58/21.33 | | End of split
% 142.58/21.33 | |
% 142.58/21.33 | End of split
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #673 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) all_54_14 = all_52_11
% 142.58/21.33 (2) all_54_14 = e1
% 142.58/21.33 (3) ~ (all_52_11 = e1)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.33 | (4) all_52_11 = e1
% 142.58/21.33 |
% 142.58/21.33 | SIMP: (4) implies:
% 142.58/21.33 | (5) all_52_11 = e1
% 142.58/21.33 |
% 142.58/21.33 | REDUCE: (3), (5) imply:
% 142.58/21.33 | (6) $false
% 142.58/21.33 |
% 142.58/21.33 | CLOSE: (6) is inconsistent.
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #674 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.33 (2) all_57_12 = e1
% 142.58/21.33 (3) ~ (e2 = e1)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | ALPHA: (1) implies:
% 142.58/21.33 | (4) all_57_12 = e2
% 142.58/21.33 |
% 142.58/21.33 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.33 | (5) e2 = e1
% 142.58/21.33 |
% 142.58/21.33 | REDUCE: (3), (5) imply:
% 142.58/21.33 | (6) $false
% 142.58/21.33 |
% 142.58/21.33 | CLOSE: (6) is inconsistent.
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #675 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) all_54_7 = all_52_13
% 142.58/21.33 (2) ~ (all_52_9 = all_52_13)
% 142.58/21.33 (3) all_54_7 = e1 | all_54_7 = e0
% 142.58/21.33 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.33 (5) op(e2, e1) = e0
% 142.58/21.33 (6) op(e2, e1) = all_52_9
% 142.58/21.33 (7) ~ (all_52_13 = e1)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | BETA: splitting (3) gives:
% 142.58/21.33 |
% 142.58/21.33 | Case 1:
% 142.58/21.33 | |
% 142.58/21.33 | | (8) all_54_7 = e1
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (1), (7), (8) are inconsistent by sub-proof #676.
% 142.58/21.33 | |
% 142.58/21.33 | Case 2:
% 142.58/21.33 | |
% 142.58/21.33 | | (9) all_54_7 = e0
% 142.58/21.33 | |
% 142.58/21.33 | | COMBINE_EQS: (1), (9) imply:
% 142.58/21.33 | | (10) all_52_13 = e0
% 142.58/21.33 | |
% 142.58/21.33 | | SIMP: (10) implies:
% 142.58/21.33 | | (11) all_52_13 = e0
% 142.58/21.33 | |
% 142.58/21.33 | | REDUCE: (2), (11) imply:
% 142.58/21.33 | | (12) ~ (all_52_9 = e0)
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (4), (5), (6), (12) are inconsistent by sub-proof #1091.
% 142.58/21.33 | |
% 142.58/21.33 | End of split
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #676 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) all_54_7 = all_52_13
% 142.58/21.33 (2) all_54_7 = e1
% 142.58/21.33 (3) ~ (all_52_13 = e1)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.33 | (4) all_52_13 = e1
% 142.58/21.33 |
% 142.58/21.33 | SIMP: (4) implies:
% 142.58/21.33 | (5) all_52_13 = e1
% 142.58/21.33 |
% 142.58/21.33 | REDUCE: (3), (5) imply:
% 142.58/21.33 | (6) $false
% 142.58/21.33 |
% 142.58/21.33 | CLOSE: (6) is inconsistent.
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #677 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) all_54_4 = all_52_1
% 142.58/21.33 (2) all_54_4 = e2
% 142.58/21.33 (3) ~ (all_52_1 = e2)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.33 | (4) all_52_1 = e2
% 142.58/21.33 |
% 142.58/21.33 | SIMP: (4) implies:
% 142.58/21.33 | (5) all_52_1 = e2
% 142.58/21.33 |
% 142.58/21.33 | REDUCE: (3), (5) imply:
% 142.58/21.33 | (6) $false
% 142.58/21.33 |
% 142.58/21.33 | CLOSE: (6) is inconsistent.
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #678 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) ~ (all_52_1 = e2)
% 142.58/21.33 (2) ~ (e2 = e1)
% 142.58/21.33 (3) ~ (e3 = e0)
% 142.58/21.33 (4) op(e1, e1) = e1
% 142.58/21.33 (5) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.58/21.33 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.33 (6) op(e2, e3) = all_52_1
% 142.58/21.33 (7) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.33 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.33 (8) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.33 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.33 (9) all_57_11 = e2
% 142.58/21.33 (10) ~ (e1 = e0)
% 142.58/21.33 (11) ~ (e2 = e0)
% 142.58/21.33 (12) ~ (e3 = e2)
% 142.58/21.33 (13) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.58/21.33 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.58/21.33 (14) all_57_6 = e1
% 142.58/21.33 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.33 (16) ~ (e3 = e1)
% 142.58/21.33 (17) all_57_0 = e0
% 142.58/21.33 (18) op(e3, e3) = e0
% 142.58/21.33 (19) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.58/21.33 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | BETA: splitting (13) gives:
% 142.58/21.33 |
% 142.58/21.33 | Case 1:
% 142.58/21.33 | |
% 142.58/21.33 | | (20) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.58/21.33 | | e3)
% 142.58/21.33 | |
% 142.58/21.33 | | BETA: splitting (20) gives:
% 142.58/21.33 | |
% 142.58/21.33 | | Case 1:
% 142.58/21.33 | | |
% 142.58/21.33 | | | (21) all_57_6 = e3 & op(e1, e3) = e3
% 142.58/21.33 | | |
% 142.58/21.33 | | | REF_CLOSE: (14), (16), (21) are inconsistent by sub-proof #1099.
% 142.58/21.33 | | |
% 142.58/21.33 | | Case 2:
% 142.58/21.33 | | |
% 142.58/21.33 | | | (22) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.33 | | |
% 142.58/21.33 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.58/21.33 | | | (15), (16), (17), (18), (19), (22) are inconsistent by
% 142.58/21.33 | | | sub-proof #679.
% 142.58/21.33 | | |
% 142.58/21.33 | | End of split
% 142.58/21.33 | |
% 142.58/21.33 | Case 2:
% 142.58/21.33 | |
% 142.58/21.33 | | (23) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.58/21.33 | | e3)
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (4), (9), (12), (15), (16), (23) are inconsistent by sub-proof
% 142.58/21.33 | | #1054.
% 142.58/21.33 | |
% 142.58/21.33 | End of split
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #679 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) ~ (all_52_1 = e2)
% 142.58/21.33 (2) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.33 (3) ~ (e2 = e1)
% 142.58/21.33 (4) ~ (e3 = e0)
% 142.58/21.33 (5) op(e1, e1) = e1
% 142.58/21.33 (6) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.58/21.33 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.33 (7) op(e2, e3) = all_52_1
% 142.58/21.33 (8) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.33 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.33 (9) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.33 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.33 (10) all_57_11 = e2
% 142.58/21.33 (11) ~ (e1 = e0)
% 142.58/21.33 (12) ~ (e2 = e0)
% 142.58/21.33 (13) ~ (e3 = e2)
% 142.58/21.33 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.33 (15) ~ (e3 = e1)
% 142.58/21.33 (16) all_57_0 = e0
% 142.58/21.33 (17) op(e3, e3) = e0
% 142.58/21.33 (18) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.58/21.33 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | ALPHA: (2) implies:
% 142.58/21.33 | (19) all_57_7 = e3
% 142.58/21.33 |
% 142.58/21.33 | BETA: splitting (6) gives:
% 142.58/21.33 |
% 142.58/21.33 | Case 1:
% 142.58/21.33 | |
% 142.58/21.33 | | (20) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 142.58/21.33 | | e0)
% 142.58/21.33 | |
% 142.58/21.33 | | BETA: splitting (20) gives:
% 142.58/21.33 | |
% 142.58/21.33 | | Case 1:
% 142.58/21.33 | | |
% 142.58/21.33 | | | (21) all_57_6 = e0 & op(e1, e3) = e0
% 142.58/21.33 | | |
% 142.58/21.33 | | | ALPHA: (21) implies:
% 142.58/21.33 | | | (22) all_57_6 = e0
% 142.58/21.33 | | |
% 142.58/21.33 | | | BETA: splitting (18) gives:
% 142.58/21.33 | | |
% 142.58/21.33 | | | Case 1:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | (23) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3)
% 142.58/21.33 | | | | = e2)
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | REF_CLOSE: (1), (7), (12), (14), (17), (23) are inconsistent by
% 142.58/21.33 | | | | sub-proof #707.
% 142.58/21.33 | | | |
% 142.58/21.33 | | | Case 2:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | (24) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3)
% 142.58/21.33 | | | | = e2)
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | BETA: splitting (24) gives:
% 142.58/21.33 | | | |
% 142.58/21.33 | | | | Case 1:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | (25) all_57_6 = e2 & op(e1, e3) = e2
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | ALPHA: (25) implies:
% 142.58/21.33 | | | | | (26) all_57_6 = e2
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | BETA: splitting (6) gives:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | Case 1:
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | BETA: splitting (20) gives:
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | Case 1:
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | REF_CLOSE: (12), (21), (26) are inconsistent by sub-proof #994.
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | Case 2:
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | (27) all_57_7 = e0 & op(e1, e2) = e0
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | | REF_CLOSE: (4), (19), (27) are inconsistent by sub-proof #1061.
% 142.58/21.33 | | | | | | |
% 142.58/21.33 | | | | | | End of split
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | Case 2:
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | (28) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1,
% 142.58/21.33 | | | | | | e0) = e0)
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | | REF_CLOSE: (5), (10), (11), (12), (14), (28) are inconsistent by
% 142.58/21.33 | | | | | | sub-proof #680.
% 142.58/21.33 | | | | | |
% 142.58/21.33 | | | | | End of split
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | Case 2:
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | (29) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | ALPHA: (29) implies:
% 142.58/21.33 | | | | | (30) all_57_12 = e2
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | | REF_CLOSE: (3), (4), (8), (9), (11), (13), (14), (15), (16), (17),
% 142.58/21.33 | | | | | (22), (30) are inconsistent by sub-proof #771.
% 142.58/21.33 | | | | |
% 142.58/21.33 | | | | End of split
% 142.58/21.33 | | | |
% 142.58/21.33 | | | End of split
% 142.58/21.33 | | |
% 142.58/21.33 | | Case 2:
% 142.58/21.33 | | |
% 142.58/21.33 | | | (31) all_57_7 = e0 & op(e1, e2) = e0
% 142.58/21.33 | | |
% 142.58/21.33 | | | REF_CLOSE: (4), (19), (31) are inconsistent by sub-proof #1061.
% 142.58/21.33 | | |
% 142.58/21.33 | | End of split
% 142.58/21.33 | |
% 142.58/21.33 | Case 2:
% 142.58/21.33 | |
% 142.58/21.33 | | (32) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.58/21.33 | | e0)
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (5), (10), (11), (12), (14), (32) are inconsistent by sub-proof
% 142.58/21.33 | | #991.
% 142.58/21.33 | |
% 142.58/21.33 | End of split
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #680 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.33 (1) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.33 (2) op(e1, e1) = e1
% 142.58/21.33 (3) all_57_11 = e2
% 142.58/21.33 (4) ~ (e1 = e0)
% 142.58/21.33 (5) ~ (e2 = e0)
% 142.58/21.33 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.33 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.33
% 142.58/21.33 Begin of proof
% 142.58/21.33 |
% 142.58/21.33 | BETA: splitting (1) gives:
% 142.58/21.33 |
% 142.58/21.33 | Case 1:
% 142.58/21.33 | |
% 142.58/21.33 | | (7) all_57_8 = e0 & op(e1, e1) = e0
% 142.58/21.33 | |
% 142.58/21.33 | | ALPHA: (7) implies:
% 142.58/21.33 | | (8) op(e1, e1) = e0
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (2), (4), (6), (8) are inconsistent by sub-proof #1089.
% 142.58/21.33 | |
% 142.58/21.33 | Case 2:
% 142.58/21.33 | |
% 142.58/21.33 | | (9) all_57_11 = e0 & op(e1, e0) = e0
% 142.58/21.33 | |
% 142.58/21.33 | | ALPHA: (9) implies:
% 142.58/21.33 | | (10) all_57_11 = e0
% 142.58/21.33 | |
% 142.58/21.33 | | REF_CLOSE: (3), (5), (10) are inconsistent by sub-proof #996.
% 142.58/21.33 | |
% 142.58/21.33 | End of split
% 142.58/21.33 |
% 142.58/21.33 End of proof
% 142.58/21.33
% 142.58/21.33 Sub-proof #681 shows that the following formulas are inconsistent:
% 142.58/21.33 ----------------------------------------------------------------
% 142.58/21.34 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.34 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.34 (2) ~ (all_52_4 = e0)
% 142.58/21.34 (3) ~ (e2 = e1)
% 142.58/21.34 (4) ~ (e3 = e0)
% 142.58/21.34 (5) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.34 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.34 (6) ~ (e1 = e0)
% 142.58/21.34 (7) op(e2, e2) = e2
% 142.58/21.34 (8) op(e3, e2) = all_52_4
% 142.58/21.34 (9) ~ (e2 = e0)
% 142.58/21.34 (10) ~ (e3 = e2)
% 142.58/21.34 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (12) ~ (e3 = e1)
% 142.58/21.34 (13) all_57_7 = e2 & op(e1, e2) = e2
% 142.58/21.34 (14) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.34 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | ALPHA: (13) implies:
% 142.58/21.34 | (15) all_57_7 = e2
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (5) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (16) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.58/21.34 | | e0)
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (2), (7), (8), (9), (11), (16) are inconsistent by sub-proof
% 142.58/21.34 | | #714.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (17) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.58/21.34 | | e0)
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (3), (4), (6), (7), (9), (10), (11), (12), (14), (15), (17)
% 142.58/21.34 | | are inconsistent by sub-proof #682.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #682 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.34 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.34 (2) ~ (e2 = e1)
% 142.58/21.34 (3) all_57_7 = e2
% 142.58/21.34 (4) ~ (e3 = e0)
% 142.58/21.34 (5) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.34 (6) ~ (e1 = e0)
% 142.58/21.34 (7) op(e2, e2) = e2
% 142.58/21.34 (8) ~ (e2 = e0)
% 142.58/21.34 (9) ~ (e3 = e2)
% 142.58/21.34 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (11) ~ (e3 = e1)
% 142.58/21.34 (12) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.34 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (5) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (13) all_57_7 = e0 & op(e1, e2) = e0
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (3), (8), (13) are inconsistent by sub-proof #1017.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (14) all_57_13 = e0 & op(e0, e2) = e0
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (14) implies:
% 142.58/21.34 | | (15) all_57_13 = e0
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (9), (10), (11), (12), (15) are
% 142.58/21.34 | | inconsistent by sub-proof #720.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #683 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) op(e3, e0) = e1
% 142.58/21.34 (2) ( ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) = all_14_1
% 142.58/21.34 & $i(all_14_0) & $i(all_14_1)) | ( ~ (all_14_1 = e2) & op(e3, e0) =
% 142.58/21.34 all_14_1 & $i(all_14_1))
% 142.58/21.34 (3) op(e1, e3) = e2
% 142.58/21.34 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (5) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) = all_28_1
% 142.58/21.34 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e0) =
% 142.58/21.34 all_28_1 & $i(all_28_1))
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (2) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (6) ~ (all_14_0 = e1) & op(all_14_1, e3) = all_14_0 & op(e3, e0) =
% 142.58/21.34 | | all_14_1 & $i(all_14_0) & $i(all_14_1)
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (6) implies:
% 142.58/21.34 | | (7) op(e3, e0) = all_14_1
% 142.58/21.34 | | (8) op(all_14_1, e3) = all_14_0
% 142.58/21.34 | |
% 142.58/21.34 | | GROUND_INST: instantiating (4) with e1, all_14_1, e0, e3, simplifying with
% 142.58/21.34 | | (1), (7) gives:
% 142.58/21.34 | | (9) all_14_1 = e1
% 142.58/21.34 | |
% 142.58/21.34 | | REDUCE: (8), (9) imply:
% 142.58/21.34 | | (10) op(e1, e3) = all_14_0
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (5) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (11) ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.58/21.34 | | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (11) implies:
% 142.58/21.34 | | | (12) ~ (all_28_0 = e2)
% 142.58/21.34 | | | (13) op(e3, e0) = all_28_1
% 142.58/21.34 | | | (14) op(all_28_1, e3) = all_28_0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (1), (3), (4), (10), (12), (13), (14) are inconsistent by
% 142.58/21.34 | | | sub-proof #686.
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (15) ~ (all_28_1 = e1) & op(e3, e0) = all_28_1 & $i(all_28_1)
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (15) implies:
% 142.58/21.34 | | | (16) ~ (all_28_1 = e1)
% 142.58/21.34 | | | (17) op(e3, e0) = all_28_1
% 142.58/21.34 | | |
% 142.58/21.34 | | | GROUND_INST: instantiating (4) with e1, all_28_1, e0, e3, simplifying with
% 142.58/21.34 | | | (1), (17) gives:
% 142.58/21.34 | | | (18) all_28_1 = e1
% 142.58/21.34 | | |
% 142.58/21.34 | | | REDUCE: (16), (18) imply:
% 142.58/21.34 | | | (19) $false
% 142.58/21.34 | | |
% 142.58/21.34 | | | CLOSE: (19) is inconsistent.
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (20) ~ (all_14_1 = e2) & op(e3, e0) = all_14_1 & $i(all_14_1)
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (20) implies:
% 142.58/21.34 | | (21) op(e3, e0) = all_14_1
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (3), (4), (5), (21) are inconsistent by sub-proof #684.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #684 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) op(e3, e0) = e1
% 142.58/21.34 (2) op(e3, e0) = all_14_1
% 142.58/21.34 (3) op(e1, e3) = e2
% 142.58/21.34 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (5) ( ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) = all_28_1
% 142.58/21.34 & $i(all_28_0) & $i(all_28_1)) | ( ~ (all_28_1 = e1) & op(e3, e0) =
% 142.58/21.34 all_28_1 & $i(all_28_1))
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | GROUND_INST: instantiating (4) with e1, all_14_1, e0, e3, simplifying with
% 142.58/21.34 | (1), (2) gives:
% 142.58/21.34 | (6) all_14_1 = e1
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (5) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (7) ~ (all_28_0 = e2) & op(all_28_1, e3) = all_28_0 & op(e3, e0) =
% 142.58/21.34 | | all_28_1 & $i(all_28_0) & $i(all_28_1)
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (7) implies:
% 142.58/21.34 | | (8) ~ (all_28_0 = e2)
% 142.58/21.34 | | (9) op(e3, e0) = all_28_1
% 142.58/21.34 | | (10) op(all_28_1, e3) = all_28_0
% 142.58/21.34 | |
% 142.58/21.34 | | GROUND_INST: instantiating (4) with e1, all_28_1, e0, e3, simplifying with
% 142.58/21.34 | | (1), (9) gives:
% 142.58/21.34 | | (11) all_28_1 = e1
% 142.58/21.34 | |
% 142.58/21.34 | | REDUCE: (10), (11) imply:
% 142.58/21.34 | | (12) op(e1, e3) = all_28_0
% 142.58/21.34 | |
% 142.58/21.34 | | GROUND_INST: instantiating (4) with e2, all_28_0, e3, e1, simplifying with
% 142.58/21.34 | | (3), (12) gives:
% 142.58/21.34 | | (13) all_28_0 = e2
% 142.58/21.34 | |
% 142.58/21.34 | | REDUCE: (8), (13) imply:
% 142.58/21.34 | | (14) $false
% 142.58/21.34 | |
% 142.58/21.34 | | CLOSE: (14) is inconsistent.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (15) ~ (all_28_1 = e1) & op(e3, e0) = all_28_1 & $i(all_28_1)
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (15) implies:
% 142.58/21.34 | | (16) ~ (all_28_1 = e1)
% 142.58/21.34 | | (17) op(e3, e0) = all_28_1
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (4), (16), (17) are inconsistent by sub-proof #685.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #685 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (2) op(e3, e0) = all_28_1
% 142.58/21.34 (3) op(e3, e0) = e1
% 142.58/21.34 (4) ~ (all_28_1 = e1)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | GROUND_INST: instantiating (1) with e1, all_28_1, e0, e3, simplifying with
% 142.58/21.34 | (2), (3) gives:
% 142.58/21.34 | (5) all_28_1 = e1
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (4), (5) imply:
% 142.58/21.34 | (6) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (6) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #686 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) op(e3, e0) = e1
% 142.58/21.34 (2) ~ (all_28_0 = e2)
% 142.58/21.34 (3) op(e3, e0) = all_28_1
% 142.58/21.34 (4) op(e1, e3) = e2
% 142.58/21.34 (5) op(e1, e3) = all_14_0
% 142.58/21.34 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (7) op(all_28_1, e3) = all_28_0
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | GROUND_INST: instantiating (6) with e2, all_14_0, e3, e1, simplifying with
% 142.58/21.34 | (4), (5) gives:
% 142.58/21.34 | (8) all_14_0 = e2
% 142.58/21.34 |
% 142.58/21.34 | GROUND_INST: instantiating (6) with e1, all_28_1, e0, e3, simplifying with
% 142.58/21.34 | (1), (3) gives:
% 142.58/21.34 | (9) all_28_1 = e1
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (7), (9) imply:
% 142.58/21.34 | (10) op(e1, e3) = all_28_0
% 142.58/21.34 |
% 142.58/21.34 | GROUND_INST: instantiating (6) with e2, all_28_0, e3, e1, simplifying with
% 142.58/21.34 | (4), (10) gives:
% 142.58/21.34 | (11) all_28_0 = e2
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (2), (11) imply:
% 142.58/21.34 | (12) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (12) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #687 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) ~ (e2 = e1)
% 142.58/21.34 (2) op(e0, e0) = e3
% 142.58/21.34 (3) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.58/21.34 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.34 (4) ~ (e3 = e0)
% 142.58/21.34 (5) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.58/21.34 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.34 (6) ~ (e1 = e0)
% 142.58/21.34 (7) ~ (e2 = e0)
% 142.58/21.34 (8) ~ (e3 = e2)
% 142.58/21.34 (9) all_57_10 = e3
% 142.58/21.34 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (11) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.58/21.34 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.34 (12) ~ (e3 = e1)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (5) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (13) all_57_9 = e0 & op(e3, e0) = e0
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (13) implies:
% 142.58/21.34 | | (14) all_57_9 = e0
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (3) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (15) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.58/21.34 | | | e2)
% 142.58/21.34 | | |
% 142.58/21.34 | | | BETA: splitting (15) gives:
% 142.58/21.34 | | |
% 142.58/21.34 | | | Case 1:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | (16) all_57_9 = e2 & op(e3, e0) = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | ALPHA: (16) implies:
% 142.58/21.34 | | | | (17) all_57_9 = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | REF_CLOSE: (7), (14), (17) are inconsistent by sub-proof #1018.
% 142.58/21.34 | | | |
% 142.58/21.34 | | | Case 2:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | (18) all_57_10 = e2 & op(e2, e0) = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | REF_CLOSE: (8), (9), (18) are inconsistent by sub-proof #694.
% 142.58/21.34 | | | |
% 142.58/21.34 | | | End of split
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (19) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0)
% 142.58/21.34 | | | = e2)
% 142.58/21.34 | | |
% 142.58/21.34 | | | BETA: splitting (19) gives:
% 142.58/21.34 | | |
% 142.58/21.34 | | | Case 1:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | (20) all_57_11 = e2 & op(e1, e0) = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | ALPHA: (20) implies:
% 142.58/21.34 | | | | (21) all_57_11 = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | BETA: splitting (11) gives:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | Case 1:
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | (22) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2,
% 142.58/21.34 | | | | | e0) = e1)
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | REF_CLOSE: (6), (9), (12), (14), (22) are inconsistent by sub-proof
% 142.58/21.34 | | | | | #854.
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | Case 2:
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | (23) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 142.58/21.34 | | | | | e0) = e1)
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | REF_CLOSE: (1), (2), (10), (12), (21), (23) are inconsistent by
% 142.58/21.34 | | | | | sub-proof #693.
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | End of split
% 142.58/21.34 | | | |
% 142.58/21.34 | | | Case 2:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | (24) all_57_15 = e2 & op(e0, e0) = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | ALPHA: (24) implies:
% 142.58/21.34 | | | | (25) op(e0, e0) = e2
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | REF_CLOSE: (2), (8), (10), (25) are inconsistent by sub-proof #1066.
% 142.58/21.34 | | | |
% 142.58/21.34 | | | End of split
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (26) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.58/21.34 | | e0)
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (26) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (27) all_57_10 = e0 & op(e2, e0) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (4), (9), (27) are inconsistent by sub-proof #692.
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (28) all_57_11 = e0 & op(e1, e0) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (28) implies:
% 142.58/21.34 | | | (29) all_57_11 = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (1), (2), (3), (6), (7), (8), (9), (10), (11), (12), (29) are
% 142.58/21.34 | | | inconsistent by sub-proof #688.
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #688 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_11 = e0
% 142.58/21.34 (2) ~ (e2 = e1)
% 142.58/21.34 (3) op(e0, e0) = e3
% 142.58/21.34 (4) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) = e2) |
% 142.58/21.34 (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.34 (5) ~ (e1 = e0)
% 142.58/21.34 (6) ~ (e2 = e0)
% 142.58/21.34 (7) ~ (e3 = e2)
% 142.58/21.34 (8) all_57_10 = e3
% 142.58/21.34 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (10) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.58/21.34 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.34 (11) ~ (e3 = e1)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (4) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (12) (all_57_9 = e2 & op(e3, e0) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.58/21.34 | | e2)
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (12) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (13) all_57_9 = e2 & op(e3, e0) = e2
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (13) implies:
% 142.58/21.34 | | | (14) all_57_9 = e2
% 142.58/21.34 | | |
% 142.58/21.34 | | | BETA: splitting (10) gives:
% 142.58/21.34 | | |
% 142.58/21.34 | | | Case 1:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | (15) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 142.58/21.34 | | | | = e1)
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | BETA: splitting (15) gives:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | Case 1:
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | (16) all_57_9 = e1 & op(e3, e0) = e1
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | REF_CLOSE: (2), (14), (16) are inconsistent by sub-proof #691.
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | Case 2:
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | (17) all_57_10 = e1 & op(e2, e0) = e1
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | REF_CLOSE: (8), (11), (17) are inconsistent by sub-proof #929.
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | End of split
% 142.58/21.34 | | | |
% 142.58/21.34 | | | Case 2:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | (18) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 142.58/21.34 | | | | e0) = e1)
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | BETA: splitting (18) gives:
% 142.58/21.34 | | | |
% 142.58/21.34 | | | | Case 1:
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | (19) all_57_11 = e1 & op(e1, e0) = e1
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | ALPHA: (19) implies:
% 142.58/21.34 | | | | | (20) all_57_11 = e1
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | REF_CLOSE: (1), (5), (20) are inconsistent by sub-proof #690.
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | Case 2:
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | (21) all_57_15 = e1 & op(e0, e0) = e1
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | ALPHA: (21) implies:
% 142.58/21.34 | | | | | (22) op(e0, e0) = e1
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | | REF_CLOSE: (3), (9), (11), (22) are inconsistent by sub-proof #732.
% 142.58/21.34 | | | | |
% 142.58/21.34 | | | | End of split
% 142.58/21.34 | | | |
% 142.58/21.34 | | | End of split
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (23) all_57_10 = e2 & op(e2, e0) = e2
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (7), (8), (23) are inconsistent by sub-proof #694.
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (24) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.34 | | e2)
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (3), (6), (7), (9), (24) are inconsistent by sub-proof #689.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #689 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_11 = e0
% 142.58/21.34 (2) op(e0, e0) = e3
% 142.58/21.34 (3) (all_57_11 = e2 & op(e1, e0) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.34 (4) ~ (e2 = e0)
% 142.58/21.34 (5) ~ (e3 = e2)
% 142.58/21.34 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (3) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (7) all_57_11 = e2 & op(e1, e0) = e2
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (7) implies:
% 142.58/21.34 | | (8) all_57_11 = e2
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (4), (8) are inconsistent by sub-proof #996.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (9) all_57_15 = e2 & op(e0, e0) = e2
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (9) implies:
% 142.58/21.34 | | (10) op(e0, e0) = e2
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (2), (5), (6), (10) are inconsistent by sub-proof #1066.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #690 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_11 = e1
% 142.58/21.34 (2) all_57_11 = e0
% 142.58/21.34 (3) ~ (e1 = e0)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.34 | (4) e1 = e0
% 142.58/21.34 |
% 142.58/21.34 | SIMP: (4) implies:
% 142.58/21.34 | (5) e1 = e0
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (3), (5) imply:
% 142.58/21.34 | (6) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (6) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #691 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_9 = e1 & op(e3, e0) = e1
% 142.58/21.34 (2) all_57_9 = e2
% 142.58/21.34 (3) ~ (e2 = e1)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | ALPHA: (1) implies:
% 142.58/21.34 | (4) all_57_9 = e1
% 142.58/21.34 |
% 142.58/21.34 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.34 | (5) e2 = e1
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (3), (5) imply:
% 142.58/21.34 | (6) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (6) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #692 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_10 = e0 & op(e2, e0) = e0
% 142.58/21.34 (2) all_57_10 = e3
% 142.58/21.34 (3) ~ (e3 = e0)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | ALPHA: (1) implies:
% 142.58/21.34 | (4) all_57_10 = e0
% 142.58/21.34 |
% 142.58/21.34 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.34 | (5) e3 = e0
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (3), (5) imply:
% 142.58/21.34 | (6) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (6) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #693 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) ~ (e2 = e1)
% 142.58/21.34 (2) op(e0, e0) = e3
% 142.58/21.34 (3) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.34 (4) all_57_11 = e2
% 142.58/21.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (6) ~ (e3 = e1)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (3) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (7) all_57_11 = e1 & op(e1, e0) = e1
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #862.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (8) implies:
% 142.58/21.34 | | (9) op(e0, e0) = e1
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #732.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #694 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_10 = e2 & op(e2, e0) = e2
% 142.58/21.34 (2) all_57_10 = e3
% 142.58/21.34 (3) ~ (e3 = e2)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | ALPHA: (1) implies:
% 142.58/21.34 | (4) all_57_10 = e2
% 142.58/21.34 |
% 142.58/21.34 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.34 | (5) e3 = e2
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (3), (5) imply:
% 142.58/21.34 | (6) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (6) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #695 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) ~ (all_52_13 = e0)
% 142.58/21.34 (2) ~ (e3 = e0)
% 142.58/21.34 (3) op(e2, e2) = e2
% 142.58/21.34 (4) ~ (e2 = e0)
% 142.58/21.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (6) all_57_5 = e2
% 142.58/21.34 (7) all_57_2 = e3
% 142.58/21.34 (8) op(e2, e0) = all_52_13
% 142.58/21.34 (9) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.34 (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) = e0)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (9) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (10) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.58/21.34 | | e0)
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (10) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (11) all_57_2 = e0 & op(e2, e3) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (11) implies:
% 142.58/21.34 | | | (12) all_57_2 = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (2), (7), (12) are inconsistent by sub-proof #879.
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (13) all_57_3 = e0 & op(e2, e2) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (13) implies:
% 142.58/21.34 | | | (14) op(e2, e2) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (3), (4), (5), (14) are inconsistent by sub-proof #1076.
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (15) (all_57_5 = e0 & op(e2, e1) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.58/21.34 | | e0)
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (15) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (16) all_57_5 = e0 & op(e2, e1) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (16) implies:
% 142.58/21.34 | | | (17) all_57_5 = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (4), (6), (17) are inconsistent by sub-proof #1042.
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (18) all_57_10 = e0 & op(e2, e0) = e0
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (1), (5), (8), (18) are inconsistent by sub-proof #1078.
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #696 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) ~ (e3 = e0)
% 142.58/21.34 (2) op(e2, e2) = e2
% 142.58/21.34 (3) ~ (e2 = e0)
% 142.58/21.34 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (5) (all_57_2 = e0 & op(e2, e3) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 142.58/21.34 (6) all_57_2 = e3
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (5) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (7) all_57_2 = e0 & op(e2, e3) = e0
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (6), (7) are inconsistent by sub-proof #697.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (8) implies:
% 142.58/21.34 | | (9) op(e2, e2) = e0
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1076.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #697 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) all_57_2 = e0 & op(e2, e3) = e0
% 142.58/21.34 (2) all_57_2 = e3
% 142.58/21.34 (3) ~ (e3 = e0)
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | ALPHA: (1) implies:
% 142.58/21.34 | (4) all_57_2 = e0
% 142.58/21.34 |
% 142.58/21.34 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.34 | (5) e3 = e0
% 142.58/21.34 |
% 142.58/21.34 | REDUCE: (3), (5) imply:
% 142.58/21.34 | (6) $false
% 142.58/21.34 |
% 142.58/21.34 | CLOSE: (6) is inconsistent.
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #698 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) ~ (e2 = e1)
% 142.58/21.34 (2) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.34 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.34 (3) ~ (e1 = e0)
% 142.58/21.34 (4) all_57_6 = e2
% 142.58/21.34 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.34 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.34 (6) ~ (e3 = e1)
% 142.58/21.34 (7) op(e3, e3) = e0
% 142.58/21.34 (8) all_57_2 = e3
% 142.58/21.34 (9) all_57_12 = e2
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (2) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 142.58/21.34 | | e1)
% 142.58/21.34 | |
% 142.58/21.34 | | BETA: splitting (10) gives:
% 142.58/21.34 | |
% 142.58/21.34 | | Case 1:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (11) all_57_0 = e1 & op(e3, e3) = e1
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (11) implies:
% 142.58/21.34 | | | (12) op(e3, e3) = e1
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (3), (5), (7), (12) are inconsistent by sub-proof #840.
% 142.58/21.34 | | |
% 142.58/21.34 | | Case 2:
% 142.58/21.34 | | |
% 142.58/21.34 | | | (13) all_57_2 = e1 & op(e2, e3) = e1
% 142.58/21.34 | | |
% 142.58/21.34 | | | ALPHA: (13) implies:
% 142.58/21.34 | | | (14) all_57_2 = e1
% 142.58/21.34 | | |
% 142.58/21.34 | | | REF_CLOSE: (6), (8), (14) are inconsistent by sub-proof #701.
% 142.58/21.34 | | |
% 142.58/21.34 | | End of split
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (15) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 142.58/21.34 | | e1)
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (1), (4), (9), (15) are inconsistent by sub-proof #699.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #699 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.34 (1) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.34 (2) all_57_6 = e2
% 142.58/21.34 (3) ~ (e2 = e1)
% 142.58/21.34 (4) all_57_12 = e2
% 142.58/21.34
% 142.58/21.34 Begin of proof
% 142.58/21.34 |
% 142.58/21.34 | BETA: splitting (1) gives:
% 142.58/21.34 |
% 142.58/21.34 | Case 1:
% 142.58/21.34 | |
% 142.58/21.34 | | (5) all_57_6 = e1 & op(e1, e3) = e1
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (5) implies:
% 142.58/21.34 | | (6) all_57_6 = e1
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #700.
% 142.58/21.34 | |
% 142.58/21.34 | Case 2:
% 142.58/21.34 | |
% 142.58/21.34 | | (7) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.34 | |
% 142.58/21.34 | | ALPHA: (7) implies:
% 142.58/21.34 | | (8) all_57_12 = e1
% 142.58/21.34 | |
% 142.58/21.34 | | REF_CLOSE: (3), (4), (8) are inconsistent by sub-proof #970.
% 142.58/21.34 | |
% 142.58/21.34 | End of split
% 142.58/21.34 |
% 142.58/21.34 End of proof
% 142.58/21.34
% 142.58/21.34 Sub-proof #700 shows that the following formulas are inconsistent:
% 142.58/21.34 ----------------------------------------------------------------
% 142.58/21.35 (1) all_57_6 = e2
% 142.58/21.35 (2) all_57_6 = e1
% 142.58/21.35 (3) ~ (e2 = e1)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.35 | (4) e2 = e1
% 142.58/21.35 |
% 142.58/21.35 | SIMP: (4) implies:
% 142.58/21.35 | (5) e2 = e1
% 142.58/21.35 |
% 142.58/21.35 | REDUCE: (3), (5) imply:
% 142.58/21.35 | (6) $false
% 142.58/21.35 |
% 142.58/21.35 | CLOSE: (6) is inconsistent.
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #701 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) all_57_2 = e3
% 142.58/21.35 (2) all_57_2 = e1
% 142.58/21.35 (3) ~ (e3 = e1)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.35 | (4) e3 = e1
% 142.58/21.35 |
% 142.58/21.35 | SIMP: (4) implies:
% 142.58/21.35 | (5) e3 = e1
% 142.58/21.35 |
% 142.58/21.35 | REDUCE: (3), (5) imply:
% 142.58/21.35 | (6) $false
% 142.58/21.35 |
% 142.58/21.35 | CLOSE: (6) is inconsistent.
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #702 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.35 (2) ~ (e2 = e1)
% 142.58/21.35 (3) op(e0, e0) = e3
% 142.58/21.35 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.35 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.35 (5) all_57_14 = e3
% 142.58/21.35 (6) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.35 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.35 (7) ~ (e1 = e0)
% 142.58/21.35 (8) ~ (e2 = e0)
% 142.58/21.35 (9) ~ (e3 = e2)
% 142.58/21.35 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.35 (11) ~ (e3 = e1)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | ALPHA: (1) implies:
% 142.58/21.35 | (12) all_57_12 = e0
% 142.58/21.35 |
% 142.58/21.35 | BETA: splitting (6) gives:
% 142.58/21.35 |
% 142.58/21.35 | Case 1:
% 142.58/21.35 | |
% 142.58/21.35 | | (13) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.58/21.35 | | e2)
% 142.58/21.35 | |
% 142.58/21.35 | | BETA: splitting (13) gives:
% 142.58/21.35 | |
% 142.58/21.35 | | Case 1:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (14) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (14) implies:
% 142.58/21.35 | | | (15) all_57_12 = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | REF_CLOSE: (8), (12), (15) are inconsistent by sub-proof #1025.
% 142.58/21.35 | | |
% 142.58/21.35 | | Case 2:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (16) all_57_13 = e2 & op(e0, e2) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (16) implies:
% 142.58/21.35 | | | (17) all_57_13 = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | BETA: splitting (4) gives:
% 142.58/21.35 | | |
% 142.58/21.35 | | | Case 1:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 142.58/21.35 | | | | e2) = e1)
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | BETA: splitting (18) gives:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | Case 1:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (19) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | ALPHA: (19) implies:
% 142.58/21.35 | | | | | (20) all_57_12 = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (7), (12), (20) are inconsistent by sub-proof #1002.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | Case 2:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (21) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (2), (17), (21) are inconsistent by sub-proof #1072.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | End of split
% 142.58/21.35 | | | |
% 142.58/21.35 | | | Case 2:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | (22) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 142.58/21.35 | | | | e0) = e1)
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | BETA: splitting (22) gives:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | Case 1:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (23) all_57_14 = e1 & op(e0, e1) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (5), (11), (23) are inconsistent by sub-proof #705.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | Case 2:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (24) all_57_15 = e1 & op(e0, e0) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | ALPHA: (24) implies:
% 142.58/21.35 | | | | | (25) op(e0, e0) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (3), (10), (11), (25) are inconsistent by sub-proof #732.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | End of split
% 142.58/21.35 | | | |
% 142.58/21.35 | | | End of split
% 142.58/21.35 | | |
% 142.58/21.35 | | End of split
% 142.58/21.35 | |
% 142.58/21.35 | Case 2:
% 142.58/21.35 | |
% 142.58/21.35 | | (26) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.35 | | e2)
% 142.58/21.35 | |
% 142.58/21.35 | | REF_CLOSE: (3), (5), (9), (10), (26) are inconsistent by sub-proof #703.
% 142.58/21.35 | |
% 142.58/21.35 | End of split
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #703 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) op(e0, e0) = e3
% 142.58/21.35 (2) all_57_14 = e3
% 142.58/21.35 (3) ~ (e3 = e2)
% 142.58/21.35 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.35 (5) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | BETA: splitting (5) gives:
% 142.58/21.35 |
% 142.58/21.35 | Case 1:
% 142.58/21.35 | |
% 142.58/21.35 | | (6) all_57_14 = e2 & op(e0, e1) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | REF_CLOSE: (2), (3), (6) are inconsistent by sub-proof #704.
% 142.58/21.35 | |
% 142.58/21.35 | Case 2:
% 142.58/21.35 | |
% 142.58/21.35 | | (7) all_57_15 = e2 & op(e0, e0) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | ALPHA: (7) implies:
% 142.58/21.35 | | (8) op(e0, e0) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | REF_CLOSE: (1), (3), (4), (8) are inconsistent by sub-proof #1066.
% 142.58/21.35 | |
% 142.58/21.35 | End of split
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #704 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) all_57_14 = e2 & op(e0, e1) = e2
% 142.58/21.35 (2) all_57_14 = e3
% 142.58/21.35 (3) ~ (e3 = e2)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | ALPHA: (1) implies:
% 142.58/21.35 | (4) all_57_14 = e2
% 142.58/21.35 |
% 142.58/21.35 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.35 | (5) e3 = e2
% 142.58/21.35 |
% 142.58/21.35 | REDUCE: (3), (5) imply:
% 142.58/21.35 | (6) $false
% 142.58/21.35 |
% 142.58/21.35 | CLOSE: (6) is inconsistent.
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #705 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) all_57_14 = e1 & op(e0, e1) = e1
% 142.58/21.35 (2) all_57_14 = e3
% 142.58/21.35 (3) ~ (e3 = e1)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | ALPHA: (1) implies:
% 142.58/21.35 | (4) all_57_14 = e1
% 142.58/21.35 |
% 142.58/21.35 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.35 | (5) e3 = e1
% 142.58/21.35 |
% 142.58/21.35 | REDUCE: (3), (5) imply:
% 142.58/21.35 | (6) $false
% 142.58/21.35 |
% 142.58/21.35 | CLOSE: (6) is inconsistent.
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #706 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) ~ (all_52_1 = e2)
% 142.58/21.35 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.35 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.58/21.35 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.35 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.35 (4) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.35 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.58/21.35 (5) ~ (all_52_4 = e0)
% 142.58/21.35 (6) ~ (e2 = e1)
% 142.58/21.35 (7) op(e0, e0) = e3
% 142.58/21.35 (8) all_57_8 = e0
% 142.58/21.35 (9) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.35 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.35 (10) all_57_13 = e0
% 142.58/21.35 (11) ~ (e3 = e0)
% 142.58/21.35 (12) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.58/21.35 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.35 e2)
% 142.58/21.35 (13) op(e2, e3) = all_52_1
% 142.58/21.35 (14) ~ (all_52_12 = e0)
% 142.58/21.35 (15) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.58/21.35 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.58/21.35 (16) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.58/21.35 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.58/21.35 (17) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.35 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.35 (18) ~ (e1 = e0)
% 142.58/21.35 (19) op(e2, e2) = e2
% 142.58/21.35 (20) op(e3, e2) = all_52_4
% 142.58/21.35 (21) ~ (e2 = e0)
% 142.58/21.35 (22) ~ (e3 = e2)
% 142.58/21.35 (23) op(e3, e0) = all_52_12
% 142.58/21.35 (24) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.58/21.35 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.58/21.35 (25) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.35 (26) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.35 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.35 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.35 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.35 (27) ~ (e3 = e1)
% 142.58/21.35 (28) all_57_0 = e0
% 142.58/21.35 (29) op(e3, e3) = e0
% 142.58/21.35 (30) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.58/21.35 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.58/21.35 (31) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.35 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.35 (32) all_57_2 = e0
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | BETA: splitting (2) gives:
% 142.58/21.35 |
% 142.58/21.35 | Case 1:
% 142.58/21.35 | |
% 142.58/21.35 | | (33) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 142.58/21.35 | | e3)
% 142.58/21.35 | |
% 142.58/21.35 | | REF_CLOSE: (11), (19), (22), (25), (32), (33) are inconsistent by sub-proof
% 142.58/21.35 | | #727.
% 142.58/21.35 | |
% 142.58/21.35 | Case 2:
% 142.58/21.35 | |
% 142.58/21.35 | | (34) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 142.58/21.35 | | e3)
% 142.58/21.35 | |
% 142.58/21.35 | | BETA: splitting (34) gives:
% 142.58/21.35 | |
% 142.58/21.35 | | Case 1:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (35) all_57_5 = e3 & op(e2, e1) = e3
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (35) implies:
% 142.58/21.35 | | | (36) all_57_5 = e3
% 142.58/21.35 | | |
% 142.58/21.35 | | | BETA: splitting (4) gives:
% 142.58/21.35 | | |
% 142.58/21.35 | | | Case 1:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | (37) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2)
% 142.58/21.35 | | | | = e1)
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | BETA: splitting (37) gives:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | Case 1:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (38) all_57_2 = e1 & op(e2, e3) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (18), (32), (38) are inconsistent by sub-proof #878.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | Case 2:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (39) all_57_3 = e1 & op(e2, e2) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | ALPHA: (39) implies:
% 142.58/21.35 | | | | | (40) op(e2, e2) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (6), (19), (25), (40) are inconsistent by sub-proof #749.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | End of split
% 142.58/21.35 | | | |
% 142.58/21.35 | | | Case 2:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | (41) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0)
% 142.58/21.35 | | | | = e1)
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | BETA: splitting (41) gives:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | Case 1:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (42) all_57_5 = e1 & op(e2, e1) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (27), (36), (42) are inconsistent by sub-proof #726.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | Case 2:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (43) all_57_10 = e1 & op(e2, e0) = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | ALPHA: (43) implies:
% 142.58/21.35 | | | | | (44) all_57_10 = e1
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | BETA: splitting (15) gives:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | Case 1:
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | (45) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2,
% 142.58/21.35 | | | | | | e3) = e3)
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | REF_CLOSE: (11), (28), (32), (45) are inconsistent by sub-proof
% 142.58/21.35 | | | | | | #725.
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | Case 2:
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | (46) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0,
% 142.58/21.35 | | | | | | e3) = e3)
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | BETA: splitting (46) gives:
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | Case 1:
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | (47) all_57_6 = e3 & op(e1, e3) = e3
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | ALPHA: (47) implies:
% 142.58/21.35 | | | | | | | (48) all_57_6 = e3
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | BETA: splitting (24) gives:
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | (49) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 &
% 142.58/21.35 | | | | | | | | op(e1, e2) = e2)
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | REF_CLOSE: (3), (6), (10), (11), (18), (19), (22), (25), (27),
% 142.58/21.35 | | | | | | | | (31), (48), (49) are inconsistent by sub-proof #719.
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | (50) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 142.58/21.35 | | | | | | | | op(e1, e0) = e2)
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | BETA: splitting (50) gives:
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | (51) all_57_8 = e2 & op(e1, e1) = e2
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | REF_CLOSE: (8), (21), (51) are inconsistent by sub-proof #718.
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | (52) all_57_11 = e2 & op(e1, e0) = e2
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | ALPHA: (52) implies:
% 142.58/21.35 | | | | | | | | | (53) all_57_11 = e2
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | REF_CLOSE: (7), (11), (14), (18), (21), (23), (25), (26),
% 142.58/21.35 | | | | | | | | | (44), (53) are inconsistent by sub-proof #715.
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | End of split
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | End of split
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | Case 2:
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | (54) all_57_12 = e3 & op(e0, e3) = e3
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | ALPHA: (54) implies:
% 142.58/21.35 | | | | | | | (55) all_57_12 = e3
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | REF_CLOSE: (3), (5), (6), (7), (9), (10), (11), (12), (17), (18),
% 142.58/21.35 | | | | | | | (19), (20), (21), (22), (25), (27), (31), (55) are
% 142.58/21.35 | | | | | | | inconsistent by sub-proof #708.
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | End of split
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | End of split
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | End of split
% 142.58/21.35 | | | |
% 142.58/21.35 | | | End of split
% 142.58/21.35 | | |
% 142.58/21.35 | | Case 2:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (56) all_57_10 = e3 & op(e2, e0) = e3
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (56) implies:
% 142.58/21.35 | | | (57) all_57_10 = e3
% 142.58/21.35 | | |
% 142.58/21.35 | | | BETA: splitting (15) gives:
% 142.58/21.35 | | |
% 142.58/21.35 | | | Case 1:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | (58) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 142.58/21.35 | | | | = e3)
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | REF_CLOSE: (11), (28), (32), (58) are inconsistent by sub-proof #725.
% 142.58/21.35 | | | |
% 142.58/21.35 | | | Case 2:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | (59) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 142.58/21.35 | | | | = e3)
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | BETA: splitting (59) gives:
% 142.58/21.35 | | | |
% 142.58/21.35 | | | | Case 1:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (60) all_57_6 = e3 & op(e1, e3) = e3
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | ALPHA: (60) implies:
% 142.58/21.35 | | | | | (61) all_57_6 = e3
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | BETA: splitting (24) gives:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | Case 1:
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | (62) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 142.58/21.35 | | | | | | e2) = e2)
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | REF_CLOSE: (3), (6), (10), (11), (18), (19), (22), (25), (27), (31),
% 142.58/21.35 | | | | | | (61), (62) are inconsistent by sub-proof #719.
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | Case 2:
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | (63) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 142.58/21.35 | | | | | | e0) = e2)
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | BETA: splitting (63) gives:
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | | Case 1:
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | (64) all_57_8 = e2 & op(e1, e1) = e2
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | REF_CLOSE: (8), (21), (64) are inconsistent by sub-proof #718.
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | Case 2:
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | (65) all_57_11 = e2 & op(e1, e0) = e2
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | ALPHA: (65) implies:
% 142.58/21.35 | | | | | | | (66) all_57_11 = e2
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | BETA: splitting (30) gives:
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | (67) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 &
% 142.58/21.35 | | | | | | | | op(e2, e3) = e2)
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | REF_CLOSE: (1), (13), (21), (25), (29), (67) are inconsistent by
% 142.58/21.35 | | | | | | | | sub-proof #707.
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | (68) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 &
% 142.58/21.35 | | | | | | | | op(e0, e3) = e2)
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | BETA: splitting (68) gives:
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | (69) all_57_6 = e2 & op(e1, e3) = e2
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | REF_CLOSE: (22), (61), (69) are inconsistent by sub-proof
% 142.58/21.35 | | | | | | | | | #998.
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | (70) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | ALPHA: (70) implies:
% 142.58/21.35 | | | | | | | | | (71) all_57_12 = e2
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | BETA: splitting (16) gives:
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | (72) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 &
% 142.58/21.35 | | | | | | | | | | op(e2, e3) = e1)
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | BETA: splitting (72) gives:
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | (73) all_57_0 = e1 & op(e3, e3) = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | ALPHA: (73) implies:
% 142.58/21.35 | | | | | | | | | | | (74) op(e3, e3) = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | REF_CLOSE: (18), (25), (29), (74) are inconsistent by
% 142.58/21.35 | | | | | | | | | | | sub-proof #840.
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | (75) all_57_2 = e1 & op(e2, e3) = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | REF_CLOSE: (18), (32), (75) are inconsistent by sub-proof
% 142.58/21.35 | | | | | | | | | | | #878.
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | End of split
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | (76) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1
% 142.58/21.35 | | | | | | | | | | & op(e0, e3) = e1)
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | BETA: splitting (76) gives:
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | Case 1:
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | (77) all_57_6 = e1 & op(e1, e3) = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | ALPHA: (77) implies:
% 142.58/21.35 | | | | | | | | | | | (78) all_57_6 = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | COMBINE_EQS: (61), (78) imply:
% 142.58/21.35 | | | | | | | | | | | (79) e3 = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | COMBINE_EQS: (57), (79) imply:
% 142.58/21.35 | | | | | | | | | | | (80) all_57_10 = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | REF_CLOSE: (7), (11), (14), (18), (21), (23), (25), (26),
% 142.58/21.35 | | | | | | | | | | | (66), (80) are inconsistent by sub-proof #715.
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | Case 2:
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | (81) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | | REF_CLOSE: (6), (71), (81) are inconsistent by sub-proof
% 142.58/21.35 | | | | | | | | | | | #848.
% 142.58/21.35 | | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | | End of split
% 142.58/21.35 | | | | | | | | | |
% 142.58/21.35 | | | | | | | | | End of split
% 142.58/21.35 | | | | | | | | |
% 142.58/21.35 | | | | | | | | End of split
% 142.58/21.35 | | | | | | | |
% 142.58/21.35 | | | | | | | End of split
% 142.58/21.35 | | | | | | |
% 142.58/21.35 | | | | | | End of split
% 142.58/21.35 | | | | | |
% 142.58/21.35 | | | | | End of split
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | Case 2:
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | (82) all_57_12 = e3 & op(e0, e3) = e3
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | ALPHA: (82) implies:
% 142.58/21.35 | | | | | (83) all_57_12 = e3
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | | REF_CLOSE: (3), (5), (6), (7), (9), (10), (11), (12), (17), (18),
% 142.58/21.35 | | | | | (19), (20), (21), (22), (25), (27), (31), (83) are
% 142.58/21.35 | | | | | inconsistent by sub-proof #708.
% 142.58/21.35 | | | | |
% 142.58/21.35 | | | | End of split
% 142.58/21.35 | | | |
% 142.58/21.35 | | | End of split
% 142.58/21.35 | | |
% 142.58/21.35 | | End of split
% 142.58/21.35 | |
% 142.58/21.35 | End of split
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #707 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) ~ (all_52_1 = e2)
% 142.58/21.35 (2) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2)
% 142.58/21.35 (3) op(e2, e3) = all_52_1
% 142.58/21.35 (4) ~ (e2 = e0)
% 142.58/21.35 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.35 (6) op(e3, e3) = e0
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | BETA: splitting (2) gives:
% 142.58/21.35 |
% 142.58/21.35 | Case 1:
% 142.58/21.35 | |
% 142.58/21.35 | | (7) all_57_0 = e2 & op(e3, e3) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | ALPHA: (7) implies:
% 142.58/21.35 | | (8) op(e3, e3) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #880.
% 142.58/21.35 | |
% 142.58/21.35 | Case 2:
% 142.58/21.35 | |
% 142.58/21.35 | | (9) all_57_2 = e2 & op(e2, e3) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | ALPHA: (9) implies:
% 142.58/21.35 | | (10) op(e2, e3) = e2
% 142.58/21.35 | |
% 142.58/21.35 | | REF_CLOSE: (1), (3), (5), (10) are inconsistent by sub-proof #882.
% 142.58/21.35 | |
% 142.58/21.35 | End of split
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #708 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.35 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.35 (2) ~ (all_52_4 = e0)
% 142.58/21.35 (3) ~ (e2 = e1)
% 142.58/21.35 (4) op(e0, e0) = e3
% 142.58/21.35 (5) all_57_12 = e3
% 142.58/21.35 (6) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.35 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.35 (7) all_57_13 = e0
% 142.58/21.35 (8) ~ (e3 = e0)
% 142.58/21.35 (9) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2) |
% 142.58/21.35 (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) = e2)
% 142.58/21.35 (10) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.35 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.35 (11) ~ (e1 = e0)
% 142.58/21.35 (12) op(e2, e2) = e2
% 142.58/21.35 (13) op(e3, e2) = all_52_4
% 142.58/21.35 (14) ~ (e2 = e0)
% 142.58/21.35 (15) ~ (e3 = e2)
% 142.58/21.35 (16) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.35 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.35 (17) ~ (e3 = e1)
% 142.58/21.35 (18) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.35 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.35
% 142.58/21.35 Begin of proof
% 142.58/21.35 |
% 142.58/21.35 | BETA: splitting (9) gives:
% 142.58/21.35 |
% 142.58/21.35 | Case 1:
% 142.58/21.35 | |
% 142.58/21.35 | | (19) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) =
% 142.58/21.35 | | e2)
% 142.58/21.35 | |
% 142.58/21.35 | | BETA: splitting (19) gives:
% 142.58/21.35 | |
% 142.58/21.35 | | Case 1:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (20) all_57_12 = e2 & op(e0, e3) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (20) implies:
% 142.58/21.35 | | | (21) all_57_12 = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | REF_CLOSE: (5), (15), (21) are inconsistent by sub-proof #772.
% 142.58/21.35 | | |
% 142.58/21.35 | | Case 2:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (22) all_57_13 = e2 & op(e0, e2) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (22) implies:
% 142.58/21.35 | | | (23) all_57_13 = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | REF_CLOSE: (1), (2), (3), (8), (10), (11), (12), (13), (14), (15), (16),
% 142.58/21.35 | | | (17), (18), (23) are inconsistent by sub-proof #710.
% 142.58/21.35 | | |
% 142.58/21.35 | | End of split
% 142.58/21.35 | |
% 142.58/21.35 | Case 2:
% 142.58/21.35 | |
% 142.58/21.35 | | (24) (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.58/21.35 | | e2)
% 142.58/21.35 | |
% 142.58/21.35 | | BETA: splitting (24) gives:
% 142.58/21.35 | |
% 142.58/21.35 | | Case 1:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (25) all_57_14 = e2 & op(e0, e1) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (25) implies:
% 142.58/21.35 | | | (26) all_57_14 = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | REF_CLOSE: (3), (4), (5), (6), (7), (11), (16), (17), (26) are
% 142.58/21.35 | | | inconsistent by sub-proof #709.
% 142.58/21.35 | | |
% 142.58/21.35 | | Case 2:
% 142.58/21.35 | | |
% 142.58/21.35 | | | (27) all_57_15 = e2 & op(e0, e0) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | ALPHA: (27) implies:
% 142.58/21.35 | | | (28) op(e0, e0) = e2
% 142.58/21.35 | | |
% 142.58/21.35 | | | REF_CLOSE: (4), (15), (16), (28) are inconsistent by sub-proof #1066.
% 142.58/21.35 | | |
% 142.58/21.35 | | End of split
% 142.58/21.35 | |
% 142.58/21.35 | End of split
% 142.58/21.35 |
% 142.58/21.35 End of proof
% 142.58/21.35
% 142.58/21.35 Sub-proof #709 shows that the following formulas are inconsistent:
% 142.58/21.35 ----------------------------------------------------------------
% 142.58/21.35 (1) ~ (e2 = e1)
% 142.58/21.35 (2) op(e0, e0) = e3
% 142.58/21.35 (3) all_57_14 = e2
% 142.58/21.35 (4) all_57_12 = e3
% 142.58/21.35 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.58/21.35 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.58/21.35 (6) all_57_13 = e0
% 142.58/21.35 (7) ~ (e1 = e0)
% 142.58/21.36 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (9) ~ (e3 = e1)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (5) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (10) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.58/21.36 | | e1)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (10) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (11) all_57_12 = e1 & op(e0, e3) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (4), (9), (11) are inconsistent by sub-proof #1073.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (12) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (12) implies:
% 142.58/21.36 | | | (13) all_57_13 = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (6), (7), (13) are inconsistent by sub-proof #721.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (14) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.58/21.36 | | e1)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (14) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (15) all_57_14 = e1 & op(e0, e1) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (1), (3), (15) are inconsistent by sub-proof #768.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (16) all_57_15 = e1 & op(e0, e0) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (16) implies:
% 142.58/21.36 | | | (17) op(e0, e0) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (2), (8), (9), (17) are inconsistent by sub-proof #732.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #710 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.36 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.36 (2) ~ (all_52_4 = e0)
% 142.58/21.36 (3) ~ (e2 = e1)
% 142.58/21.36 (4) ~ (e3 = e0)
% 142.58/21.36 (5) all_57_13 = e2
% 142.58/21.36 (6) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.58/21.36 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.58/21.36 (7) ~ (e1 = e0)
% 142.58/21.36 (8) op(e2, e2) = e2
% 142.58/21.36 (9) op(e3, e2) = all_52_4
% 142.58/21.36 (10) ~ (e2 = e0)
% 142.58/21.36 (11) ~ (e3 = e2)
% 142.58/21.36 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (13) ~ (e3 = e1)
% 142.58/21.36 (14) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.36 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (6) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (15) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) =
% 142.58/21.36 | | e0)
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (8), (9), (10), (12), (15) are inconsistent by sub-proof
% 142.58/21.36 | | #714.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (16) (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.58/21.36 | | e0)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (16) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (17) all_57_7 = e0 & op(e1, e2) = e0
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (17) implies:
% 142.58/21.36 | | | (18) all_57_7 = e0
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (11), (12), (13), (14), (18) are
% 142.58/21.36 | | | inconsistent by sub-proof #711.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (19) all_57_13 = e0 & op(e0, e2) = e0
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (5), (10), (19) are inconsistent by sub-proof #1060.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #711 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.36 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.36 (2) ~ (e2 = e1)
% 142.58/21.36 (3) ~ (e3 = e0)
% 142.58/21.36 (4) all_57_13 = e2
% 142.58/21.36 (5) ~ (e1 = e0)
% 142.58/21.36 (6) op(e2, e2) = e2
% 142.58/21.36 (7) ~ (e3 = e2)
% 142.58/21.36 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (9) ~ (e3 = e1)
% 142.58/21.36 (10) all_57_7 = e0
% 142.58/21.36 (11) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.36 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (1) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (12) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 142.58/21.36 | | e1)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (12) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (13) all_57_1 = e1 & op(e3, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (13) implies:
% 142.58/21.36 | | | (14) all_57_1 = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | BETA: splitting (11) gives:
% 142.58/21.36 | | |
% 142.58/21.36 | | | Case 1:
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | (15) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2)
% 142.58/21.36 | | | | = e3)
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | REF_CLOSE: (6), (7), (8), (9), (14), (15) are inconsistent by sub-proof
% 142.58/21.36 | | | | #723.
% 142.58/21.36 | | | |
% 142.58/21.36 | | | Case 2:
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | (16) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2)
% 142.58/21.36 | | | | = e3)
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | BETA: splitting (16) gives:
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | Case 1:
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | | (17) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | | REF_CLOSE: (3), (10), (17) are inconsistent by sub-proof #713.
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | Case 2:
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | | (18) all_57_13 = e3 & op(e0, e2) = e3
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | | ALPHA: (18) implies:
% 142.58/21.36 | | | | | (19) all_57_13 = e3
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | | REF_CLOSE: (4), (7), (19) are inconsistent by sub-proof #1068.
% 142.58/21.36 | | | | |
% 142.58/21.36 | | | | End of split
% 142.58/21.36 | | | |
% 142.58/21.36 | | | End of split
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (20) all_57_3 = e1 & op(e2, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (20) implies:
% 142.58/21.36 | | | (21) op(e2, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (2), (6), (8), (21) are inconsistent by sub-proof #749.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (22) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.58/21.36 | | e1)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (22) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (23) all_57_7 = e1 & op(e1, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (23) implies:
% 142.58/21.36 | | | (24) all_57_7 = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (5), (10), (24) are inconsistent by sub-proof #712.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (25) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (2), (4), (25) are inconsistent by sub-proof #1072.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #712 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_7 = e1
% 142.58/21.36 (2) all_57_7 = e0
% 142.58/21.36 (3) ~ (e1 = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.36 | (4) e1 = e0
% 142.58/21.36 |
% 142.58/21.36 | SIMP: (4) implies:
% 142.58/21.36 | (5) e1 = e0
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (5) imply:
% 142.58/21.36 | (6) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (6) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #713 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.36 (2) all_57_7 = e0
% 142.58/21.36 (3) ~ (e3 = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | ALPHA: (1) implies:
% 142.58/21.36 | (4) all_57_7 = e3
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.36 | (5) e3 = e0
% 142.58/21.36 |
% 142.58/21.36 | SIMP: (5) implies:
% 142.58/21.36 | (6) e3 = e0
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (6) imply:
% 142.58/21.36 | (7) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (7) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #714 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) ~ (all_52_4 = e0)
% 142.58/21.36 (2) op(e2, e2) = e2
% 142.58/21.36 (3) op(e3, e2) = all_52_4
% 142.58/21.36 (4) ~ (e2 = e0)
% 142.58/21.36 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (6) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (6) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (7) all_57_1 = e0 & op(e3, e2) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (1), (3), (5), (7) are inconsistent by sub-proof #1102.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (8) all_57_3 = e0 & op(e2, e2) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (8) implies:
% 142.58/21.36 | | (9) op(e2, e2) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1076.
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #715 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) op(e0, e0) = e3
% 142.58/21.36 (2) ~ (e3 = e0)
% 142.58/21.36 (3) all_57_10 = e1
% 142.58/21.36 (4) ~ (all_52_12 = e0)
% 142.58/21.36 (5) all_57_11 = e2
% 142.58/21.36 (6) ~ (e1 = e0)
% 142.58/21.36 (7) ~ (e2 = e0)
% 142.58/21.36 (8) op(e3, e0) = all_52_12
% 142.58/21.36 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.36 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.36 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.36 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (10) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (11) all_57_15 = e0 & op(e0, e0) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (11) implies:
% 142.58/21.36 | | (12) op(e0, e0) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (1), (2), (9), (12) are inconsistent by sub-proof #751.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (13) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.58/21.36 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.58/21.36 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.36 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (13) implies:
% 142.58/21.36 | | (14) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.58/21.36 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (3), (4), (5), (6), (7), (8), (9), (14) are inconsistent by
% 142.58/21.36 | | sub-proof #716.
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #716 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_10 = e1
% 142.58/21.36 (2) ~ (all_52_12 = e0)
% 142.58/21.36 (3) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.58/21.36 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.58/21.36 (4) all_57_11 = e2
% 142.58/21.36 (5) ~ (e1 = e0)
% 142.58/21.36 (6) ~ (e2 = e0)
% 142.58/21.36 (7) op(e3, e0) = all_52_12
% 142.58/21.36 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (3) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (9) all_57_9 = e0 & op(e3, e0) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (9) implies:
% 142.58/21.36 | | (10) op(e3, e0) = e0
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (7), (8), (10) are inconsistent by sub-proof #941.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (11) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.58/21.36 | | e0)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (11) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (12) all_57_10 = e0 & op(e2, e0) = e0
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (1), (5), (12) are inconsistent by sub-proof #717.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (13) all_57_11 = e0 & op(e1, e0) = e0
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (4), (6), (13) are inconsistent by sub-proof #992.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #717 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_10 = e0 & op(e2, e0) = e0
% 142.58/21.36 (2) all_57_10 = e1
% 142.58/21.36 (3) ~ (e1 = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | ALPHA: (1) implies:
% 142.58/21.36 | (4) all_57_10 = e0
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.36 | (5) e1 = e0
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (5) imply:
% 142.58/21.36 | (6) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (6) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #718 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_8 = e2 & op(e1, e1) = e2
% 142.58/21.36 (2) all_57_8 = e0
% 142.58/21.36 (3) ~ (e2 = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | ALPHA: (1) implies:
% 142.58/21.36 | (4) all_57_8 = e2
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.36 | (5) e2 = e0
% 142.58/21.36 |
% 142.58/21.36 | SIMP: (5) implies:
% 142.58/21.36 | (6) e2 = e0
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (6) imply:
% 142.58/21.36 | (7) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (7) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #719 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.36 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.36 (2) all_57_6 = e3
% 142.58/21.36 (3) ~ (e2 = e1)
% 142.58/21.36 (4) all_57_13 = e0
% 142.58/21.36 (5) ~ (e3 = e0)
% 142.58/21.36 (6) ~ (e1 = e0)
% 142.58/21.36 (7) op(e2, e2) = e2
% 142.58/21.36 (8) ~ (e3 = e2)
% 142.58/21.36 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (10) ~ (e3 = e1)
% 142.58/21.36 (11) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2)
% 142.58/21.36 (12) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.36 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (11) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (13) all_57_6 = e2 & op(e1, e3) = e2
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #998.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (14) all_57_7 = e2 & op(e1, e2) = e2
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (14) implies:
% 142.58/21.36 | | (15) all_57_7 = e2
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (12), (15) are
% 142.58/21.36 | | inconsistent by sub-proof #720.
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #720 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.58/21.36 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.58/21.36 (2) ~ (e2 = e1)
% 142.58/21.36 (3) all_57_7 = e2
% 142.58/21.36 (4) all_57_13 = e0
% 142.58/21.36 (5) ~ (e3 = e0)
% 142.58/21.36 (6) ~ (e1 = e0)
% 142.58/21.36 (7) op(e2, e2) = e2
% 142.58/21.36 (8) ~ (e3 = e2)
% 142.58/21.36 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (10) ~ (e3 = e1)
% 142.58/21.36 (11) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.36 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (1) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (12) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 142.58/21.36 | | e1)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (12) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (13) all_57_1 = e1 & op(e3, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (13) implies:
% 142.58/21.36 | | | (14) all_57_1 = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (3), (4), (5), (7), (8), (9), (10), (11), (14) are inconsistent
% 142.58/21.36 | | | by sub-proof #722.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (15) all_57_3 = e1 & op(e2, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (15) implies:
% 142.58/21.36 | | | (16) op(e2, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (2), (7), (9), (16) are inconsistent by sub-proof #749.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (17) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.58/21.36 | | e1)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (17) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (18) all_57_7 = e1 & op(e1, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (2), (3), (18) are inconsistent by sub-proof #864.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (19) all_57_13 = e1 & op(e0, e2) = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (19) implies:
% 142.58/21.36 | | | (20) all_57_13 = e1
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (4), (6), (20) are inconsistent by sub-proof #721.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #721 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_13 = e1
% 142.58/21.36 (2) all_57_13 = e0
% 142.58/21.36 (3) ~ (e1 = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.36 | (4) e1 = e0
% 142.58/21.36 |
% 142.58/21.36 | SIMP: (4) implies:
% 142.58/21.36 | (5) e1 = e0
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (5) imply:
% 142.58/21.36 | (6) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (6) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #722 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_7 = e2
% 142.58/21.36 (2) all_57_13 = e0
% 142.58/21.36 (3) ~ (e3 = e0)
% 142.58/21.36 (4) all_57_1 = e1
% 142.58/21.36 (5) op(e2, e2) = e2
% 142.58/21.36 (6) ~ (e3 = e2)
% 142.58/21.36 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (8) ~ (e3 = e1)
% 142.58/21.36 (9) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.58/21.36 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (9) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (10) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 142.58/21.36 | | e3)
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (4), (5), (6), (7), (8), (10) are inconsistent by sub-proof #723.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (11) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 142.58/21.36 | | e3)
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (11) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (12) all_57_7 = e3 & op(e1, e2) = e3
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (12) implies:
% 142.58/21.36 | | | (13) all_57_7 = e3
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (1), (6), (13) are inconsistent by sub-proof #1098.
% 142.58/21.36 | | |
% 142.58/21.36 | | Case 2:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (14) all_57_13 = e3 & op(e0, e2) = e3
% 142.58/21.36 | | |
% 142.58/21.36 | | | ALPHA: (14) implies:
% 142.58/21.36 | | | (15) all_57_13 = e3
% 142.58/21.36 | | |
% 142.58/21.36 | | | REF_CLOSE: (2), (3), (15) are inconsistent by sub-proof #804.
% 142.58/21.36 | | |
% 142.58/21.36 | | End of split
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #723 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.58/21.36 (2) all_57_1 = e1
% 142.58/21.36 (3) op(e2, e2) = e2
% 142.58/21.36 (4) ~ (e3 = e2)
% 142.58/21.36 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (6) ~ (e3 = e1)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (1) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (7) all_57_1 = e3 & op(e3, e2) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (6), (7) are inconsistent by sub-proof #724.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (8) all_57_3 = e3 & op(e2, e2) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (8) implies:
% 142.58/21.36 | | (9) op(e2, e2) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #728.
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #724 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_1 = e3 & op(e3, e2) = e3
% 142.58/21.36 (2) all_57_1 = e1
% 142.58/21.36 (3) ~ (e3 = e1)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | ALPHA: (1) implies:
% 142.58/21.36 | (4) all_57_1 = e3
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.36 | (5) e3 = e1
% 142.58/21.36 |
% 142.58/21.36 | SIMP: (5) implies:
% 142.58/21.36 | (6) e3 = e1
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (6) imply:
% 142.58/21.36 | (7) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (7) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #725 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3)
% 142.58/21.36 (2) all_57_0 = e0
% 142.58/21.36 (3) ~ (e3 = e0)
% 142.58/21.36 (4) all_57_2 = e0
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (1) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (5) all_57_0 = e3 & op(e3, e3) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #1108.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (6) all_57_2 = e3 & op(e2, e3) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (6) implies:
% 142.58/21.36 | | (7) all_57_2 = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #879.
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #726 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_5 = e1 & op(e2, e1) = e1
% 142.58/21.36 (2) all_57_5 = e3
% 142.58/21.36 (3) ~ (e3 = e1)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | ALPHA: (1) implies:
% 142.58/21.36 | (4) all_57_5 = e1
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.36 | (5) e3 = e1
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (5) imply:
% 142.58/21.36 | (6) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (6) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #727 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.58/21.36 (2) ~ (e3 = e0)
% 142.58/21.36 (3) op(e2, e2) = e2
% 142.58/21.36 (4) ~ (e3 = e2)
% 142.58/21.36 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (6) all_57_2 = e0
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (1) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (7) all_57_2 = e3 & op(e2, e3) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (7) implies:
% 142.58/21.36 | | (8) all_57_2 = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (2), (6), (8) are inconsistent by sub-proof #879.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (9) all_57_3 = e3 & op(e2, e2) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (9) implies:
% 142.58/21.36 | | (10) op(e2, e2) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #728.
% 142.58/21.36 | |
% 142.58/21.36 | End of split
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #728 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (2) op(e2, e2) = e3
% 142.58/21.36 (3) op(e2, e2) = e2
% 142.58/21.36 (4) ~ (e3 = e2)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | GROUND_INST: instantiating (1) with e2, e3, e2, e2, simplifying with (2), (3)
% 142.58/21.36 | gives:
% 142.58/21.36 | (5) e3 = e2
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (4), (5) imply:
% 142.58/21.36 | (6) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (6) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #729 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) all_57_5 = e0 & op(e2, e1) = e0
% 142.58/21.36 (2) all_57_5 = e3
% 142.58/21.36 (3) ~ (e3 = e0)
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | ALPHA: (1) implies:
% 142.58/21.36 | (4) all_57_5 = e0
% 142.58/21.36 |
% 142.58/21.36 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.36 | (5) e3 = e0
% 142.58/21.36 |
% 142.58/21.36 | REDUCE: (3), (5) imply:
% 142.58/21.36 | (6) $false
% 142.58/21.36 |
% 142.58/21.36 | CLOSE: (6) is inconsistent.
% 142.58/21.36 |
% 142.58/21.36 End of proof
% 142.58/21.36
% 142.58/21.36 Sub-proof #730 shows that the following formulas are inconsistent:
% 142.58/21.36 ----------------------------------------------------------------
% 142.58/21.36 (1) ~ (all_52_12 = e3)
% 142.58/21.36 (2) ~ (e2 = e1)
% 142.58/21.36 (3) op(e0, e0) = e3
% 142.58/21.36 (4) op(e1, e1) = e1
% 142.58/21.36 (5) ~ (e1 = e0)
% 142.58/21.36 (6) ~ (e2 = e0)
% 142.58/21.36 (7) ~ (e3 = e2)
% 142.58/21.36 (8) op(e3, e0) = all_52_12
% 142.58/21.36 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.36 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.36 (10) ~ (e3 = e1)
% 142.58/21.36 (11) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.36 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.36 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.58/21.36 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.58/21.36 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.58/21.36 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.58/21.36 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.58/21.36 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.58/21.36 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.58/21.36 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.58/21.36 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.58/21.36 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.58/21.36 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.58/21.36 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.58/21.36 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.58/21.36 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.36 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.58/21.36 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.58/21.36 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.36 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.36 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.36 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.58/21.36 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.36 $i(all_56_14))))
% 142.58/21.36 (12) op(e3, e3) = e0
% 142.58/21.36 (13) (all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 142.58/21.36 all_56_9 & $i(all_56_9))
% 142.58/21.36
% 142.58/21.36 Begin of proof
% 142.58/21.36 |
% 142.58/21.36 | BETA: splitting (13) gives:
% 142.58/21.36 |
% 142.58/21.36 | Case 1:
% 142.58/21.36 | |
% 142.58/21.36 | | (14) all_56_2 = e3 & op(e3, e0) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (14) implies:
% 142.58/21.36 | | (15) op(e3, e0) = e3
% 142.58/21.36 | |
% 142.58/21.36 | | REF_CLOSE: (1), (8), (9), (15) are inconsistent by sub-proof #1105.
% 142.58/21.36 | |
% 142.58/21.36 | Case 2:
% 142.58/21.36 | |
% 142.58/21.36 | | (16) ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 142.58/21.36 | |
% 142.58/21.36 | | ALPHA: (16) implies:
% 142.58/21.36 | | (17) ~ (all_56_9 = e0)
% 142.58/21.36 | | (18) op(e3, e3) = all_56_9
% 142.58/21.36 | |
% 142.58/21.36 | | BETA: splitting (11) gives:
% 142.58/21.36 | |
% 142.58/21.36 | | Case 1:
% 142.58/21.36 | | |
% 142.58/21.36 | | | (19) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3)
% 142.58/21.36 | | | = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.58/21.36 | | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3)
% 142.58/21.36 | | | = e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) |
% 142.58/21.36 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3)
% 142.58/21.36 | | | = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.58/21.36 | | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3)
% 142.58/21.36 | | | = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.58/21.36 | | |
% 142.58/21.36 | | | BETA: splitting (19) gives:
% 142.58/21.36 | | |
% 142.58/21.36 | | | Case 1:
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | (20) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3,
% 142.58/21.36 | | | | e3) = e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 &
% 142.58/21.36 | | | | $i(all_56_0)) | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3
% 142.58/21.36 | | | | = e2) & op(e3, e3) = e2 & op(e2, e3) = all_56_3 & op(e2, e2)
% 142.58/21.36 | | | | = e3 & $i(all_56_3))
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | REF_CLOSE: (6), (9), (12), (20) are inconsistent by sub-proof #753.
% 142.58/21.36 | | | |
% 142.58/21.36 | | | Case 2:
% 142.58/21.36 | | | |
% 142.58/21.36 | | | | (21) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3,
% 142.58/21.36 | | | | e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 142.58/21.36 | | | | $i(all_56_1)) | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6
% 142.58/21.36 | | | | = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 & op(e1, e1)
% 142.58/21.36 | | | | = e3 & $i(all_56_6))
% 142.58/21.36 | | | |
% 142.58/21.37 | | | | BETA: splitting (21) gives:
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | Case 1:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | (22) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3,
% 142.58/21.37 | | | | | e3) = e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 &
% 142.58/21.37 | | | | | $i(all_56_1)
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | ALPHA: (22) implies:
% 142.58/21.37 | | | | | (23) all_56_9 = e1
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | REDUCE: (18), (23) imply:
% 142.58/21.37 | | | | | (24) op(e3, e3) = e1
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | REF_CLOSE: (5), (9), (12), (24) are inconsistent by sub-proof #840.
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | Case 2:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | (25) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3,
% 142.58/21.37 | | | | | e3) = e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 &
% 142.58/21.37 | | | | | $i(all_56_6)
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | ALPHA: (25) implies:
% 142.58/21.37 | | | | | (26) op(e3, e3) = e1
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | REF_CLOSE: (5), (9), (12), (26) are inconsistent by sub-proof #840.
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | End of split
% 142.58/21.37 | | | |
% 142.58/21.37 | | | End of split
% 142.58/21.37 | | |
% 142.58/21.37 | | Case 2:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (27) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3)
% 142.58/21.37 | | | = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) |
% 142.58/21.37 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2)
% 142.58/21.37 | | | = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) |
% 142.58/21.37 | | | (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2)
% 142.58/21.37 | | | = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) |
% 142.58/21.37 | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2)
% 142.58/21.37 | | | = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) |
% 142.58/21.37 | | | (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.58/21.37 | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.37 | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.58/21.37 | | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 &
% 142.58/21.37 | | | op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.58/21.37 | | | all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.58/21.37 | | | op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.58/21.37 | | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 &
% 142.58/21.37 | | | op(e0, e1) = all_56_14 & $i(all_56_14))))
% 142.58/21.37 | | |
% 142.58/21.37 | | | BETA: splitting (27) gives:
% 142.58/21.37 | | |
% 142.58/21.37 | | | Case 1:
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | (28) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.58/21.37 | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.58/21.37 | | | | $i(all_56_2)) | (all_56_11 = e1 & all_56_13 = e2 & ~
% 142.58/21.37 | | | | (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) = all_56_4 &
% 142.58/21.37 | | | | op(e1, e1) = e2 & $i(all_56_4))
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | BETA: splitting (28) gives:
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | Case 1:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | (29) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3,
% 142.58/21.37 | | | | | e3) = e0 & op(e3, e0) = all_56_2 & op(e0, e0) = e3 &
% 142.58/21.37 | | | | | $i(all_56_2)
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | ALPHA: (29) implies:
% 142.58/21.37 | | | | | (30) all_56_9 = e0
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | REDUCE: (17), (30) imply:
% 142.58/21.37 | | | | | (31) $false
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | CLOSE: (31) is inconsistent.
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | Case 2:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | (32) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2,
% 142.58/21.37 | | | | | e2) = e1 & op(e2, e1) = all_56_4 & op(e1, e1) = e2 &
% 142.58/21.37 | | | | | $i(all_56_4)
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | ALPHA: (32) implies:
% 142.58/21.37 | | | | | (33) op(e1, e1) = e2
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | REF_CLOSE: (2), (4), (9), (33) are inconsistent by sub-proof #1085.
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | End of split
% 142.58/21.37 | | | |
% 142.58/21.37 | | | Case 2:
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | (34) (all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.58/21.37 | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.58/21.37 | | | | $i(all_56_7)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.58/21.37 | | | | (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) = all_56_5 &
% 142.58/21.37 | | | | op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.58/21.37 | | | | $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~
% 142.58/21.37 | | | | (all_56_10 = e0) & op(e3, e3) = e0 & op(e0, e3) =
% 142.58/21.37 | | | | all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.58/21.37 | | | | e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.58/21.37 | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15 =
% 142.58/21.37 | | | | e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0) =
% 142.58/21.37 | | | | all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 142.58/21.37 | | | | e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) =
% 142.58/21.37 | | | | all_56_14 & $i(all_56_14))))
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | BETA: splitting (34) gives:
% 142.58/21.37 | | | |
% 142.58/21.37 | | | | Case 1:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | (35) all_56_11 = e1 & all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2,
% 142.58/21.37 | | | | | e2) = e1 & op(e1, e2) = all_56_7 & op(e1, e1) = e2 &
% 142.58/21.37 | | | | | $i(all_56_7)
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | ALPHA: (35) implies:
% 142.58/21.37 | | | | | (36) op(e1, e1) = e2
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | REF_CLOSE: (2), (4), (9), (36) are inconsistent by sub-proof #1085.
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | Case 2:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | (37) (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2,
% 142.58/21.37 | | | | | e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.58/21.37 | | | | | $i(all_56_5)) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.58/21.37 | | | | | ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.37 | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 &
% 142.58/21.37 | | | | | $i(all_56_10)) | (all_56_11 = e0 & all_56_15 = e2 & ~
% 142.58/21.37 | | | | | (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) =
% 142.58/21.37 | | | | | all_56_12 & $i(all_56_12)) | (all_56_13 = e0 & all_56_15
% 142.58/21.37 | | | | | = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.58/21.37 | | | | | = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15
% 142.58/21.37 | | | | | = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.37 | | | | | e1) = all_56_14 & $i(all_56_14))))
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | BETA: splitting (37) gives:
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | | Case 1:
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | | (38) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_5 = e2) &
% 142.58/21.37 | | | | | | op(e2, e2) = e0 & op(e2, e0) = all_56_5 & op(e0, e0) = e2 &
% 142.58/21.37 | | | | | | $i(all_56_5)
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | | ALPHA: (38) implies:
% 142.58/21.37 | | | | | | (39) op(e0, e0) = e2
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | | REF_CLOSE: (3), (7), (9), (39) are inconsistent by sub-proof #1066.
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | Case 2:
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | | (40) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_9 = e0 &
% 142.58/21.37 | | | | | | all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.37 | | | | | | op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 =
% 142.58/21.37 | | | | | | e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) =
% 142.58/21.37 | | | | | | e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) |
% 142.58/21.37 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.58/21.37 | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8))
% 142.58/21.37 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.58/21.37 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.37 | | | | | | $i(all_56_14)))
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | | ALPHA: (40) implies:
% 142.58/21.37 | | | | | | (41) op(e0, e0) = all_56_15
% 142.58/21.37 | | | | | | (42) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) &
% 142.58/21.37 | | | | | | op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10))
% 142.58/21.37 | | | | | | | (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) &
% 142.58/21.37 | | | | | | op(e2, e2) = e0 & op(e0, e2) = all_56_12 & $i(all_56_12))
% 142.58/21.37 | | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) &
% 142.58/21.37 | | | | | | op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) |
% 142.58/21.37 | | | | | | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) &
% 142.58/21.37 | | | | | | op(e1, e1) = e0 & op(e0, e1) = all_56_14 & $i(all_56_14))
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | | REF_CLOSE: (3), (7), (9), (10), (17), (41), (42) are inconsistent by
% 142.58/21.37 | | | | | | sub-proof #731.
% 142.58/21.37 | | | | | |
% 142.58/21.37 | | | | | End of split
% 142.58/21.37 | | | | |
% 142.58/21.37 | | | | End of split
% 142.58/21.37 | | | |
% 142.58/21.37 | | | End of split
% 142.58/21.37 | | |
% 142.58/21.37 | | End of split
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #731 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) op(e0, e0) = e3
% 142.58/21.37 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.37 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.58/21.37 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.58/21.37 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.58/21.37 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.58/21.37 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.37 e1) = all_56_14 & $i(all_56_14))
% 142.58/21.37 (3) ~ (e3 = e2)
% 142.58/21.37 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (5) ~ (e3 = e1)
% 142.58/21.37 (6) op(e0, e0) = all_56_15
% 142.58/21.37 (7) ~ (all_56_9 = e0)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (2) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (8) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.58/21.37 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.58/21.37 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2)
% 142.58/21.37 | | = all_56_12 & $i(all_56_12))
% 142.58/21.37 | |
% 142.58/21.37 | | BETA: splitting (8) gives:
% 142.58/21.37 | |
% 142.58/21.37 | | Case 1:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (9) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.58/21.37 | | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (9) implies:
% 142.58/21.37 | | | (10) all_56_9 = e0
% 142.58/21.37 | | |
% 142.58/21.37 | | | REDUCE: (7), (10) imply:
% 142.58/21.37 | | | (11) $false
% 142.58/21.37 | | |
% 142.58/21.37 | | | CLOSE: (11) is inconsistent.
% 142.58/21.37 | | |
% 142.58/21.37 | | Case 2:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (12) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.37 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (12) implies:
% 142.58/21.37 | | | (13) all_56_15 = e2
% 142.58/21.37 | | |
% 142.58/21.37 | | | REDUCE: (6), (13) imply:
% 142.58/21.37 | | | (14) op(e0, e0) = e2
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (1), (3), (4), (14) are inconsistent by sub-proof #1066.
% 142.58/21.37 | | |
% 142.58/21.37 | | End of split
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (15) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.58/21.37 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.58/21.37 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.37 | | e1) = all_56_14 & $i(all_56_14))
% 142.58/21.37 | |
% 142.58/21.37 | | BETA: splitting (15) gives:
% 142.58/21.37 | |
% 142.58/21.37 | | Case 1:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (16) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1)
% 142.58/21.37 | | | = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (16) implies:
% 142.58/21.37 | | | (17) all_56_15 = e1
% 142.58/21.37 | | |
% 142.58/21.37 | | | REDUCE: (6), (17) imply:
% 142.58/21.37 | | | (18) op(e0, e0) = e1
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (1), (4), (5), (18) are inconsistent by sub-proof #732.
% 142.58/21.37 | | |
% 142.58/21.37 | | Case 2:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (19) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1)
% 142.58/21.37 | | | = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (19) implies:
% 142.58/21.37 | | | (20) all_56_15 = e1
% 142.58/21.37 | | |
% 142.58/21.37 | | | REDUCE: (6), (20) imply:
% 142.58/21.37 | | | (21) op(e0, e0) = e1
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (1), (4), (5), (21) are inconsistent by sub-proof #732.
% 142.58/21.37 | | |
% 142.58/21.37 | | End of split
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #732 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (2) op(e0, e0) = e3
% 142.58/21.37 (3) op(e0, e0) = e1
% 142.58/21.37 (4) ~ (e3 = e1)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | GROUND_INST: instantiating (1) with e1, e3, e0, e0, simplifying with (2), (3)
% 142.58/21.37 | gives:
% 142.58/21.37 | (5) e3 = e1
% 142.58/21.37 |
% 142.58/21.37 | REDUCE: (4), (5) imply:
% 142.58/21.37 | (6) $false
% 142.58/21.37 |
% 142.58/21.37 | CLOSE: (6) is inconsistent.
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #733 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.58/21.37 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 142.58/21.37 ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2, e2) =
% 142.58/21.37 all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | (
% 142.58/21.37 ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 142.58/21.37 ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.58/21.37 all_56_4 & $i(all_56_4))) & ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~
% 142.58/21.37 (all_56_15 = e1) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 142.58/21.37 ((all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.58/21.37 all_56_14 & $i(all_56_14)))
% 142.58/21.37 (2) ~ (e1 = e0)
% 142.58/21.37 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (4) op(e3, e3) = e0
% 142.58/21.37 (5) op(e3, e1) = e3
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | ALPHA: (1) implies:
% 142.58/21.37 | (6) (all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) =
% 142.58/21.37 | all_56_1 & $i(all_56_1))
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (6) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (7) all_56_9 = e1 & op(e3, e3) = e1
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (7) implies:
% 142.58/21.37 | | (8) op(e3, e3) = e1
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #840.
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (9) ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1)
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (9) implies:
% 142.58/21.37 | | (10) ~ (all_56_1 = e3)
% 142.58/21.37 | | (11) op(e3, e1) = all_56_1
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (3), (5), (10), (11) are inconsistent by sub-proof #734.
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #734 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (2) op(e3, e1) = all_56_1
% 142.58/21.37 (3) op(e3, e1) = e3
% 142.58/21.37 (4) ~ (all_56_1 = e3)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | GROUND_INST: instantiating (1) with e3, all_56_1, e1, e3, simplifying with
% 142.58/21.37 | (2), (3) gives:
% 142.58/21.37 | (5) all_56_1 = e3
% 142.58/21.37 |
% 142.58/21.37 | REDUCE: (4), (5) imply:
% 142.58/21.37 | (6) $false
% 142.58/21.37 |
% 142.58/21.37 | CLOSE: (6) is inconsistent.
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #735 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 142.58/21.37 all_56_12 & $i(all_56_12))
% 142.58/21.37 (2) op(e0, e0) = e3
% 142.58/21.37 (3) op(e0, e3) = all_52_3
% 142.58/21.37 (4) ~ (e3 = e0)
% 142.58/21.37 (5) ~ (all_52_11 = e0)
% 142.58/21.37 (6) ~ (e3 = e2)
% 142.58/21.37 (7) op(e0, e1) = all_52_11
% 142.58/21.37 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (9) ~ (all_52_3 = e0)
% 142.58/21.37 (10) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.58/21.37 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.58/21.37 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.58/21.37 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (10) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (11) all_57_15 = e0 & op(e0, e0) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (11) implies:
% 142.58/21.37 | | (12) op(e0, e0) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (2), (4), (8), (12) are inconsistent by sub-proof #751.
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (13) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.58/21.37 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.58/21.37 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.37 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (13) implies:
% 142.58/21.37 | | (14) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.58/21.37 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (1), (2), (3), (5), (6), (7), (8), (9), (14) are inconsistent by
% 142.58/21.37 | | sub-proof #736.
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #736 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 142.58/21.37 all_56_12 & $i(all_56_12))
% 142.58/21.37 (2) op(e0, e0) = e3
% 142.58/21.37 (3) op(e0, e3) = all_52_3
% 142.58/21.37 (4) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.37 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.37 (5) ~ (all_52_11 = e0)
% 142.58/21.37 (6) ~ (e3 = e2)
% 142.58/21.37 (7) op(e0, e1) = all_52_11
% 142.58/21.37 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (9) ~ (all_52_3 = e0)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (4) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (10) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (10) implies:
% 142.58/21.37 | | (11) op(e0, e3) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (3), (8), (9), (11) are inconsistent by sub-proof #986.
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (12) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.58/21.37 | | e0)
% 142.58/21.37 | |
% 142.58/21.37 | | BETA: splitting (12) gives:
% 142.58/21.37 | |
% 142.58/21.37 | | Case 1:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (13) all_57_13 = e0 & op(e0, e2) = e0
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (13) implies:
% 142.58/21.37 | | | (14) op(e0, e2) = e0
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (1), (2), (6), (8), (14) are inconsistent by sub-proof #737.
% 142.58/21.37 | | |
% 142.58/21.37 | | Case 2:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (15) all_57_14 = e0 & op(e0, e1) = e0
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (15) implies:
% 142.58/21.37 | | | (16) op(e0, e1) = e0
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (5), (7), (8), (16) are inconsistent by sub-proof #886.
% 142.58/21.37 | | |
% 142.58/21.37 | | End of split
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #737 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) =
% 142.58/21.37 all_56_12 & $i(all_56_12))
% 142.58/21.37 (2) op(e0, e0) = e3
% 142.58/21.37 (3) op(e0, e2) = e0
% 142.58/21.37 (4) ~ (e3 = e2)
% 142.58/21.37 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (1) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (6) all_56_15 = e2 & op(e0, e0) = e2
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (6) implies:
% 142.58/21.37 | | (7) op(e0, e0) = e2
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #1066.
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (8) ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (8) implies:
% 142.58/21.37 | | (9) ~ (all_56_12 = e0)
% 142.58/21.37 | | (10) op(e0, e2) = all_56_12
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (3), (5), (9), (10) are inconsistent by sub-proof #738.
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #738 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (2) op(e0, e2) = all_56_12
% 142.58/21.37 (3) op(e0, e2) = e0
% 142.58/21.37 (4) ~ (all_56_12 = e0)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | GROUND_INST: instantiating (1) with e0, all_56_12, e2, e0, simplifying with
% 142.58/21.37 | (2), (3) gives:
% 142.58/21.37 | (5) all_56_12 = e0
% 142.58/21.37 |
% 142.58/21.37 | REDUCE: (4), (5) imply:
% 142.58/21.37 | (6) $false
% 142.58/21.37 |
% 142.58/21.37 | CLOSE: (6) is inconsistent.
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #739 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) op(e0, e0) = e3
% 142.58/21.37 (2) op(e0, e3) = all_52_3
% 142.58/21.37 (3) (all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0) =
% 142.58/21.37 all_56_15 & $i(all_56_15))
% 142.58/21.37 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (5) ~ (all_52_3 = e0)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (3) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (6) all_56_10 = e0 & op(e0, e3) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (6) implies:
% 142.58/21.37 | | (7) op(e0, e3) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (2), (4), (5), (7) are inconsistent by sub-proof #986.
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (8) ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 & $i(all_56_15)
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (8) implies:
% 142.58/21.37 | | (9) ~ (all_56_15 = e3)
% 142.58/21.37 | | (10) op(e0, e0) = all_56_15
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (1), (4), (9), (10) are inconsistent by sub-proof #740.
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #740 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (2) op(e0, e0) = all_56_15
% 142.58/21.37 (3) op(e0, e0) = e3
% 142.58/21.37 (4) ~ (all_56_15 = e3)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | GROUND_INST: instantiating (1) with e3, all_56_15, e0, e0, simplifying with
% 142.58/21.37 | (2), (3) gives:
% 142.58/21.37 | (5) all_56_15 = e3
% 142.58/21.37 |
% 142.58/21.37 | REDUCE: (4), (5) imply:
% 142.58/21.37 | (6) $false
% 142.58/21.37 |
% 142.58/21.37 | CLOSE: (6) is inconsistent.
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #741 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) all_54_6 = all_52_9
% 142.58/21.37 (2) all_54_6 = e1
% 142.58/21.37 (3) ~ (all_52_9 = e1)
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.37 | (4) all_52_9 = e1
% 142.58/21.37 |
% 142.58/21.37 | SIMP: (4) implies:
% 142.58/21.37 | (5) all_52_9 = e1
% 142.58/21.37 |
% 142.58/21.37 | REDUCE: (3), (5) imply:
% 142.58/21.37 | (6) $false
% 142.58/21.37 |
% 142.58/21.37 | CLOSE: (6) is inconsistent.
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #742 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) ~ (all_52_7 = e0)
% 142.58/21.37 (2) op(e0, e3) = all_52_3
% 142.58/21.37 (3) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.58/21.37 (all_57_14 = e0 & op(e0, e1) = e0)
% 142.58/21.37 (4) ~ (all_52_11 = e0)
% 142.58/21.37 (5) op(e0, e1) = all_52_11
% 142.58/21.37 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (7) ~ (all_52_3 = e0)
% 142.58/21.37 (8) op(e0, e2) = all_52_7
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (3) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (9) all_57_12 = e0 & op(e0, e3) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (9) implies:
% 142.58/21.37 | | (10) op(e0, e3) = e0
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (2), (6), (7), (10) are inconsistent by sub-proof #986.
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (11) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.58/21.37 | | e0)
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (1), (4), (5), (6), (8), (11) are inconsistent by sub-proof #885.
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #743 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) op(e0, e0) = e0
% 142.58/21.37 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.37 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.58/21.37 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.58/21.37 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.58/21.37 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.58/21.37 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.37 e1) = all_56_14 & $i(all_56_14))
% 142.58/21.37 (3) all_56_15 = e0
% 142.58/21.37 (4) ~ (e3 = e0)
% 142.58/21.37 (5) op(e1, e1) = all_4_2
% 142.58/21.37 (6) ~ (all_4_2 = e3)
% 142.58/21.37 (7) ~ (e1 = e0)
% 142.58/21.37 (8) op(e2, e2) = e2
% 142.58/21.37 (9) ~ (e2 = e0)
% 142.58/21.37 (10) ~ (all_4_2 = e2)
% 142.58/21.37 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (12) op(e0, e0) = all_56_15
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (2) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (13) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.58/21.37 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.58/21.37 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 142.58/21.37 | | e2) = all_56_12 & $i(all_56_12))
% 142.58/21.37 | |
% 142.58/21.37 | | BETA: splitting (13) gives:
% 142.58/21.37 | |
% 142.58/21.37 | | Case 1:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (14) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 142.58/21.37 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #747.
% 142.58/21.37 | | |
% 142.58/21.37 | | Case 2:
% 142.58/21.37 | | |
% 142.58/21.37 | | | (15) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.37 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.58/21.37 | | |
% 142.58/21.37 | | | ALPHA: (15) implies:
% 142.58/21.37 | | | (16) op(e2, e2) = e0
% 142.58/21.37 | | |
% 142.58/21.37 | | | REF_CLOSE: (8), (9), (11), (16) are inconsistent by sub-proof #1076.
% 142.58/21.37 | | |
% 142.58/21.37 | | End of split
% 142.58/21.37 | |
% 142.58/21.37 | Case 2:
% 142.58/21.37 | |
% 142.58/21.37 | | (17) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.58/21.37 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.58/21.37 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.37 | | e1) = all_56_14 & $i(all_56_14))
% 142.58/21.37 | |
% 142.58/21.37 | | REF_CLOSE: (1), (2), (5), (6), (7), (10), (11), (12), (17) are inconsistent
% 142.58/21.37 | | by sub-proof #744.
% 142.58/21.37 | |
% 142.58/21.37 | End of split
% 142.58/21.37 |
% 142.58/21.37 End of proof
% 142.58/21.37
% 142.58/21.37 Sub-proof #744 shows that the following formulas are inconsistent:
% 142.58/21.37 ----------------------------------------------------------------
% 142.58/21.37 (1) op(e0, e0) = e0
% 142.58/21.37 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.37 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.58/21.37 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.58/21.37 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.58/21.37 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.58/21.37 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.37 e1) = all_56_14 & $i(all_56_14))
% 142.58/21.37 (3) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 &
% 142.58/21.37 op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 =
% 142.58/21.37 e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.58/21.37 $i(all_56_14))
% 142.58/21.37 (4) op(e1, e1) = all_4_2
% 142.58/21.37 (5) ~ (all_4_2 = e3)
% 142.58/21.37 (6) ~ (e1 = e0)
% 142.58/21.37 (7) ~ (all_4_2 = e2)
% 142.58/21.37 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.37 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.37 (9) op(e0, e0) = all_56_15
% 142.58/21.37
% 142.58/21.37 Begin of proof
% 142.58/21.37 |
% 142.58/21.37 | BETA: splitting (3) gives:
% 142.58/21.37 |
% 142.58/21.37 | Case 1:
% 142.58/21.37 | |
% 142.58/21.37 | | (10) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.58/21.37 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 142.58/21.37 | |
% 142.58/21.37 | | ALPHA: (10) implies:
% 142.58/21.38 | | (11) op(e1, e1) = e0
% 142.58/21.38 | |
% 142.58/21.38 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11) are inconsistent by
% 142.58/21.38 | | sub-proof #745.
% 142.58/21.38 | |
% 142.58/21.38 | Case 2:
% 142.58/21.38 | |
% 142.58/21.38 | | (12) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) =
% 142.58/21.38 | | e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.58/21.38 | |
% 142.58/21.38 | | ALPHA: (12) implies:
% 142.58/21.38 | | (13) op(e1, e1) = e0
% 142.58/21.38 | |
% 142.58/21.38 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (13) are inconsistent by
% 142.58/21.38 | | sub-proof #745.
% 142.58/21.38 | |
% 142.58/21.38 | End of split
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #745 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) op(e0, e0) = e0
% 142.58/21.38 (2) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.38 op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 & all_56_15 =
% 142.58/21.38 e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0, e2) = all_56_12 &
% 142.58/21.38 $i(all_56_12)) | (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1)
% 142.58/21.38 & op(e1, e1) = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13
% 142.58/21.38 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.38 e1) = all_56_14 & $i(all_56_14))
% 142.58/21.38 (3) op(e1, e1) = e0
% 142.58/21.38 (4) op(e1, e1) = all_4_2
% 142.58/21.38 (5) ~ (all_4_2 = e3)
% 142.58/21.38 (6) ~ (e1 = e0)
% 142.58/21.38 (7) ~ (all_4_2 = e2)
% 142.58/21.38 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.38 (9) op(e0, e0) = all_56_15
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | GROUND_INST: instantiating (8) with e0, all_56_15, e0, e0, simplifying with
% 142.58/21.38 | (1), (9) gives:
% 142.58/21.38 | (10) all_56_15 = e0
% 142.58/21.38 |
% 142.58/21.38 | GROUND_INST: instantiating (8) with all_4_2, e0, e1, e1, simplifying with (3),
% 142.58/21.38 | (4) gives:
% 142.58/21.38 | (11) all_4_2 = e0
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (5), (11) imply:
% 142.58/21.38 | (12) ~ (e3 = e0)
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (12) implies:
% 142.58/21.38 | (13) ~ (e3 = e0)
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (7), (11) imply:
% 142.58/21.38 | (14) ~ (e2 = e0)
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (14) implies:
% 142.58/21.38 | (15) ~ (e2 = e0)
% 142.58/21.38 |
% 142.58/21.38 | BETA: splitting (2) gives:
% 142.58/21.38 |
% 142.58/21.38 | Case 1:
% 142.58/21.38 | |
% 142.58/21.38 | | (16) (all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) =
% 142.58/21.38 | | e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) | (all_56_11 = e0 &
% 142.58/21.38 | | all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2) = e0 & op(e0,
% 142.58/21.38 | | e2) = all_56_12 & $i(all_56_12))
% 142.58/21.38 | |
% 142.58/21.38 | | BETA: splitting (16) gives:
% 142.58/21.38 | |
% 142.58/21.38 | | Case 1:
% 142.58/21.38 | | |
% 142.58/21.38 | | | (17) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3)
% 142.58/21.38 | | | = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.58/21.38 | | |
% 142.58/21.38 | | | REF_CLOSE: (10), (13), (17) are inconsistent by sub-proof #747.
% 142.58/21.38 | | |
% 142.58/21.38 | | Case 2:
% 142.58/21.38 | | |
% 142.58/21.38 | | | (18) all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.58/21.38 | | | = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)
% 142.58/21.38 | | |
% 142.58/21.38 | | | ALPHA: (18) implies:
% 142.58/21.38 | | | (19) all_56_15 = e2
% 142.58/21.38 | | |
% 142.58/21.38 | | | COMBINE_EQS: (10), (19) imply:
% 142.58/21.38 | | | (20) e2 = e0
% 142.58/21.38 | | |
% 142.58/21.38 | | | SIMP: (20) implies:
% 142.58/21.38 | | | (21) e2 = e0
% 142.58/21.38 | | |
% 142.58/21.38 | | | REDUCE: (15), (21) imply:
% 142.58/21.38 | | | (22) $false
% 142.58/21.38 | | |
% 142.58/21.38 | | | CLOSE: (22) is inconsistent.
% 142.58/21.38 | | |
% 142.58/21.38 | | End of split
% 142.58/21.38 | |
% 142.58/21.38 | Case 2:
% 142.58/21.38 | |
% 142.58/21.38 | | (23) (all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) =
% 142.58/21.38 | | e0 & op(e1, e0) = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 &
% 142.58/21.38 | | all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1) = e0 & op(e0,
% 142.58/21.38 | | e1) = all_56_14 & $i(all_56_14))
% 142.58/21.38 | |
% 142.58/21.38 | | BETA: splitting (23) gives:
% 142.58/21.38 | |
% 142.58/21.38 | | Case 1:
% 142.58/21.38 | | |
% 142.58/21.38 | | | (24) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1)
% 142.58/21.38 | | | = e0 & op(e1, e0) = all_56_8 & $i(all_56_8)
% 142.58/21.38 | | |
% 142.58/21.38 | | | ALPHA: (24) implies:
% 142.58/21.38 | | | (25) all_56_15 = e1
% 142.58/21.38 | | |
% 142.58/21.38 | | | REF_CLOSE: (6), (10), (25) are inconsistent by sub-proof #746.
% 142.58/21.38 | | |
% 142.58/21.38 | | Case 2:
% 142.58/21.38 | | |
% 142.58/21.38 | | | (26) all_56_13 = e0 & all_56_15 = e1 & ~ (all_56_14 = e0) & op(e1, e1)
% 142.58/21.38 | | | = e0 & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.58/21.38 | | |
% 142.58/21.38 | | | ALPHA: (26) implies:
% 142.58/21.38 | | | (27) all_56_15 = e1
% 142.58/21.38 | | |
% 142.58/21.38 | | | REF_CLOSE: (6), (10), (27) are inconsistent by sub-proof #746.
% 142.58/21.38 | | |
% 142.58/21.38 | | End of split
% 142.58/21.38 | |
% 142.58/21.38 | End of split
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #746 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) all_56_15 = e1
% 142.58/21.38 (2) all_56_15 = e0
% 142.58/21.38 (3) ~ (e1 = e0)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.38 | (4) e1 = e0
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (4) implies:
% 142.58/21.38 | (5) e1 = e0
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (3), (5) imply:
% 142.58/21.38 | (6) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (6) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #747 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0) & op(e3, e3) = e0 &
% 142.58/21.38 op(e0, e3) = all_56_10 & $i(all_56_10)
% 142.58/21.38 (2) all_56_15 = e0
% 142.58/21.38 (3) ~ (e3 = e0)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | ALPHA: (1) implies:
% 142.58/21.38 | (4) all_56_15 = e3
% 142.58/21.38 |
% 142.58/21.38 | COMBINE_EQS: (2), (4) imply:
% 142.58/21.38 | (5) e3 = e0
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (5) implies:
% 142.58/21.38 | (6) e3 = e0
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (3), (6) imply:
% 142.58/21.38 | (7) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (7) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #748 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) all_54_15 = all_10_2
% 142.58/21.38 (2) all_54_15 = e1
% 142.58/21.38 (3) ~ (all_10_2 = e1)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.38 | (4) all_10_2 = e1
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (4) implies:
% 142.58/21.38 | (5) all_10_2 = e1
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (3), (5) imply:
% 142.58/21.38 | (6) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (6) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #749 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.38 (2) op(e2, e2) = e2
% 142.58/21.38 (3) op(e2, e2) = e1
% 142.58/21.38 (4) ~ (e2 = e1)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | GROUND_INST: instantiating (1) with e1, e2, e2, e2, simplifying with (2), (3)
% 142.58/21.38 | gives:
% 142.58/21.38 | (5) e2 = e1
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (4), (5) imply:
% 142.58/21.38 | (6) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (6) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #750 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) op(e0, e0) = e3
% 142.58/21.38 (2) ~ (all_10_2 = e3)
% 142.58/21.38 (3) ~ (all_10_2 = e1)
% 142.58/21.38 (4) op(e0, e0) = all_10_2
% 142.58/21.38 (5) all_54_15 = e1 | all_54_15 = e0
% 142.58/21.38 (6) all_54_15 = all_10_2
% 142.58/21.38 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | BETA: splitting (5) gives:
% 142.58/21.38 |
% 142.58/21.38 | Case 1:
% 142.58/21.38 | |
% 142.58/21.38 | | (8) all_54_15 = e1
% 142.58/21.38 | |
% 142.58/21.38 | | COMBINE_EQS: (6), (8) imply:
% 142.58/21.38 | | (9) all_10_2 = e1
% 142.58/21.38 | |
% 142.58/21.38 | | REDUCE: (3), (9) imply:
% 142.58/21.38 | | (10) $false
% 142.58/21.38 | |
% 142.58/21.38 | | CLOSE: (10) is inconsistent.
% 142.58/21.38 | |
% 142.58/21.38 | Case 2:
% 142.58/21.38 | |
% 142.58/21.38 | | (11) all_54_15 = e0
% 142.58/21.38 | |
% 142.58/21.38 | | COMBINE_EQS: (6), (11) imply:
% 142.58/21.38 | | (12) all_10_2 = e0
% 142.58/21.38 | |
% 142.58/21.38 | | REDUCE: (2), (12) imply:
% 142.58/21.38 | | (13) ~ (e3 = e0)
% 142.58/21.38 | |
% 142.58/21.38 | | SIMP: (13) implies:
% 142.58/21.38 | | (14) ~ (e3 = e0)
% 142.58/21.38 | |
% 142.58/21.38 | | REDUCE: (4), (12) imply:
% 142.58/21.38 | | (15) op(e0, e0) = e0
% 142.58/21.38 | |
% 142.58/21.38 | | REF_CLOSE: (1), (7), (14), (15) are inconsistent by sub-proof #751.
% 142.58/21.38 | |
% 142.58/21.38 | End of split
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #751 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.38 (2) op(e0, e0) = e3
% 142.58/21.38 (3) op(e0, e0) = e0
% 142.58/21.38 (4) ~ (e3 = e0)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | GROUND_INST: instantiating (1) with e0, e3, e0, e0, simplifying with (2), (3)
% 142.58/21.38 | gives:
% 142.58/21.38 | (5) e3 = e0
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (4), (5) imply:
% 142.58/21.38 | (6) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (6) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #752 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) ~ (e1 = e0)
% 142.58/21.38 (2) ~ (e2 = e0)
% 142.58/21.38 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.38 (4) op(e3, e3) = e0
% 142.58/21.38 (5) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.38 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.38 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 142.58/21.38 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.58/21.38 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.58/21.38 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 & all_56_13
% 142.58/21.38 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) = all_56_6 &
% 142.58/21.38 op(e1, e1) = e3 & $i(all_56_6))
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | BETA: splitting (5) gives:
% 142.58/21.38 |
% 142.58/21.38 | Case 1:
% 142.58/21.38 | |
% 142.58/21.38 | | (6) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) =
% 142.58/21.38 | | e2 & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) |
% 142.58/21.38 | | (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) =
% 142.58/21.38 | | e2 & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 142.58/21.38 | |
% 142.58/21.38 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #753.
% 142.58/21.38 | |
% 142.58/21.38 | Case 2:
% 142.58/21.38 | |
% 142.58/21.38 | | (7) (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 142.58/21.38 | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) |
% 142.58/21.38 | | (all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 142.58/21.38 | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6))
% 142.58/21.38 | |
% 142.58/21.38 | | BETA: splitting (7) gives:
% 142.58/21.38 | |
% 142.58/21.38 | | Case 1:
% 142.58/21.38 | | |
% 142.58/21.38 | | | (8) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) =
% 142.58/21.38 | | | e1 & op(e3, e1) = all_56_1 & op(e1, e1) = e3 & $i(all_56_1)
% 142.58/21.38 | | |
% 142.58/21.38 | | | ALPHA: (8) implies:
% 142.58/21.38 | | | (9) op(e3, e3) = e1
% 142.58/21.38 | | |
% 142.58/21.38 | | | REF_CLOSE: (1), (3), (4), (9) are inconsistent by sub-proof #840.
% 142.58/21.38 | | |
% 142.58/21.38 | | Case 2:
% 142.58/21.38 | | |
% 142.58/21.38 | | | (10) all_56_9 = e1 & all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) =
% 142.58/21.38 | | | e1 & op(e1, e3) = all_56_6 & op(e1, e1) = e3 & $i(all_56_6)
% 142.58/21.38 | | |
% 142.58/21.38 | | | ALPHA: (10) implies:
% 142.58/21.38 | | | (11) op(e3, e3) = e1
% 142.58/21.38 | | |
% 142.58/21.38 | | | REF_CLOSE: (1), (3), (4), (11) are inconsistent by sub-proof #840.
% 142.58/21.38 | | |
% 142.58/21.38 | | End of split
% 142.58/21.38 | |
% 142.58/21.38 | End of split
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #753 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.58/21.38 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.58/21.38 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2, e3)
% 142.58/21.38 = all_56_3 & op(e2, e2) = e3 & $i(all_56_3))
% 142.58/21.38 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.58/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.58/21.38 (3) op(e3, e3) = e0
% 142.58/21.38 (4) ~ (e2 = e0)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | BETA: splitting (1) gives:
% 142.58/21.38 |
% 142.58/21.38 | Case 1:
% 142.58/21.38 | |
% 142.58/21.38 | | (5) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2
% 142.58/21.38 | | & op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)
% 142.58/21.38 | |
% 142.58/21.38 | | ALPHA: (5) implies:
% 142.58/21.38 | | (6) op(e3, e3) = e2
% 142.58/21.38 | |
% 142.58/21.38 | | REF_CLOSE: (2), (3), (4), (6) are inconsistent by sub-proof #880.
% 142.58/21.38 | |
% 142.58/21.38 | Case 2:
% 142.58/21.38 | |
% 142.58/21.38 | | (7) all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2
% 142.58/21.38 | | & op(e2, e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)
% 142.58/21.38 | |
% 142.58/21.38 | | ALPHA: (7) implies:
% 142.58/21.38 | | (8) op(e3, e3) = e2
% 142.58/21.38 | |
% 142.58/21.38 | | REF_CLOSE: (2), (3), (4), (8) are inconsistent by sub-proof #880.
% 142.58/21.38 | |
% 142.58/21.38 | End of split
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #754 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) all_54_15 = all_10_2
% 142.58/21.38 (2) all_54_15 = e2
% 142.58/21.38 (3) ~ (all_10_2 = e2)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.38 | (4) all_10_2 = e2
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (4) implies:
% 142.58/21.38 | (5) all_10_2 = e2
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (3), (5) imply:
% 142.58/21.38 | (6) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (6) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #755 shows that the following formulas are inconsistent:
% 142.58/21.38 ----------------------------------------------------------------
% 142.58/21.38 (1) all_54_15 = all_10_2
% 142.58/21.38 (2) all_54_15 = e3
% 142.58/21.38 (3) ~ (all_10_2 = e3)
% 142.58/21.38
% 142.58/21.38 Begin of proof
% 142.58/21.38 |
% 142.58/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.58/21.38 | (4) all_10_2 = e3
% 142.58/21.38 |
% 142.58/21.38 | SIMP: (4) implies:
% 142.58/21.38 | (5) all_10_2 = e3
% 142.58/21.38 |
% 142.58/21.38 | REDUCE: (3), (5) imply:
% 142.58/21.38 | (6) $false
% 142.58/21.38 |
% 142.58/21.38 | CLOSE: (6) is inconsistent.
% 142.58/21.38 |
% 142.58/21.38 End of proof
% 142.58/21.38
% 142.58/21.38 Sub-proof #756 shows that the following formulas are inconsistent:
% 142.77/21.38 ----------------------------------------------------------------
% 142.77/21.38 (1) ~ (all_52_8 = all_52_11)
% 142.77/21.38 (2) ~ (all_52_8 = all_52_9)
% 142.77/21.38 (3) ~ (e2 = e1)
% 142.77/21.38 (4) ~ (all_52_11 = e2)
% 142.77/21.38 (5) ~ (all_52_9 = all_52_11)
% 142.77/21.38 (6) op(e3, e1) = all_52_8
% 142.77/21.38 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.77/21.38 (8) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 142.77/21.38 (9) ~ (e1 = e0)
% 142.77/21.38 (10) (all_56_15 = e1 & op(e0, e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.77/21.38 all_56_14 & $i(all_56_14))
% 142.77/21.38 (11) op(e0, e1) = all_52_11
% 142.77/21.38 (12) op(e3, e3) = e1
% 142.77/21.38 (13) op(e0, e0) = e2
% 142.77/21.38 (14) all_54_14 = all_52_11
% 142.77/21.38 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.77/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.77/21.38 (16) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.77/21.38 all_56_4 & $i(all_56_4))
% 142.77/21.38 (17) op(e2, e2) = e0
% 142.77/21.38 (18) op(e2, e1) = all_52_9
% 142.77/21.38 (19) all_54_6 = all_52_9
% 142.77/21.38 (20) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.77/21.38 all_56_9 & $i(all_56_9))
% 142.77/21.38 (21) ~ (all_52_9 = e0)
% 142.77/21.38
% 142.77/21.38 Begin of proof
% 142.77/21.38 |
% 142.77/21.38 | BETA: splitting (10) gives:
% 142.77/21.38 |
% 142.77/21.38 | Case 1:
% 142.77/21.38 | |
% 142.77/21.38 | | (22) all_56_15 = e1 & op(e0, e0) = e1
% 142.77/21.38 | |
% 142.77/21.38 | | ALPHA: (22) implies:
% 142.77/21.38 | | (23) op(e0, e0) = e1
% 142.77/21.38 | |
% 142.77/21.38 | | REF_CLOSE: (3), (13), (15), (23) are inconsistent by sub-proof #1070.
% 142.77/21.38 | |
% 142.77/21.38 | Case 2:
% 142.77/21.38 | |
% 142.77/21.38 | | (24) ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)
% 142.77/21.38 | |
% 142.77/21.38 | | ALPHA: (24) implies:
% 142.77/21.38 | | (25) ~ (all_56_14 = e0)
% 142.77/21.38 | | (26) op(e0, e1) = all_56_14
% 142.77/21.38 | |
% 142.77/21.38 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (11), (12), (14), (15),
% 142.77/21.38 | | (16), (17), (18), (19), (20), (21), (25), (26) are inconsistent
% 142.77/21.38 | | by sub-proof #757.
% 142.77/21.38 | |
% 142.77/21.38 | End of split
% 142.77/21.38 |
% 142.77/21.38 End of proof
% 142.77/21.38
% 142.77/21.38 Sub-proof #757 shows that the following formulas are inconsistent:
% 142.77/21.38 ----------------------------------------------------------------
% 142.77/21.38 (1) ~ (all_52_8 = all_52_11)
% 142.77/21.38 (2) ~ (all_52_8 = all_52_9)
% 142.77/21.38 (3) op(e0, e1) = all_56_14
% 142.77/21.38 (4) ~ (all_52_11 = e2)
% 142.77/21.38 (5) ~ (all_52_9 = all_52_11)
% 142.77/21.38 (6) op(e3, e1) = all_52_8
% 142.77/21.38 (7) all_54_14 = e3 | all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.77/21.38 (8) all_54_6 = e3 | all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 142.77/21.38 (9) ~ (all_56_14 = e0)
% 142.77/21.38 (10) ~ (e1 = e0)
% 142.77/21.38 (11) op(e0, e1) = all_52_11
% 142.77/21.38 (12) op(e3, e3) = e1
% 142.77/21.38 (13) all_54_14 = all_52_11
% 142.77/21.38 (14) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.77/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.77/21.38 (15) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1) =
% 142.77/21.38 all_56_4 & $i(all_56_4))
% 142.77/21.38 (16) op(e2, e2) = e0
% 142.77/21.38 (17) op(e2, e1) = all_52_9
% 142.77/21.38 (18) all_54_6 = all_52_9
% 142.77/21.38 (19) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.77/21.38 all_56_9 & $i(all_56_9))
% 142.77/21.38 (20) ~ (all_52_9 = e0)
% 142.77/21.38
% 142.77/21.38 Begin of proof
% 142.77/21.38 |
% 142.77/21.38 | BETA: splitting (15) gives:
% 142.77/21.38 |
% 142.77/21.38 | Case 1:
% 142.77/21.38 | |
% 142.77/21.38 | | (21) all_56_11 = e1 & op(e2, e2) = e1
% 142.77/21.38 | |
% 142.77/21.38 | | ALPHA: (21) implies:
% 142.77/21.38 | | (22) op(e2, e2) = e1
% 142.77/21.38 | |
% 142.77/21.38 | | REF_CLOSE: (10), (14), (16), (22) are inconsistent by sub-proof #1117.
% 142.77/21.38 | |
% 142.77/21.38 | Case 2:
% 142.77/21.38 | |
% 142.77/21.38 | | (23) ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4)
% 142.77/21.38 | |
% 142.77/21.38 | | ALPHA: (23) implies:
% 142.77/21.38 | | (24) ~ (all_56_4 = e2)
% 142.77/21.38 | | (25) op(e2, e1) = all_56_4
% 142.77/21.38 | |
% 142.77/21.38 | | BETA: splitting (19) gives:
% 142.77/21.38 | |
% 142.77/21.38 | | Case 1:
% 142.77/21.38 | | |
% 142.77/21.38 | | | (26) all_56_1 = e3 & op(e3, e1) = e3
% 142.77/21.38 | | |
% 142.77/21.38 | | | ALPHA: (26) implies:
% 142.77/21.38 | | | (27) op(e3, e1) = e3
% 142.77/21.38 | | |
% 142.77/21.38 | | | GROUND_INST: instantiating (14) with all_52_11, all_56_14, e1, e0,
% 142.77/21.38 | | | simplifying with (3), (11) gives:
% 142.77/21.38 | | | (28) all_56_14 = all_52_11
% 142.77/21.38 | | |
% 142.77/21.38 | | | GROUND_INST: instantiating (14) with all_52_9, all_56_4, e1, e2,
% 142.77/21.38 | | | simplifying with (17), (25) gives:
% 142.77/21.38 | | | (29) all_56_4 = all_52_9
% 142.77/21.38 | | |
% 142.77/21.38 | | | GROUND_INST: instantiating (14) with all_52_8, e3, e1, e3, simplifying
% 142.77/21.38 | | | with (6), (27) gives:
% 142.77/21.38 | | | (30) all_52_8 = e3
% 142.77/21.38 | | |
% 142.77/21.38 | | | REDUCE: (24), (29) imply:
% 142.78/21.38 | | | (31) ~ (all_52_9 = e2)
% 142.78/21.38 | | |
% 142.78/21.38 | | | REDUCE: (9), (28) imply:
% 142.78/21.38 | | | (32) ~ (all_52_11 = e0)
% 142.78/21.38 | | |
% 142.78/21.38 | | | REDUCE: (2), (30) imply:
% 142.78/21.38 | | | (33) ~ (all_52_9 = e3)
% 142.78/21.38 | | |
% 142.78/21.38 | | | SIMP: (33) implies:
% 142.78/21.38 | | | (34) ~ (all_52_9 = e3)
% 142.78/21.38 | | |
% 142.78/21.38 | | | REDUCE: (1), (30) imply:
% 142.78/21.38 | | | (35) ~ (all_52_11 = e3)
% 142.78/21.38 | | |
% 142.78/21.38 | | | SIMP: (35) implies:
% 142.78/21.38 | | | (36) ~ (all_52_11 = e3)
% 142.78/21.38 | | |
% 142.78/21.38 | | | BETA: splitting (7) gives:
% 142.78/21.38 | | |
% 142.78/21.38 | | | Case 1:
% 142.78/21.38 | | | |
% 142.78/21.38 | | | | (37) all_54_14 = e3
% 142.78/21.38 | | | |
% 142.78/21.38 | | | | REF_CLOSE: (13), (36), (37) are inconsistent by sub-proof #764.
% 142.78/21.38 | | | |
% 142.78/21.38 | | | Case 2:
% 142.78/21.38 | | | |
% 142.78/21.38 | | | | (38) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.78/21.38 | | | |
% 142.78/21.38 | | | | BETA: splitting (8) gives:
% 142.78/21.38 | | | |
% 142.78/21.38 | | | | Case 1:
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | | (39) all_54_6 = e3
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | | REF_CLOSE: (18), (34), (39) are inconsistent by sub-proof #763.
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | Case 2:
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | | (40) all_54_6 = e2 | all_54_6 = e1 | all_54_6 = e0
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | | BETA: splitting (40) gives:
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | | Case 1:
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | | (41) all_54_6 = e2
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | | REF_CLOSE: (18), (31), (41) are inconsistent by sub-proof #762.
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | Case 2:
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | | (42) all_54_6 = e1 | all_54_6 = e0
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | | BETA: splitting (42) gives:
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | | Case 1:
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | (43) all_54_6 = e1
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | COMBINE_EQS: (18), (43) imply:
% 142.78/21.38 | | | | | | | (44) all_52_9 = e1
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | SIMP: (44) implies:
% 142.78/21.38 | | | | | | | (45) all_52_9 = e1
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | REDUCE: (5), (45) imply:
% 142.78/21.38 | | | | | | | (46) ~ (all_52_11 = e1)
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | SIMP: (46) implies:
% 142.78/21.38 | | | | | | | (47) ~ (all_52_11 = e1)
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | REF_CLOSE: (4), (13), (32), (38), (47) are inconsistent by
% 142.78/21.38 | | | | | | | sub-proof #760.
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | Case 2:
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | (48) all_54_6 = e0
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | | REF_CLOSE: (18), (20), (48) are inconsistent by sub-proof #759.
% 142.78/21.38 | | | | | | |
% 142.78/21.38 | | | | | | End of split
% 142.78/21.38 | | | | | |
% 142.78/21.38 | | | | | End of split
% 142.78/21.38 | | | | |
% 142.78/21.38 | | | | End of split
% 142.78/21.38 | | | |
% 142.78/21.38 | | | End of split
% 142.78/21.38 | | |
% 142.78/21.38 | | Case 2:
% 142.78/21.38 | | |
% 142.78/21.38 | | | (49) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 142.78/21.38 | | |
% 142.78/21.38 | | | ALPHA: (49) implies:
% 142.78/21.38 | | | (50) ~ (all_56_9 = e1)
% 142.78/21.38 | | | (51) op(e3, e3) = all_56_9
% 142.78/21.38 | | |
% 142.78/21.38 | | | REF_CLOSE: (12), (14), (50), (51) are inconsistent by sub-proof #758.
% 142.78/21.38 | | |
% 142.78/21.38 | | End of split
% 142.78/21.38 | |
% 142.78/21.38 | End of split
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #758 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.38 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.38 (2) op(e3, e3) = all_56_9
% 142.78/21.38 (3) op(e3, e3) = e1
% 142.78/21.38 (4) ~ (all_56_9 = e1)
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | GROUND_INST: instantiating (1) with e1, all_56_9, e3, e3, simplifying with
% 142.78/21.38 | (2), (3) gives:
% 142.78/21.38 | (5) all_56_9 = e1
% 142.78/21.38 |
% 142.78/21.38 | REDUCE: (4), (5) imply:
% 142.78/21.38 | (6) $false
% 142.78/21.38 |
% 142.78/21.38 | CLOSE: (6) is inconsistent.
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #759 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) all_54_6 = all_52_9
% 142.78/21.38 (2) all_54_6 = e0
% 142.78/21.38 (3) ~ (all_52_9 = e0)
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.78/21.38 | (4) all_52_9 = e0
% 142.78/21.38 |
% 142.78/21.38 | SIMP: (4) implies:
% 142.78/21.38 | (5) all_52_9 = e0
% 142.78/21.38 |
% 142.78/21.38 | REDUCE: (3), (5) imply:
% 142.78/21.38 | (6) $false
% 142.78/21.38 |
% 142.78/21.38 | CLOSE: (6) is inconsistent.
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #760 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) ~ (all_52_11 = e1)
% 142.78/21.38 (2) ~ (all_52_11 = e2)
% 142.78/21.38 (3) all_54_14 = e2 | all_54_14 = e1 | all_54_14 = e0
% 142.78/21.38 (4) ~ (all_52_11 = e0)
% 142.78/21.38 (5) all_54_14 = all_52_11
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | BETA: splitting (3) gives:
% 142.78/21.38 |
% 142.78/21.38 | Case 1:
% 142.78/21.38 | |
% 142.78/21.38 | | (6) all_54_14 = e2
% 142.78/21.38 | |
% 142.78/21.38 | | COMBINE_EQS: (5), (6) imply:
% 142.78/21.38 | | (7) all_52_11 = e2
% 142.78/21.38 | |
% 142.78/21.38 | | SIMP: (7) implies:
% 142.78/21.38 | | (8) all_52_11 = e2
% 142.78/21.38 | |
% 142.78/21.38 | | REDUCE: (2), (8) imply:
% 142.78/21.38 | | (9) $false
% 142.78/21.38 | |
% 142.78/21.38 | | CLOSE: (9) is inconsistent.
% 142.78/21.38 | |
% 142.78/21.38 | Case 2:
% 142.78/21.38 | |
% 142.78/21.38 | | (10) all_54_14 = e1 | all_54_14 = e0
% 142.78/21.38 | |
% 142.78/21.38 | | REF_CLOSE: (1), (4), (5), (10) are inconsistent by sub-proof #761.
% 142.78/21.38 | |
% 142.78/21.38 | End of split
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #761 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) all_54_14 = e1 | all_54_14 = e0
% 142.78/21.38 (2) all_54_14 = all_52_11
% 142.78/21.38 (3) ~ (all_52_11 = e1)
% 142.78/21.38 (4) ~ (all_52_11 = e0)
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | BETA: splitting (1) gives:
% 142.78/21.38 |
% 142.78/21.38 | Case 1:
% 142.78/21.38 | |
% 142.78/21.38 | | (5) all_54_14 = e1
% 142.78/21.38 | |
% 142.78/21.38 | | COMBINE_EQS: (2), (5) imply:
% 142.78/21.38 | | (6) all_52_11 = e1
% 142.78/21.38 | |
% 142.78/21.38 | | REDUCE: (3), (6) imply:
% 142.78/21.38 | | (7) $false
% 142.78/21.38 | |
% 142.78/21.38 | | CLOSE: (7) is inconsistent.
% 142.78/21.38 | |
% 142.78/21.38 | Case 2:
% 142.78/21.38 | |
% 142.78/21.38 | | (8) all_54_14 = e0
% 142.78/21.38 | |
% 142.78/21.38 | | COMBINE_EQS: (2), (8) imply:
% 142.78/21.38 | | (9) all_52_11 = e0
% 142.78/21.38 | |
% 142.78/21.38 | | REDUCE: (4), (9) imply:
% 142.78/21.38 | | (10) $false
% 142.78/21.38 | |
% 142.78/21.38 | | CLOSE: (10) is inconsistent.
% 142.78/21.38 | |
% 142.78/21.38 | End of split
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #762 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) all_54_6 = all_52_9
% 142.78/21.38 (2) all_54_6 = e2
% 142.78/21.38 (3) ~ (all_52_9 = e2)
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.78/21.38 | (4) all_52_9 = e2
% 142.78/21.38 |
% 142.78/21.38 | SIMP: (4) implies:
% 142.78/21.38 | (5) all_52_9 = e2
% 142.78/21.38 |
% 142.78/21.38 | REDUCE: (3), (5) imply:
% 142.78/21.38 | (6) $false
% 142.78/21.38 |
% 142.78/21.38 | CLOSE: (6) is inconsistent.
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #763 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) all_54_6 = all_52_9
% 142.78/21.38 (2) all_54_6 = e3
% 142.78/21.38 (3) ~ (all_52_9 = e3)
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.78/21.38 | (4) all_52_9 = e3
% 142.78/21.38 |
% 142.78/21.38 | SIMP: (4) implies:
% 142.78/21.38 | (5) all_52_9 = e3
% 142.78/21.38 |
% 142.78/21.38 | REDUCE: (3), (5) imply:
% 142.78/21.38 | (6) $false
% 142.78/21.38 |
% 142.78/21.38 | CLOSE: (6) is inconsistent.
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #764 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) all_54_14 = all_52_11
% 142.78/21.38 (2) all_54_14 = e3
% 142.78/21.38 (3) ~ (all_52_11 = e3)
% 142.78/21.38
% 142.78/21.38 Begin of proof
% 142.78/21.38 |
% 142.78/21.38 | COMBINE_EQS: (1), (2) imply:
% 142.78/21.38 | (4) all_52_11 = e3
% 142.78/21.38 |
% 142.78/21.38 | SIMP: (4) implies:
% 142.78/21.38 | (5) all_52_11 = e3
% 142.78/21.38 |
% 142.78/21.38 | REDUCE: (3), (5) imply:
% 142.78/21.38 | (6) $false
% 142.78/21.38 |
% 142.78/21.38 | CLOSE: (6) is inconsistent.
% 142.78/21.38 |
% 142.78/21.38 End of proof
% 142.78/21.38
% 142.78/21.38 Sub-proof #765 shows that the following formulas are inconsistent:
% 142.78/21.38 ----------------------------------------------------------------
% 142.78/21.38 (1) ~ (e2 = e1)
% 142.78/21.38 (2) ~ (e3 = e0)
% 142.78/21.38 (3) op(e1, e1) = all_4_2
% 142.78/21.38 (4) ~ (e1 = e0)
% 142.78/21.38 (5) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.78/21.38 (6) ~ (e3 = e2)
% 142.78/21.39 (7) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.78/21.39 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.78/21.39 (8) ~ (all_4_2 = e2)
% 142.78/21.39 (9) op(e0, e0) = e2
% 142.78/21.39 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (11) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.78/21.39 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.78/21.39 (12) ~ (e3 = e1)
% 142.78/21.39 (13) all_57_9 = e0
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (5) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (14) all_57_8 = e2 & op(e1, e1) = e2
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (14) implies:
% 142.78/21.39 | | (15) op(e1, e1) = e2
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (3), (8), (10), (15) are inconsistent by sub-proof #1124.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (16) all_57_11 = e2 & op(e1, e0) = e2
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (16) implies:
% 142.78/21.39 | | (17) all_57_11 = e2
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (2), (4), (6), (7), (9), (10), (11), (12), (13), (17) are
% 142.78/21.39 | | inconsistent by sub-proof #851.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #766 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.78/21.39 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.78/21.39 (2) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.78/21.39 (3) ~ (e2 = e1)
% 142.78/21.39 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.78/21.39 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.78/21.39 (5) ~ (e3 = e0)
% 142.78/21.39 (6) op(e1, e1) = all_4_2
% 142.78/21.39 (7) ~ (e1 = e0)
% 142.78/21.39 (8) ~ (e2 = e0)
% 142.78/21.39 (9) ~ (e3 = e2)
% 142.78/21.39 (10) ~ (all_4_2 = e2)
% 142.78/21.39 (11) op(e0, e0) = e2
% 142.78/21.39 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.78/21.39 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.78/21.39 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.78/21.39 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.78/21.39 (14) ~ (e3 = e1)
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (2) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (15) all_57_8 = e2 & op(e1, e1) = e2
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (15) implies:
% 142.78/21.39 | | (16) op(e1, e1) = e2
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (6), (10), (12), (16) are inconsistent by sub-proof #1124.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (17) all_57_14 = e2 & op(e0, e1) = e2
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (17) implies:
% 142.78/21.39 | | (18) all_57_14 = e2
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (11), (12), (13), (14), (18)
% 142.78/21.39 | | are inconsistent by sub-proof #767.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #767 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.78/21.39 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.78/21.39 (2) ~ (e2 = e1)
% 142.78/21.39 (3) all_57_14 = e2
% 142.78/21.39 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.78/21.39 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.78/21.39 (5) ~ (e3 = e0)
% 142.78/21.39 (6) ~ (e1 = e0)
% 142.78/21.39 (7) ~ (e2 = e0)
% 142.78/21.39 (8) ~ (e3 = e2)
% 142.78/21.39 (9) op(e0, e0) = e2
% 142.78/21.39 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (11) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.78/21.39 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.78/21.39 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.78/21.39 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.78/21.39 (12) ~ (e3 = e1)
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (4) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (13) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.78/21.39 | | e1)
% 142.78/21.39 | |
% 142.78/21.39 | | BETA: splitting (13) gives:
% 142.78/21.39 | |
% 142.78/21.39 | | Case 1:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (14) all_57_12 = e1 & op(e0, e3) = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (14) implies:
% 142.78/21.39 | | | (15) all_57_12 = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | BETA: splitting (11) gives:
% 142.78/21.39 | | |
% 142.78/21.39 | | | Case 1:
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | (16) all_57_15 = e0 & op(e0, e0) = e0
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | ALPHA: (16) implies:
% 142.78/21.39 | | | | (17) op(e0, e0) = e0
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | REF_CLOSE: (7), (9), (10), (17) are inconsistent by sub-proof #1094.
% 142.78/21.39 | | | |
% 142.78/21.39 | | | Case 2:
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | (18) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 142.78/21.39 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.78/21.39 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.78/21.39 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | ALPHA: (18) implies:
% 142.78/21.39 | | | | (19) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.78/21.39 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | BETA: splitting (19) gives:
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | Case 1:
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | (20) all_57_12 = e0 & op(e0, e3) = e0
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | REF_CLOSE: (6), (15), (20) are inconsistent by sub-proof #837.
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | Case 2:
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | (21) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 142.78/21.39 | | | | | e1) = e0)
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (12),
% 142.78/21.39 | | | | | (21) are inconsistent by sub-proof #801.
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | End of split
% 142.78/21.39 | | | |
% 142.78/21.39 | | | End of split
% 142.78/21.39 | | |
% 142.78/21.39 | | Case 2:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (22) all_57_13 = e1 & op(e0, e2) = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (22) implies:
% 142.78/21.39 | | | (23) all_57_13 = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.78/21.39 | | | (23) are inconsistent by sub-proof #800.
% 142.78/21.39 | | |
% 142.78/21.39 | | End of split
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (24) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.78/21.39 | | e1)
% 142.78/21.39 | |
% 142.78/21.39 | | BETA: splitting (24) gives:
% 142.78/21.39 | |
% 142.78/21.39 | | Case 1:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (25) all_57_14 = e1 & op(e0, e1) = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (2), (3), (25) are inconsistent by sub-proof #768.
% 142.78/21.39 | | |
% 142.78/21.39 | | Case 2:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (26) all_57_15 = e1 & op(e0, e0) = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (26) implies:
% 142.78/21.39 | | | (27) op(e0, e0) = e1
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (2), (9), (10), (27) are inconsistent by sub-proof #1070.
% 142.78/21.39 | | |
% 142.78/21.39 | | End of split
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #768 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) all_57_14 = e1 & op(e0, e1) = e1
% 142.78/21.39 (2) all_57_14 = e2
% 142.78/21.39 (3) ~ (e2 = e1)
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | ALPHA: (1) implies:
% 142.78/21.39 | (4) all_57_14 = e1
% 142.78/21.39 |
% 142.78/21.39 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.39 | (5) e2 = e1
% 142.78/21.39 |
% 142.78/21.39 | REDUCE: (3), (5) imply:
% 142.78/21.39 | (6) $false
% 142.78/21.39 |
% 142.78/21.39 | CLOSE: (6) is inconsistent.
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #769 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.78/21.39 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.78/21.39 (2) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.78/21.39 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.78/21.39 (3) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.78/21.39 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.78/21.39 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.78/21.39 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.78/21.39 (5) ~ (all_52_4 = e0)
% 142.78/21.39 (6) ~ (e2 = e1)
% 142.78/21.39 (7) ~ (all_52_4 = e1)
% 142.78/21.39 (8) ~ (all_52_7 = e0)
% 142.78/21.39 (9) all_57_7 = e2
% 142.78/21.39 (10) ~ (e3 = e0)
% 142.78/21.39 (11) op(e1, e1) = all_4_2
% 142.78/21.39 (12) all_57_6 = e0
% 142.78/21.39 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.78/21.39 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.78/21.39 (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.78/21.39 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.78/21.39 (15) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.78/21.39 | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.78/21.39 (16) ~ (all_4_2 = e3)
% 142.78/21.39 (17) ~ (e1 = e0)
% 142.78/21.39 (18) op(e3, e2) = all_52_4
% 142.78/21.39 (19) ~ (e2 = e0)
% 142.78/21.39 (20) ~ (e3 = e2)
% 142.78/21.39 (21) op(e3, e3) = e1
% 142.78/21.39 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (23) ~ (all_52_13 = e2)
% 142.78/21.39 (24) ~ (e3 = e1)
% 142.78/21.39 (25) op(e0, e2) = all_52_7
% 142.78/21.39 (26) op(e2, e2) = e0
% 142.78/21.39 (27) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.78/21.39 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.78/21.39 (28) op(e2, e0) = all_52_13
% 142.78/21.39 (29) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.78/21.39 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.78/21.39 (30) all_57_12 = e2
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (15) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (31) all_57_12 = e0 & op(e0, e3) = e0
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (19), (30), (31) are inconsistent by sub-proof #958.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (32) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.78/21.39 | | e0)
% 142.78/21.39 | |
% 142.78/21.39 | | BETA: splitting (32) gives:
% 142.78/21.39 | |
% 142.78/21.39 | | Case 1:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (33) all_57_13 = e0 & op(e0, e2) = e0
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (33) implies:
% 142.78/21.39 | | | (34) op(e0, e2) = e0
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (8), (22), (25), (34) are inconsistent by sub-proof #977.
% 142.78/21.39 | | |
% 142.78/21.39 | | Case 2:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (35) all_57_14 = e0 & op(e0, e1) = e0
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (35) implies:
% 142.78/21.39 | | | (36) all_57_14 = e0
% 142.78/21.39 | | |
% 142.78/21.39 | | | BETA: splitting (2) gives:
% 142.78/21.39 | | |
% 142.78/21.39 | | | Case 1:
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | (37) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2)
% 142.78/21.39 | | | | = e1)
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | REF_CLOSE: (7), (17), (18), (22), (26), (37) are inconsistent by
% 142.78/21.39 | | | | sub-proof #843.
% 142.78/21.39 | | | |
% 142.78/21.39 | | | Case 2:
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | (38) (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2)
% 142.78/21.39 | | | | = e1)
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | BETA: splitting (38) gives:
% 142.78/21.39 | | | |
% 142.78/21.39 | | | | Case 1:
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | (39) all_57_7 = e1 & op(e1, e2) = e1
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | REF_CLOSE: (6), (9), (39) are inconsistent by sub-proof #864.
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | Case 2:
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | (40) all_57_13 = e1 & op(e0, e2) = e1
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | ALPHA: (40) implies:
% 142.78/21.39 | | | | | (41) all_57_13 = e1
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | BETA: splitting (29) gives:
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | | Case 1:
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | | (42) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2,
% 142.78/21.39 | | | | | | e2) = e3)
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | | BETA: splitting (42) gives:
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | | Case 1:
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | (43) all_57_1 = e3 & op(e3, e2) = e3
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | ALPHA: (43) implies:
% 142.78/21.39 | | | | | | | (44) all_57_1 = e3
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | BETA: splitting (1) gives:
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | | (45) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 &
% 142.78/21.39 | | | | | | | | op(e3, e2) = e2)
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | | BETA: splitting (45) gives:
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | (46) all_57_0 = e2 & op(e3, e3) = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | ALPHA: (46) implies:
% 142.78/21.39 | | | | | | | | | (47) op(e3, e3) = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | REF_CLOSE: (6), (21), (22), (47) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | | | | #818.
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | (48) all_57_1 = e2 & op(e3, e2) = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | REF_CLOSE: (20), (44), (48) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | | | | #782.
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | End of split
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | | (49) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 &
% 142.78/21.39 | | | | | | | | op(e3, e0) = e2)
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | | BETA: splitting (49) gives:
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | (50) all_57_4 = e2 & op(e3, e1) = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | ALPHA: (50) implies:
% 142.78/21.39 | | | | | | | | | (51) all_57_4 = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | BETA: splitting (3) gives:
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | (52) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 142.78/21.39 | | | | | | | | | | op(e2, e1) = e3)
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | BETA: splitting (52) gives:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | (53) all_57_4 = e3 & op(e3, e1) = e3
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | ALPHA: (53) implies:
% 142.78/21.39 | | | | | | | | | | | (54) all_57_4 = e3
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | REF_CLOSE: (20), (51), (54) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | | | | | | #821.
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | (55) all_57_5 = e3 & op(e2, e1) = e3
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (13), (19), (20), (21), (22),
% 142.78/21.39 | | | | | | | | | | | (23), (24), (26), (28), (30), (55) are
% 142.78/21.39 | | | | | | | | | | | inconsistent by sub-proof #778.
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | (56) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 142.78/21.39 | | | | | | | | | | & op(e0, e1) = e3)
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | REF_CLOSE: (10), (11), (16), (22), (36), (56) are
% 142.78/21.39 | | | | | | | | | | inconsistent by sub-proof #776.
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | (57) all_57_9 = e2 & op(e3, e0) = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | ALPHA: (57) implies:
% 142.78/21.39 | | | | | | | | | (58) all_57_9 = e2
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | BETA: splitting (27) gives:
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | (59) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 &
% 142.78/21.39 | | | | | | | | | | op(e3, e2) = e0)
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | BETA: splitting (59) gives:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | (60) all_57_0 = e0 & op(e3, e3) = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | ALPHA: (60) implies:
% 142.78/21.39 | | | | | | | | | | | (61) all_57_0 = e0
% 142.78/21.39 | | | | | | | | | | | (62) op(e3, e3) = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | REF_CLOSE: (6), (10), (12), (13), (14), (17), (20), (22),
% 142.78/21.39 | | | | | | | | | | | (24), (30), (61), (62) are inconsistent by
% 142.78/21.39 | | | | | | | | | | | sub-proof #771.
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | (63) all_57_1 = e0 & op(e3, e2) = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | REF_CLOSE: (5), (18), (22), (63) are inconsistent by
% 142.78/21.39 | | | | | | | | | | | sub-proof #1102.
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | (64) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 &
% 142.78/21.39 | | | | | | | | | | op(e3, e0) = e0)
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | BETA: splitting (64) gives:
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | (65) all_57_4 = e0 & op(e3, e1) = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | ALPHA: (65) implies:
% 142.78/21.39 | | | | | | | | | | | (66) all_57_4 = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | BETA: splitting (3) gives:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | (67) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3
% 142.78/21.39 | | | | | | | | | | | | & op(e2, e1) = e3)
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | BETA: splitting (67) gives:
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | Case 1:
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | | (68) all_57_4 = e3 & op(e3, e1) = e3
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | | ALPHA: (68) implies:
% 142.78/21.39 | | | | | | | | | | | | | (69) all_57_4 = e3
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | | REF_CLOSE: (10), (66), (69) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | | | | | | | | #831.
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | | (70) all_57_5 = e3 & op(e2, e1) = e3
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | | REF_CLOSE: (4), (10), (12), (13), (19), (20), (21), (22),
% 142.78/21.39 | | | | | | | | | | | | | (23), (24), (26), (28), (30), (70) are
% 142.78/21.39 | | | | | | | | | | | | | inconsistent by sub-proof #778.
% 142.78/21.39 | | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | (71) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 =
% 142.78/21.39 | | | | | | | | | | | | e3 & op(e0, e1) = e3)
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | | REF_CLOSE: (10), (11), (16), (22), (36), (71) are
% 142.78/21.39 | | | | | | | | | | | | inconsistent by sub-proof #776.
% 142.78/21.39 | | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | Case 2:
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | (72) all_57_9 = e0 & op(e3, e0) = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | ALPHA: (72) implies:
% 142.78/21.39 | | | | | | | | | | | (73) all_57_9 = e0
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | | REF_CLOSE: (19), (58), (73) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | | | | | | #1018.
% 142.78/21.39 | | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | | |
% 142.78/21.39 | | | | | | | | | End of split
% 142.78/21.39 | | | | | | | | |
% 142.78/21.39 | | | | | | | | End of split
% 142.78/21.39 | | | | | | | |
% 142.78/21.39 | | | | | | | End of split
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | Case 2:
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | (74) all_57_3 = e3 & op(e2, e2) = e3
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | ALPHA: (74) implies:
% 142.78/21.39 | | | | | | | (75) op(e2, e2) = e3
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | | REF_CLOSE: (10), (22), (26), (75) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | | #1119.
% 142.78/21.39 | | | | | | |
% 142.78/21.39 | | | | | | End of split
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | Case 2:
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | | (76) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0,
% 142.78/21.39 | | | | | | e2) = e3)
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | | REF_CLOSE: (9), (20), (24), (41), (76) are inconsistent by sub-proof
% 142.78/21.39 | | | | | | #770.
% 142.78/21.39 | | | | | |
% 142.78/21.39 | | | | | End of split
% 142.78/21.39 | | | | |
% 142.78/21.39 | | | | End of split
% 142.78/21.39 | | | |
% 142.78/21.39 | | | End of split
% 142.78/21.39 | | |
% 142.78/21.39 | | End of split
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #770 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) all_57_7 = e2
% 142.78/21.39 (2) (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.78/21.39 (3) all_57_13 = e1
% 142.78/21.39 (4) ~ (e3 = e2)
% 142.78/21.39 (5) ~ (e3 = e1)
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (2) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (6) all_57_7 = e3 & op(e1, e2) = e3
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (6) implies:
% 142.78/21.39 | | (7) all_57_7 = e3
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #1098.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (8) all_57_13 = e3 & op(e0, e2) = e3
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (8) implies:
% 142.78/21.39 | | (9) all_57_13 = e3
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1001.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #771 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) ~ (e2 = e1)
% 142.78/21.39 (2) ~ (e3 = e0)
% 142.78/21.39 (3) all_57_6 = e0
% 142.78/21.39 (4) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.78/21.39 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.78/21.39 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.78/21.39 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.78/21.39 (6) ~ (e1 = e0)
% 142.78/21.39 (7) ~ (e3 = e2)
% 142.78/21.39 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (9) ~ (e3 = e1)
% 142.78/21.39 (10) all_57_0 = e0
% 142.78/21.39 (11) op(e3, e3) = e0
% 142.78/21.39 (12) all_57_12 = e2
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (4) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 142.78/21.39 | | e3)
% 142.78/21.39 | |
% 142.78/21.39 | | BETA: splitting (13) gives:
% 142.78/21.39 | |
% 142.78/21.39 | | Case 1:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (14) all_57_0 = e3 & op(e3, e3) = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (2), (10), (14) are inconsistent by sub-proof #1108.
% 142.78/21.39 | | |
% 142.78/21.39 | | Case 2:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (15) all_57_2 = e3 & op(e2, e3) = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (15) implies:
% 142.78/21.39 | | | (16) all_57_2 = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (1), (3), (5), (6), (8), (9), (11), (12), (16) are inconsistent
% 142.78/21.39 | | | by sub-proof #773.
% 142.78/21.39 | | |
% 142.78/21.39 | | End of split
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (17) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.78/21.39 | | e3)
% 142.78/21.39 | |
% 142.78/21.39 | | BETA: splitting (17) gives:
% 142.78/21.39 | |
% 142.78/21.39 | | Case 1:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (18) all_57_6 = e3 & op(e1, e3) = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (18) implies:
% 142.78/21.39 | | | (19) all_57_6 = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (2), (3), (19) are inconsistent by sub-proof #873.
% 142.78/21.39 | | |
% 142.78/21.39 | | Case 2:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (20) all_57_12 = e3 & op(e0, e3) = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (20) implies:
% 142.78/21.39 | | | (21) all_57_12 = e3
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (7), (12), (21) are inconsistent by sub-proof #772.
% 142.78/21.39 | | |
% 142.78/21.39 | | End of split
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #772 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) all_57_12 = e3
% 142.78/21.39 (2) all_57_12 = e2
% 142.78/21.39 (3) ~ (e3 = e2)
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | COMBINE_EQS: (1), (2) imply:
% 142.78/21.39 | (4) e3 = e2
% 142.78/21.39 |
% 142.78/21.39 | SIMP: (4) implies:
% 142.78/21.39 | (5) e3 = e2
% 142.78/21.39 |
% 142.78/21.39 | REDUCE: (3), (5) imply:
% 142.78/21.39 | (6) $false
% 142.78/21.39 |
% 142.78/21.39 | CLOSE: (6) is inconsistent.
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #773 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) ~ (e2 = e1)
% 142.78/21.39 (2) all_57_6 = e0
% 142.78/21.39 (3) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.78/21.39 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.78/21.39 (4) ~ (e1 = e0)
% 142.78/21.39 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (6) ~ (e3 = e1)
% 142.78/21.39 (7) op(e3, e3) = e0
% 142.78/21.39 (8) all_57_2 = e3
% 142.78/21.39 (9) all_57_12 = e2
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (3) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (10) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 142.78/21.39 | | e1)
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (4), (5), (6), (7), (8), (10) are inconsistent by sub-proof #775.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (11) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 142.78/21.39 | | e1)
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (2), (4), (9), (11) are inconsistent by sub-proof #774.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #774 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) ~ (e2 = e1)
% 142.78/21.39 (2) all_57_6 = e0
% 142.78/21.39 (3) ~ (e1 = e0)
% 142.78/21.39 (4) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.78/21.39 (5) all_57_12 = e2
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (4) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (6) all_57_6 = e1 & op(e1, e3) = e1
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (6) implies:
% 142.78/21.39 | | (7) all_57_6 = e1
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #1026.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (8) all_57_12 = e1 & op(e0, e3) = e1
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (5), (8) are inconsistent by sub-proof #848.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #775 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) ~ (e1 = e0)
% 142.78/21.39 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (3) ~ (e3 = e1)
% 142.78/21.39 (4) op(e3, e3) = e0
% 142.78/21.39 (5) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1)
% 142.78/21.39 (6) all_57_2 = e3
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (5) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (7) all_57_0 = e1 & op(e3, e3) = e1
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (7) implies:
% 142.78/21.39 | | (8) op(e3, e3) = e1
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (2), (4), (8) are inconsistent by sub-proof #840.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (9) all_57_2 = e1 & op(e2, e3) = e1
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (3), (6), (9) are inconsistent by sub-proof #939.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #776 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) all_57_14 = e0
% 142.78/21.39 (2) ~ (e3 = e0)
% 142.78/21.39 (3) op(e1, e1) = all_4_2
% 142.78/21.39 (4) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.78/21.39 (5) ~ (all_4_2 = e3)
% 142.78/21.39 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (4) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 142.78/21.39 | |
% 142.78/21.39 | | ALPHA: (7) implies:
% 142.78/21.39 | | (8) op(e1, e1) = e3
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1127.
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.39 | | (9) all_57_14 = e3 & op(e0, e1) = e3
% 142.78/21.39 | |
% 142.78/21.39 | | REF_CLOSE: (1), (2), (9) are inconsistent by sub-proof #777.
% 142.78/21.39 | |
% 142.78/21.39 | End of split
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #777 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) all_57_14 = e3 & op(e0, e1) = e3
% 142.78/21.39 (2) all_57_14 = e0
% 142.78/21.39 (3) ~ (e3 = e0)
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | ALPHA: (1) implies:
% 142.78/21.39 | (4) all_57_14 = e3
% 142.78/21.39 |
% 142.78/21.39 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.39 | (5) e3 = e0
% 142.78/21.39 |
% 142.78/21.39 | REDUCE: (3), (5) imply:
% 142.78/21.39 | (6) $false
% 142.78/21.39 |
% 142.78/21.39 | CLOSE: (6) is inconsistent.
% 142.78/21.39 |
% 142.78/21.39 End of proof
% 142.78/21.39
% 142.78/21.39 Sub-proof #778 shows that the following formulas are inconsistent:
% 142.78/21.39 ----------------------------------------------------------------
% 142.78/21.39 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.78/21.39 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.78/21.39 (2) ~ (e3 = e0)
% 142.78/21.39 (3) all_57_6 = e0
% 142.78/21.39 (4) all_57_5 = e3 & op(e2, e1) = e3
% 142.78/21.39 (5) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.78/21.39 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.78/21.39 (6) ~ (e2 = e0)
% 142.78/21.39 (7) ~ (e3 = e2)
% 142.78/21.39 (8) op(e3, e3) = e1
% 142.78/21.39 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.39 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.39 (10) ~ (all_52_13 = e2)
% 142.78/21.39 (11) ~ (e3 = e1)
% 142.78/21.39 (12) op(e2, e2) = e0
% 142.78/21.39 (13) op(e2, e0) = all_52_13
% 142.78/21.39 (14) all_57_12 = e2
% 142.78/21.39
% 142.78/21.39 Begin of proof
% 142.78/21.39 |
% 142.78/21.39 | ALPHA: (4) implies:
% 142.78/21.39 | (15) all_57_5 = e3
% 142.78/21.39 |
% 142.78/21.39 | BETA: splitting (1) gives:
% 142.78/21.39 |
% 142.78/21.39 | Case 1:
% 142.78/21.39 | |
% 142.78/21.39 | | (16) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) =
% 142.78/21.39 | | e2)
% 142.78/21.39 | |
% 142.78/21.39 | | BETA: splitting (16) gives:
% 142.78/21.39 | |
% 142.78/21.39 | | Case 1:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (17) all_57_2 = e2 & op(e2, e3) = e2
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (17) implies:
% 142.78/21.39 | | | (18) all_57_2 = e2
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (11), (14), (18) are inconsistent
% 142.78/21.39 | | | by sub-proof #779.
% 142.78/21.39 | | |
% 142.78/21.39 | | Case 2:
% 142.78/21.39 | | |
% 142.78/21.39 | | | (19) all_57_3 = e2 & op(e2, e2) = e2
% 142.78/21.39 | | |
% 142.78/21.39 | | | ALPHA: (19) implies:
% 142.78/21.39 | | | (20) op(e2, e2) = e2
% 142.78/21.39 | | |
% 142.78/21.39 | | | REF_CLOSE: (6), (9), (12), (20) are inconsistent by sub-proof #1076.
% 142.78/21.39 | | |
% 142.78/21.39 | | End of split
% 142.78/21.39 | |
% 142.78/21.39 | Case 2:
% 142.78/21.39 | |
% 142.78/21.40 | | (21) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) =
% 142.78/21.40 | | e2)
% 142.78/21.40 | |
% 142.78/21.40 | | BETA: splitting (21) gives:
% 142.78/21.40 | |
% 142.78/21.40 | | Case 1:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (22) all_57_5 = e2 & op(e2, e1) = e2
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (22) implies:
% 142.78/21.40 | | | (23) all_57_5 = e2
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (7), (15), (23) are inconsistent by sub-proof #936.
% 142.78/21.40 | | |
% 142.78/21.40 | | Case 2:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (24) all_57_10 = e2 & op(e2, e0) = e2
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (24) implies:
% 142.78/21.40 | | | (25) op(e2, e0) = e2
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (9), (10), (13), (25) are inconsistent by sub-proof #1030.
% 142.78/21.40 | | |
% 142.78/21.40 | | End of split
% 142.78/21.40 | |
% 142.78/21.40 | End of split
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #779 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) ~ (e3 = e0)
% 142.78/21.40 (2) all_57_6 = e0
% 142.78/21.40 (3) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.78/21.40 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.78/21.40 (4) ~ (e3 = e2)
% 142.78/21.40 (5) op(e3, e3) = e1
% 142.78/21.40 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.40 (7) ~ (e3 = e1)
% 142.78/21.40 (8) all_57_2 = e2
% 142.78/21.40 (9) all_57_12 = e2
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | BETA: splitting (3) gives:
% 142.78/21.40 |
% 142.78/21.40 | Case 1:
% 142.78/21.40 | |
% 142.78/21.40 | | (10) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) =
% 142.78/21.40 | | e3)
% 142.78/21.40 | |
% 142.78/21.40 | | BETA: splitting (10) gives:
% 142.78/21.40 | |
% 142.78/21.40 | | Case 1:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (11) all_57_0 = e3 & op(e3, e3) = e3
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (11) implies:
% 142.78/21.40 | | | (12) op(e3, e3) = e3
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (5), (6), (7), (12) are inconsistent by sub-proof #838.
% 142.78/21.40 | | |
% 142.78/21.40 | | Case 2:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (13) all_57_2 = e3 & op(e2, e3) = e3
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (4), (8), (13) are inconsistent by sub-proof #781.
% 142.78/21.40 | | |
% 142.78/21.40 | | End of split
% 142.78/21.40 | |
% 142.78/21.40 | Case 2:
% 142.78/21.40 | |
% 142.78/21.40 | | (14) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) =
% 142.78/21.40 | | e3)
% 142.78/21.40 | |
% 142.78/21.40 | | BETA: splitting (14) gives:
% 142.78/21.40 | |
% 142.78/21.40 | | Case 1:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (15) all_57_6 = e3 & op(e1, e3) = e3
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (15) implies:
% 142.78/21.40 | | | (16) all_57_6 = e3
% 142.78/21.40 | | |
% 142.78/21.40 | | | COMBINE_EQS: (2), (16) imply:
% 142.78/21.40 | | | (17) e3 = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | REDUCE: (1), (17) imply:
% 142.78/21.40 | | | (18) $false
% 142.78/21.40 | | |
% 142.78/21.40 | | | CLOSE: (18) is inconsistent.
% 142.78/21.40 | | |
% 142.78/21.40 | | Case 2:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (19) all_57_12 = e3 & op(e0, e3) = e3
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (4), (9), (19) are inconsistent by sub-proof #780.
% 142.78/21.40 | | |
% 142.78/21.40 | | End of split
% 142.78/21.40 | |
% 142.78/21.40 | End of split
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #780 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) all_57_12 = e3 & op(e0, e3) = e3
% 142.78/21.40 (2) all_57_12 = e2
% 142.78/21.40 (3) ~ (e3 = e2)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | ALPHA: (1) implies:
% 142.78/21.40 | (4) all_57_12 = e3
% 142.78/21.40 |
% 142.78/21.40 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.40 | (5) e3 = e2
% 142.78/21.40 |
% 142.78/21.40 | REDUCE: (3), (5) imply:
% 142.78/21.40 | (6) $false
% 142.78/21.40 |
% 142.78/21.40 | CLOSE: (6) is inconsistent.
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #781 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) all_57_2 = e3 & op(e2, e3) = e3
% 142.78/21.40 (2) all_57_2 = e2
% 142.78/21.40 (3) ~ (e3 = e2)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | ALPHA: (1) implies:
% 142.78/21.40 | (4) all_57_2 = e3
% 142.78/21.40 |
% 142.78/21.40 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.40 | (5) e3 = e2
% 142.78/21.40 |
% 142.78/21.40 | REDUCE: (3), (5) imply:
% 142.78/21.40 | (6) $false
% 142.78/21.40 |
% 142.78/21.40 | CLOSE: (6) is inconsistent.
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #782 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) all_57_1 = e2 & op(e3, e2) = e2
% 142.78/21.40 (2) all_57_1 = e3
% 142.78/21.40 (3) ~ (e3 = e2)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | ALPHA: (1) implies:
% 142.78/21.40 | (4) all_57_1 = e2
% 142.78/21.40 |
% 142.78/21.40 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.40 | (5) e3 = e2
% 142.78/21.40 |
% 142.78/21.40 | REDUCE: (3), (5) imply:
% 142.78/21.40 | (6) $false
% 142.78/21.40 |
% 142.78/21.40 | CLOSE: (6) is inconsistent.
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #783 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) all_57_6 = e2 & op(e1, e3) = e2
% 142.78/21.40 (2) all_57_6 = e0
% 142.78/21.40 (3) ~ (e2 = e0)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | ALPHA: (1) implies:
% 142.78/21.40 | (4) all_57_6 = e2
% 142.78/21.40 |
% 142.78/21.40 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.40 | (5) e2 = e0
% 142.78/21.40 |
% 142.78/21.40 | REDUCE: (3), (5) imply:
% 142.78/21.40 | (6) $false
% 142.78/21.40 |
% 142.78/21.40 | CLOSE: (6) is inconsistent.
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #784 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.78/21.40 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.78/21.40 (2) ~ (e2 = e1)
% 142.78/21.40 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.78/21.40 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.78/21.40 (4) ~ (e3 = e0)
% 142.78/21.40 (5) op(e1, e1) = e1
% 142.78/21.40 (6) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.78/21.40 (7) ~ (e1 = e0)
% 142.78/21.40 (8) ~ (e2 = e0)
% 142.78/21.40 (9) ~ (e3 = e2)
% 142.78/21.40 (10) op(e0, e0) = e2
% 142.78/21.40 (11) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.78/21.40 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.78/21.40 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.40 (13) ~ (e3 = e1)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | BETA: splitting (6) gives:
% 142.78/21.40 |
% 142.78/21.40 | Case 1:
% 142.78/21.40 | |
% 142.78/21.40 | | (14) all_57_14 = e1 & op(e0, e1) = e1
% 142.78/21.40 | |
% 142.78/21.40 | | ALPHA: (14) implies:
% 142.78/21.40 | | (15) all_57_14 = e1
% 142.78/21.40 | |
% 142.78/21.40 | | REF_CLOSE: (1), (2), (3), (4), (5), (7), (8), (9), (11), (12), (13), (15)
% 142.78/21.40 | | are inconsistent by sub-proof #785.
% 142.78/21.40 | |
% 142.78/21.40 | Case 2:
% 142.78/21.40 | |
% 142.78/21.40 | | (16) all_57_15 = e1 & op(e0, e0) = e1
% 142.78/21.40 | |
% 142.78/21.40 | | ALPHA: (16) implies:
% 142.78/21.40 | | (17) op(e0, e0) = e1
% 142.78/21.40 | |
% 142.78/21.40 | | REF_CLOSE: (2), (10), (12), (17) are inconsistent by sub-proof #1070.
% 142.78/21.40 | |
% 142.78/21.40 | End of split
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #785 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.78/21.40 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.78/21.40 (2) ~ (e2 = e1)
% 142.78/21.40 (3) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.78/21.40 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.78/21.40 (4) ~ (e3 = e0)
% 142.78/21.40 (5) op(e1, e1) = e1
% 142.78/21.40 (6) all_57_14 = e1
% 142.78/21.40 (7) ~ (e1 = e0)
% 142.78/21.40 (8) ~ (e2 = e0)
% 142.78/21.40 (9) ~ (e3 = e2)
% 142.78/21.40 (10) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.78/21.40 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.78/21.40 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.78/21.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.78/21.40 (12) ~ (e3 = e1)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | BETA: splitting (3) gives:
% 142.78/21.40 |
% 142.78/21.40 | Case 1:
% 142.78/21.40 | |
% 142.78/21.40 | | (13) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 142.78/21.40 | | e0)
% 142.78/21.40 | |
% 142.78/21.40 | | BETA: splitting (13) gives:
% 142.78/21.40 | |
% 142.78/21.40 | | Case 1:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (14) all_57_4 = e0 & op(e3, e1) = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (14) implies:
% 142.78/21.40 | | | (15) all_57_4 = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (15) are
% 142.78/21.40 | | | inconsistent by sub-proof #830.
% 142.78/21.40 | | |
% 142.78/21.40 | | Case 2:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (16) all_57_5 = e0 & op(e2, e1) = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (16) implies:
% 142.78/21.40 | | | (17) all_57_5 = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (1), (2), (4), (5), (6), (8), (9), (10), (11), (12), (17) are
% 142.78/21.40 | | | inconsistent by sub-proof #1040.
% 142.78/21.40 | | |
% 142.78/21.40 | | End of split
% 142.78/21.40 | |
% 142.78/21.40 | Case 2:
% 142.78/21.40 | |
% 142.78/21.40 | | (18) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.78/21.40 | | e0)
% 142.78/21.40 | |
% 142.78/21.40 | | BETA: splitting (18) gives:
% 142.78/21.40 | |
% 142.78/21.40 | | Case 1:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (19) all_57_8 = e0 & op(e1, e1) = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | ALPHA: (19) implies:
% 142.78/21.40 | | | (20) op(e1, e1) = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (5), (7), (11), (20) are inconsistent by sub-proof #1089.
% 142.78/21.40 | | |
% 142.78/21.40 | | Case 2:
% 142.78/21.40 | | |
% 142.78/21.40 | | | (21) all_57_14 = e0 & op(e0, e1) = e0
% 142.78/21.40 | | |
% 142.78/21.40 | | | REF_CLOSE: (6), (7), (21) are inconsistent by sub-proof #786.
% 142.78/21.40 | | |
% 142.78/21.40 | | End of split
% 142.78/21.40 | |
% 142.78/21.40 | End of split
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #786 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) all_57_14 = e0 & op(e0, e1) = e0
% 142.78/21.40 (2) all_57_14 = e1
% 142.78/21.40 (3) ~ (e1 = e0)
% 142.78/21.40
% 142.78/21.40 Begin of proof
% 142.78/21.40 |
% 142.78/21.40 | ALPHA: (1) implies:
% 142.78/21.40 | (4) all_57_14 = e0
% 142.78/21.40 |
% 142.78/21.40 | COMBINE_EQS: (2), (4) imply:
% 142.78/21.40 | (5) e1 = e0
% 142.78/21.40 |
% 142.78/21.40 | REDUCE: (3), (5) imply:
% 142.78/21.40 | (6) $false
% 142.78/21.40 |
% 142.78/21.40 | CLOSE: (6) is inconsistent.
% 142.78/21.40 |
% 142.78/21.40 End of proof
% 142.78/21.40
% 142.78/21.40 Sub-proof #787 shows that the following formulas are inconsistent:
% 142.78/21.40 ----------------------------------------------------------------
% 142.78/21.40 (1) ~ (all_52_14 = e2)
% 142.78/21.40 (2) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.78/21.40 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.78/21.40 (3) ( ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) = all_40_1
% 142.78/21.40 & $i(all_40_0) & $i(all_40_1)) | ( ~ (all_40_1 = e1) & op(e0, e2) =
% 142.78/21.40 all_40_1 & $i(all_40_1))
% 142.78/21.40 (4) ( ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) = all_24_1
% 142.78/21.40 & $i(all_24_0) & $i(all_24_1)) | ( ~ (all_24_1 = e3) & op(e0, e2) =
% 142.78/21.40 all_24_1 & $i(all_24_1))
% 142.78/21.40 (5) op(e1, e2) = all_52_6
% 142.78/21.40 (6) ~ (all_52_2 = all_52_14)
% 142.78/21.40 (7) ~ (all_52_4 = e0)
% 142.78/21.40 (8) all_54_11 = all_52_14
% 142.78/21.40 (9) ~ (all_52_7 = e0)
% 142.78/21.40 (10) op(e2, e0) = e1
% 142.78/21.40 (11) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 142.78/21.40 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 142.78/21.40 e0) = all_16_1 & $i(all_16_1))
% 142.78/21.40 (12) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 142.78/21.40 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2,
% 142.78/21.40 e0) = all_18_1 & $i(all_18_1))
% 142.78/21.40 (13) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 142.78/21.40 (14) ~ (all_52_2 = all_52_6)
% 142.80/21.40 (15) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.80/21.40 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.80/21.40 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.80/21.40 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.80/21.40 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.80/21.40 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.80/21.40 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.80/21.40 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.80/21.40 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.80/21.40 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.80/21.40 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.80/21.40 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.80/21.40 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.80/21.40 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.80/21.40 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.80/21.40 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.80/21.40 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.80/21.40 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.80/21.40 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.80/21.40 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.80/21.40 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.80/21.40 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.80/21.40 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.80/21.40 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.80/21.40 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.80/21.40 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.80/21.40 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.80/21.40 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.80/21.40 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.80/21.40 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.80/21.40 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.80/21.40 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.80/21.40 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.80/21.40 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.80/21.40 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.80/21.40 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.80/21.40 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.80/21.40 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.80/21.40 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.80/21.40 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.80/21.40 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.80/21.40 (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.80/21.40 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.80/21.40 e1)
% 142.80/21.40 (17) ~ (all_52_1 = e0)
% 142.80/21.40 (18) op(e1, e1) = e1
% 142.80/21.40 (19) all_57_13 = e1 & op(e0, e2) = e1
% 142.80/21.40 (20) ~ (all_52_12 = all_52_14)
% 142.80/21.40 (21) all_54_9 = all_52_6
% 142.80/21.40 (22) ~ (all_52_1 = all_52_13)
% 142.80/21.40 (23) ~ (all_52_6 = all_52_7)
% 142.80/21.40 (24) op(e2, e3) = all_52_1
% 142.80/21.40 (25) ~ (all_52_6 = all_52_14)
% 142.80/21.40 (26) ~ (all_52_13 = all_52_14)
% 142.80/21.40 (27) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.80/21.40 (28) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 142.80/21.40 (29) op(e3, e2) = all_52_4
% 142.80/21.40 (30) op(e3, e0) = all_52_12
% 142.80/21.40 (31) ~ (all_52_2 = e1)
% 142.80/21.40 (32) ~ (all_52_1 = all_52_2)
% 142.80/21.40 (33) op(e3, e3) = e1
% 142.80/21.40 (34) op(e0, e0) = e2
% 142.80/21.40 (35) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.80/21.40 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.80/21.40 (36) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.80/21.40 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.80/21.40 (37) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.80/21.40 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.80/21.40 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.80/21.40 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.80/21.40 (38) ~ (all_52_13 = e2)
% 142.80/21.40 (39) op(e0, e2) = all_52_7
% 142.80/21.40 (40) all_54_4 = all_52_1
% 142.80/21.40 (41) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 142.80/21.40 (42) all_54_8 = all_52_2
% 142.80/21.40 (43) op(e2, e2) = e0
% 142.80/21.40 (44) ~ (all_52_6 = e0)
% 142.80/21.40 (45) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.80/21.40 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.80/21.40 (46) op(e2, e0) = all_52_13
% 142.80/21.40 (47) op(e1, e0) = all_52_14
% 142.80/21.40
% 142.80/21.40 Begin of proof
% 142.80/21.40 |
% 142.80/21.40 | ALPHA: (19) implies:
% 142.80/21.40 | (48) all_57_13 = e1
% 142.80/21.40 | (49) op(e0, e2) = e1
% 142.80/21.40 |
% 142.80/21.40 | GROUND_INST: instantiating (36) with all_52_7, e1, e2, e0, simplifying with
% 142.80/21.40 | (39), (49) gives:
% 142.80/21.40 | (50) all_52_7 = e1
% 142.80/21.40 |
% 142.80/21.40 | GROUND_INST: instantiating (36) with all_52_13, e1, e0, e2, simplifying with
% 142.80/21.40 | (10), (46) gives:
% 142.80/21.40 | (51) all_52_13 = e1
% 142.80/21.40 |
% 142.80/21.40 | REDUCE: (22), (51) imply:
% 142.80/21.40 | (52) ~ (all_52_1 = e1)
% 142.80/21.40 |
% 142.80/21.40 | REDUCE: (23), (50) imply:
% 142.80/21.40 | (53) ~ (all_52_6 = e1)
% 142.80/21.40 |
% 142.80/21.40 | REDUCE: (26), (51) imply:
% 142.80/21.40 | (54) ~ (all_52_14 = e1)
% 142.80/21.40 |
% 142.80/21.40 | SIMP: (54) implies:
% 142.80/21.40 | (55) ~ (all_52_14 = e1)
% 142.80/21.40 |
% 142.80/21.40 | BETA: splitting (12) gives:
% 142.80/21.40 |
% 142.80/21.40 | Case 1:
% 142.80/21.40 | |
% 142.80/21.40 | | (56) ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 142.80/21.40 | | all_18_1 & $i(all_18_0) & $i(all_18_1)
% 142.80/21.40 | |
% 142.80/21.40 | | ALPHA: (56) implies:
% 142.80/21.40 | | (57) ~ (all_18_0 = e3)
% 142.80/21.40 | | (58) op(e2, e0) = all_18_1
% 142.80/21.40 | | (59) op(all_18_1, e2) = all_18_0
% 142.80/21.40 | |
% 142.80/21.40 | | BETA: splitting (3) gives:
% 142.80/21.40 | |
% 142.80/21.40 | | Case 1:
% 142.80/21.40 | | |
% 142.80/21.40 | | | (60) ~ (all_40_0 = e3) & op(all_40_1, e0) = all_40_0 & op(e0, e2) =
% 142.80/21.40 | | | all_40_1 & $i(all_40_0) & $i(all_40_1)
% 142.80/21.40 | | |
% 142.80/21.40 | | | ALPHA: (60) implies:
% 142.80/21.40 | | | (61) ~ (all_40_0 = e3)
% 142.80/21.40 | | | (62) op(e0, e2) = all_40_1
% 142.80/21.40 | | | (63) op(all_40_1, e0) = all_40_0
% 142.80/21.40 | | |
% 142.80/21.40 | | | BETA: splitting (4) gives:
% 142.80/21.40 | | |
% 142.80/21.40 | | | Case 1:
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | (64) ~ (all_24_0 = e1) & op(all_24_1, e0) = all_24_0 & op(e0, e2) =
% 142.80/21.40 | | | | all_24_1 & $i(all_24_0) & $i(all_24_1)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | ALPHA: (64) implies:
% 142.80/21.40 | | | | (65) op(e0, e2) = all_24_1
% 142.80/21.40 | | | | (66) op(all_24_1, e0) = all_24_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with e1, all_40_1, e2, e0, simplifying
% 142.80/21.40 | | | | with (49), (62) gives:
% 142.80/21.40 | | | | (67) all_40_1 = e1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with all_24_1, all_40_1, e2, e0,
% 142.80/21.40 | | | | simplifying with (62), (65) gives:
% 142.80/21.40 | | | | (68) all_40_1 = all_24_1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with e1, all_18_1, e0, e2, simplifying
% 142.80/21.40 | | | | with (10), (58) gives:
% 142.80/21.40 | | | | (69) all_18_1 = e1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | COMBINE_EQS: (67), (68) imply:
% 142.80/21.40 | | | | (70) all_24_1 = e1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | SIMP: (70) implies:
% 142.80/21.40 | | | | (71) all_24_1 = e1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (63), (67) imply:
% 142.80/21.40 | | | | (72) op(e1, e0) = all_40_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (66), (71) imply:
% 142.80/21.40 | | | | (73) op(e1, e0) = all_24_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (59), (69) imply:
% 142.80/21.40 | | | | (74) op(e1, e2) = all_18_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with all_52_14, all_24_0, e0, e1,
% 142.80/21.40 | | | | simplifying with (47), (73) gives:
% 142.80/21.40 | | | | (75) all_52_14 = all_24_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with all_52_14, all_40_0, e0, e1,
% 142.80/21.40 | | | | simplifying with (47), (72) gives:
% 142.80/21.40 | | | | (76) all_52_14 = all_40_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with all_52_6, all_18_0, e2, e1,
% 142.80/21.40 | | | | simplifying with (5), (74) gives:
% 142.80/21.40 | | | | (77) all_52_6 = all_18_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | COMBINE_EQS: (75), (76) imply:
% 142.80/21.40 | | | | (78) all_40_0 = all_24_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | SIMP: (78) implies:
% 142.80/21.40 | | | | (79) all_40_0 = all_24_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | COMBINE_EQS: (8), (75) imply:
% 142.80/21.40 | | | | (80) all_54_11 = all_24_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | COMBINE_EQS: (21), (77) imply:
% 142.80/21.40 | | | | (81) all_54_9 = all_18_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (14), (77) imply:
% 142.80/21.40 | | | | (82) ~ (all_52_2 = all_18_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (6), (75) imply:
% 142.80/21.40 | | | | (83) ~ (all_52_2 = all_24_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (25), (75), (77) imply:
% 142.80/21.40 | | | | (84) ~ (all_24_0 = all_18_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | SIMP: (84) implies:
% 142.80/21.40 | | | | (85) ~ (all_24_0 = all_18_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (53), (77) imply:
% 142.80/21.40 | | | | (86) ~ (all_18_0 = e1)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (20), (75) imply:
% 142.80/21.40 | | | | (87) ~ (all_52_12 = all_24_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (1), (75) imply:
% 142.80/21.40 | | | | (88) ~ (all_24_0 = e2)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (55), (75) imply:
% 142.80/21.40 | | | | (89) ~ (all_24_0 = e1)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (61), (79) imply:
% 142.80/21.40 | | | | (90) ~ (all_24_0 = e3)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | BETA: splitting (27) gives:
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | Case 1:
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | (91) all_54_11 = e3
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | COMBINE_EQS: (80), (91) imply:
% 142.80/21.40 | | | | | (92) all_24_0 = e3
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | SIMP: (92) implies:
% 142.80/21.40 | | | | | (93) all_24_0 = e3
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | REDUCE: (90), (93) imply:
% 142.80/21.40 | | | | | (94) $false
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | CLOSE: (94) is inconsistent.
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | Case 2:
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | (95) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | BETA: splitting (95) gives:
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | Case 1:
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | (96) all_54_11 = e2
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | COMBINE_EQS: (80), (96) imply:
% 142.80/21.40 | | | | | | (97) all_24_0 = e2
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | SIMP: (97) implies:
% 142.80/21.40 | | | | | | (98) all_24_0 = e2
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | REDUCE: (88), (98) imply:
% 142.80/21.40 | | | | | | (99) $false
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | CLOSE: (99) is inconsistent.
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | Case 2:
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | (100) all_54_11 = e1 | all_54_11 = e0
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | BETA: splitting (28) gives:
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | Case 1:
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | | (101) all_54_9 = e3
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | | REF_CLOSE: (57), (81), (101) are inconsistent by sub-proof #797.
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | Case 2:
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | | (102) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | | BETA: splitting (102) gives:
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | | Case 1:
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | (103) all_54_9 = e2
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | COMBINE_EQS: (81), (103) imply:
% 142.80/21.40 | | | | | | | | (104) all_18_0 = e2
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | SIMP: (104) implies:
% 142.80/21.40 | | | | | | | | (105) all_18_0 = e2
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | REDUCE: (82), (105) imply:
% 142.80/21.40 | | | | | | | | (106) ~ (all_52_2 = e2)
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | REDUCE: (86), (105) imply:
% 142.80/21.40 | | | | | | | | (107) ~ (e2 = e1)
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | BETA: splitting (100) gives:
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | Case 1:
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | (108) all_54_11 = e1
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | COMBINE_EQS: (80), (108) imply:
% 142.80/21.40 | | | | | | | | | (109) all_24_0 = e1
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | SIMP: (109) implies:
% 142.80/21.40 | | | | | | | | | (110) all_24_0 = e1
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | REDUCE: (89), (110) imply:
% 142.80/21.40 | | | | | | | | | (111) $false
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | CLOSE: (111) is inconsistent.
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | Case 2:
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | (112) all_54_11 = e0
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | COMBINE_EQS: (80), (112) imply:
% 142.80/21.40 | | | | | | | | | (113) all_24_0 = e0
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | SIMP: (113) implies:
% 142.80/21.40 | | | | | | | | | (114) all_24_0 = e0
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | REDUCE: (83), (114) imply:
% 142.80/21.40 | | | | | | | | | (115) ~ (all_52_2 = e0)
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | REDUCE: (87), (114) imply:
% 142.80/21.40 | | | | | | | | | (116) ~ (all_52_12 = e0)
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | REDUCE: (88), (114) imply:
% 142.80/21.40 | | | | | | | | | (117) ~ (e2 = e0)
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | SIMP: (117) implies:
% 142.80/21.40 | | | | | | | | | (118) ~ (e2 = e0)
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | REDUCE: (89), (114) imply:
% 142.80/21.40 | | | | | | | | | (119) ~ (e1 = e0)
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | SIMP: (119) implies:
% 142.80/21.40 | | | | | | | | | (120) ~ (e1 = e0)
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | | REF_CLOSE: (2), (7), (9), (13), (15), (16), (17), (18), (24),
% 142.80/21.40 | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 142.80/21.40 | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (45),
% 142.80/21.40 | | | | | | | | | (46), (48), (52), (106), (107), (115), (116),
% 142.80/21.40 | | | | | | | | | (118), (120) are inconsistent by sub-proof #789.
% 142.80/21.40 | | | | | | | | |
% 142.80/21.40 | | | | | | | | End of split
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | Case 2:
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | (121) all_54_9 = e1 | all_54_9 = e0
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | | REF_CLOSE: (21), (44), (53), (121) are inconsistent by sub-proof
% 142.80/21.40 | | | | | | | | #960.
% 142.80/21.40 | | | | | | | |
% 142.80/21.40 | | | | | | | End of split
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | End of split
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | End of split
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | End of split
% 142.80/21.40 | | | |
% 142.80/21.40 | | | Case 2:
% 142.80/21.40 | | | |
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with e1, all_40_1, e2, e0, simplifying
% 142.80/21.40 | | | | with (49), (62) gives:
% 142.80/21.40 | | | | (122) all_40_1 = e1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with e1, all_18_1, e0, e2, simplifying
% 142.80/21.40 | | | | with (10), (58) gives:
% 142.80/21.40 | | | | (123) all_18_1 = e1
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (63), (122) imply:
% 142.80/21.40 | | | | (124) op(e1, e0) = all_40_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (59), (123) imply:
% 142.80/21.40 | | | | (125) op(e1, e2) = all_18_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with all_52_14, all_40_0, e0, e1,
% 142.80/21.40 | | | | simplifying with (47), (124) gives:
% 142.80/21.40 | | | | (126) all_52_14 = all_40_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | GROUND_INST: instantiating (36) with all_52_6, all_18_0, e2, e1,
% 142.80/21.40 | | | | simplifying with (5), (125) gives:
% 142.80/21.40 | | | | (127) all_52_6 = all_18_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | COMBINE_EQS: (8), (126) imply:
% 142.80/21.40 | | | | (128) all_54_11 = all_40_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | COMBINE_EQS: (21), (127) imply:
% 142.80/21.40 | | | | (129) all_54_9 = all_18_0
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (14), (127) imply:
% 142.80/21.40 | | | | (130) ~ (all_52_2 = all_18_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (6), (126) imply:
% 142.80/21.40 | | | | (131) ~ (all_52_2 = all_40_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (25), (126), (127) imply:
% 142.80/21.40 | | | | (132) ~ (all_40_0 = all_18_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | SIMP: (132) implies:
% 142.80/21.40 | | | | (133) ~ (all_40_0 = all_18_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (53), (127) imply:
% 142.80/21.40 | | | | (134) ~ (all_18_0 = e1)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (20), (126) imply:
% 142.80/21.40 | | | | (135) ~ (all_52_12 = all_40_0)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (1), (126) imply:
% 142.80/21.40 | | | | (136) ~ (all_40_0 = e2)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | REDUCE: (55), (126) imply:
% 142.80/21.40 | | | | (137) ~ (all_40_0 = e1)
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | BETA: splitting (27) gives:
% 142.80/21.40 | | | |
% 142.80/21.40 | | | | Case 1:
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | (138) all_54_11 = e3
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | COMBINE_EQS: (128), (138) imply:
% 142.80/21.40 | | | | | (139) all_40_0 = e3
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | SIMP: (139) implies:
% 142.80/21.40 | | | | | (140) all_40_0 = e3
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | REDUCE: (61), (140) imply:
% 142.80/21.40 | | | | | (141) $false
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | CLOSE: (141) is inconsistent.
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | Case 2:
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | (142) all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | BETA: splitting (142) gives:
% 142.80/21.40 | | | | |
% 142.80/21.40 | | | | | Case 1:
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | (143) all_54_11 = e2
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | COMBINE_EQS: (128), (143) imply:
% 142.80/21.40 | | | | | | (144) all_40_0 = e2
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | SIMP: (144) implies:
% 142.80/21.40 | | | | | | (145) all_40_0 = e2
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | REDUCE: (136), (145) imply:
% 142.80/21.40 | | | | | | (146) $false
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | CLOSE: (146) is inconsistent.
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | Case 2:
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | (147) all_54_11 = e1 | all_54_11 = e0
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | BETA: splitting (28) gives:
% 142.80/21.40 | | | | | |
% 142.80/21.40 | | | | | | Case 1:
% 142.80/21.40 | | | | | | |
% 142.80/21.40 | | | | | | | (148) all_54_9 = e3
% 142.80/21.40 | | | | | | |
% 142.80/21.41 | | | | | | | REF_CLOSE: (57), (129), (148) are inconsistent by sub-proof #797.
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | Case 2:
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | (149) all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | BETA: splitting (149) gives:
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | Case 1:
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | (150) all_54_9 = e2
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | COMBINE_EQS: (129), (150) imply:
% 142.80/21.41 | | | | | | | | (151) all_18_0 = e2
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | SIMP: (151) implies:
% 142.80/21.41 | | | | | | | | (152) all_18_0 = e2
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | REDUCE: (130), (152) imply:
% 142.80/21.41 | | | | | | | | (153) ~ (all_52_2 = e2)
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | REDUCE: (134), (152) imply:
% 142.80/21.41 | | | | | | | | (154) ~ (e2 = e1)
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | BETA: splitting (147) gives:
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | Case 1:
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | (155) all_54_11 = e1
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | COMBINE_EQS: (128), (155) imply:
% 142.80/21.41 | | | | | | | | | (156) all_40_0 = e1
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | SIMP: (156) implies:
% 142.80/21.41 | | | | | | | | | (157) all_40_0 = e1
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REDUCE: (137), (157) imply:
% 142.80/21.41 | | | | | | | | | (158) $false
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | CLOSE: (158) is inconsistent.
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | Case 2:
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | (159) all_54_11 = e0
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | COMBINE_EQS: (128), (159) imply:
% 142.80/21.41 | | | | | | | | | (160) all_40_0 = e0
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | SIMP: (160) implies:
% 142.80/21.41 | | | | | | | | | (161) all_40_0 = e0
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REDUCE: (131), (161) imply:
% 142.80/21.41 | | | | | | | | | (162) ~ (all_52_2 = e0)
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REDUCE: (135), (161) imply:
% 142.80/21.41 | | | | | | | | | (163) ~ (all_52_12 = e0)
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REDUCE: (136), (161) imply:
% 142.80/21.41 | | | | | | | | | (164) ~ (e2 = e0)
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | SIMP: (164) implies:
% 142.80/21.41 | | | | | | | | | (165) ~ (e2 = e0)
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REDUCE: (137), (161) imply:
% 142.80/21.41 | | | | | | | | | (166) ~ (e1 = e0)
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | SIMP: (166) implies:
% 142.80/21.41 | | | | | | | | | (167) ~ (e1 = e0)
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REF_CLOSE: (2), (7), (9), (13), (15), (16), (17), (18), (24),
% 142.80/21.41 | | | | | | | | | (29), (30), (31), (32), (33), (34), (35), (36),
% 142.80/21.41 | | | | | | | | | (37), (38), (39), (40), (41), (42), (43), (45),
% 142.80/21.41 | | | | | | | | | (46), (48), (52), (153), (154), (162), (163),
% 142.80/21.41 | | | | | | | | | (165), (167) are inconsistent by sub-proof #789.
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | End of split
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | Case 2:
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | (168) all_54_9 = e1 | all_54_9 = e0
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | REF_CLOSE: (21), (44), (53), (168) are inconsistent by sub-proof
% 142.80/21.41 | | | | | | | | #960.
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | End of split
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | End of split
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | End of split
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | End of split
% 142.80/21.41 | | | |
% 142.80/21.41 | | | End of split
% 142.80/21.41 | | |
% 142.80/21.41 | | Case 2:
% 142.80/21.41 | | |
% 142.80/21.41 | | | (169) ~ (all_40_1 = e1) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 142.80/21.41 | | |
% 142.80/21.41 | | | REF_CLOSE: (36), (49), (169) are inconsistent by sub-proof #788.
% 142.80/21.41 | | |
% 142.80/21.41 | | End of split
% 142.80/21.41 | |
% 142.80/21.41 | Case 2:
% 142.80/21.41 | |
% 142.80/21.41 | | (170) ~ (all_18_1 = e1) & op(e2, e0) = all_18_1 & $i(all_18_1)
% 142.80/21.41 | |
% 142.80/21.41 | | ALPHA: (170) implies:
% 142.80/21.41 | | (171) ~ (all_18_1 = e1)
% 142.80/21.41 | | (172) op(e2, e0) = all_18_1
% 142.80/21.41 | |
% 142.80/21.41 | | BETA: splitting (11) gives:
% 142.80/21.41 | |
% 142.80/21.41 | | Case 1:
% 142.80/21.41 | | |
% 142.80/21.41 | | | (173) ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 142.80/21.41 | | | all_16_1 & $i(all_16_0) & $i(all_16_1)
% 142.80/21.41 | | |
% 142.80/21.41 | | | ALPHA: (173) implies:
% 142.80/21.41 | | | (174) op(e2, e0) = all_16_1
% 142.80/21.41 | | |
% 142.80/21.41 | | | REF_CLOSE: (10), (36), (171), (172), (174) are inconsistent by sub-proof
% 142.80/21.41 | | | #1022.
% 142.80/21.41 | | |
% 142.80/21.41 | | Case 2:
% 142.80/21.41 | | |
% 142.80/21.41 | | | (175) ~ (all_16_1 = e3) & op(e2, e0) = all_16_1 & $i(all_16_1)
% 142.80/21.41 | | |
% 142.80/21.41 | | | ALPHA: (175) implies:
% 142.80/21.41 | | | (176) op(e2, e0) = all_16_1
% 142.80/21.41 | | |
% 142.80/21.41 | | | REF_CLOSE: (10), (36), (171), (172), (176) are inconsistent by sub-proof
% 142.80/21.41 | | | #1022.
% 142.80/21.41 | | |
% 142.80/21.41 | | End of split
% 142.80/21.41 | |
% 142.80/21.41 | End of split
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #788 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) ~ (all_40_1 = e1) & op(e0, e2) = all_40_1 & $i(all_40_1)
% 142.80/21.41 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.80/21.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.80/21.41 (3) op(e0, e2) = e1
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | ALPHA: (1) implies:
% 142.80/21.41 | (4) ~ (all_40_1 = e1)
% 142.80/21.41 | (5) op(e0, e2) = all_40_1
% 142.80/21.41 |
% 142.80/21.41 | GROUND_INST: instantiating (2) with e1, all_40_1, e2, e0, simplifying with
% 142.80/21.41 | (3), (5) gives:
% 142.80/21.41 | (6) all_40_1 = e1
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (4), (6) imply:
% 142.80/21.41 | (7) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (7) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #789 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.80/21.41 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.80/21.41 (2) ~ (all_52_4 = e0)
% 142.80/21.41 (3) ~ (e2 = e1)
% 142.80/21.41 (4) ~ (all_52_7 = e0)
% 142.80/21.41 (5) all_54_4 = e3 | all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 142.80/21.41 (6) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.80/21.41 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.80/21.41 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.80/21.41 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.80/21.41 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.80/21.41 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 142.80/21.41 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 142.80/21.41 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 142.80/21.41 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 142.80/21.41 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 142.80/21.41 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 142.80/21.41 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.80/21.41 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 142.80/21.41 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 142.80/21.41 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.80/21.41 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 142.80/21.41 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 142.80/21.41 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 142.80/21.41 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 142.80/21.41 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.80/21.41 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.80/21.41 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.80/21.41 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.80/21.41 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.80/21.41 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.80/21.41 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.80/21.41 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.80/21.41 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 142.80/21.41 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 142.80/21.41 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 142.80/21.41 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.80/21.41 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.80/21.41 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.80/21.41 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 142.80/21.41 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.80/21.41 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.80/21.41 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.80/21.41 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.80/21.41 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.80/21.41 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.80/21.41 (7) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.80/21.41 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.80/21.41 (8) ~ (all_52_1 = e1)
% 142.80/21.41 (9) ~ (all_52_1 = e0)
% 142.80/21.41 (10) op(e1, e1) = e1
% 142.80/21.41 (11) op(e2, e3) = all_52_1
% 142.80/21.41 (12) ~ (all_52_12 = e0)
% 142.80/21.41 (13) ~ (e1 = e0)
% 142.80/21.41 (14) all_57_13 = e1
% 142.80/21.41 (15) op(e3, e2) = all_52_4
% 142.80/21.41 (16) ~ (e2 = e0)
% 142.80/21.41 (17) op(e3, e0) = all_52_12
% 142.80/21.41 (18) ~ (all_52_2 = e1)
% 142.80/21.41 (19) ~ (all_52_1 = all_52_2)
% 142.80/21.41 (20) op(e3, e3) = e1
% 142.80/21.41 (21) op(e0, e0) = e2
% 142.80/21.41 (22) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.80/21.41 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.80/21.41 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.80/21.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.80/21.41 (24) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.80/21.41 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.80/21.41 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.80/21.41 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.80/21.41 (25) ~ (all_52_2 = e0)
% 142.80/21.41 (26) ~ (all_52_13 = e2)
% 142.80/21.41 (27) op(e0, e2) = all_52_7
% 142.80/21.41 (28) all_54_4 = all_52_1
% 142.80/21.41 (29) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 142.80/21.41 (30) all_54_8 = all_52_2
% 142.80/21.41 (31) ~ (all_52_2 = e2)
% 142.80/21.41 (32) op(e2, e2) = e0
% 142.80/21.41 (33) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.80/21.41 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.80/21.41 (34) op(e2, e0) = all_52_13
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | BETA: splitting (29) gives:
% 142.80/21.41 |
% 142.80/21.41 | Case 1:
% 142.80/21.41 | |
% 142.80/21.41 | | (35) all_54_8 = e3
% 142.80/21.41 | |
% 142.80/21.41 | | COMBINE_EQS: (30), (35) imply:
% 142.80/21.41 | | (36) all_52_2 = e3
% 142.80/21.41 | |
% 142.80/21.41 | | SIMP: (36) implies:
% 142.80/21.41 | | (37) all_52_2 = e3
% 142.80/21.41 | |
% 142.80/21.41 | | REDUCE: (19), (37) imply:
% 142.80/21.41 | | (38) ~ (all_52_1 = e3)
% 142.80/21.41 | |
% 142.80/21.41 | | REDUCE: (31), (37) imply:
% 142.80/21.41 | | (39) ~ (e3 = e2)
% 142.80/21.41 | |
% 142.80/21.41 | | REDUCE: (18), (37) imply:
% 142.80/21.41 | | (40) ~ (e3 = e1)
% 142.80/21.41 | |
% 142.80/21.41 | | REDUCE: (25), (37) imply:
% 142.80/21.41 | | (41) ~ (e3 = e0)
% 142.80/21.41 | |
% 142.80/21.41 | | BETA: splitting (5) gives:
% 142.80/21.41 | |
% 142.80/21.41 | | Case 1:
% 142.80/21.41 | | |
% 142.80/21.41 | | | (42) all_54_4 = e3
% 142.80/21.41 | | |
% 142.80/21.41 | | | REF_CLOSE: (28), (38), (42) are inconsistent by sub-proof #796.
% 142.80/21.41 | | |
% 142.80/21.41 | | Case 2:
% 142.80/21.41 | | |
% 142.80/21.41 | | | (43) all_54_4 = e2 | all_54_4 = e1 | all_54_4 = e0
% 142.80/21.41 | | |
% 142.80/21.41 | | | BETA: splitting (6) gives:
% 142.80/21.41 | | |
% 142.80/21.41 | | | Case 1:
% 142.80/21.41 | | | |
% 142.80/21.41 | | | | (44) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2,
% 142.80/21.41 | | | | e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 142.80/21.41 | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 142.80/21.41 | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 142.80/21.41 | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 142.80/21.41 | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 142.80/21.41 | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 142.80/21.41 | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 142.80/21.41 | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 142.80/21.41 | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 142.80/21.41 | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 142.80/21.41 | | | | all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.80/21.41 | | | | $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~
% 142.80/21.41 | | | | (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 142.80/21.41 | | | | ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) &
% 142.80/21.41 | | | | op(e1, e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2
% 142.80/21.41 | | | | & op(e3, e3) = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) =
% 142.80/21.41 | | | | all_56_0 & $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2)
% 142.80/21.41 | | | | = e0) | ( ~ (all_56_15 = e2) & op(e0, e0) = all_56_15 &
% 142.80/21.41 | | | | $i(all_56_15))) & ((all_56_13 = e2 & op(e1, e1) = e2) | (
% 142.80/21.41 | | | | ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 & $i(all_56_7)))
% 142.80/21.41 | | | | & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 142.80/21.41 | | | | op(e0, e2) = all_56_12 & $i(all_56_12))))
% 142.80/21.41 | | | |
% 142.80/21.41 | | | | BETA: splitting (44) gives:
% 142.80/21.41 | | | |
% 142.80/21.41 | | | | Case 1:
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | (45) op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 &
% 142.80/21.41 | | | | | op(e2, e3) = e2) | ( ~ (all_56_11 = e3) & op(e2, e2) =
% 142.80/21.41 | | | | | all_56_11 & $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3)
% 142.80/21.41 | | | | | = e1) | ( ~ (all_56_13 = e3) & op(e1, e1) = all_56_13 &
% 142.80/21.41 | | | | | $i(all_56_13))) & ((all_56_10 = e0 & op(e0, e3) = e0) | (
% 142.80/21.41 | | | | | ~ (all_56_15 = e3) & op(e0, e0) = all_56_15 &
% 142.80/21.41 | | | | | $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3) | (
% 142.80/21.41 | | | | | ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3)))
% 142.80/21.41 | | | | | & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) &
% 142.80/21.41 | | | | | op(e1, e3) = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3
% 142.80/21.41 | | | | | & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0, e3) =
% 142.80/21.41 | | | | | all_56_10 & $i(all_56_10)))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | ALPHA: (45) implies:
% 142.80/21.41 | | | | | (46) (all_56_11 = e3 & op(e2, e2) = e3) | ( ~ (all_56_3 = e2) &
% 142.80/21.41 | | | | | op(e2, e3) = all_56_3 & $i(all_56_3))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | BETA: splitting (43) gives:
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | Case 1:
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | (47) all_54_4 = e2
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | COMBINE_EQS: (28), (47) imply:
% 142.80/21.41 | | | | | | (48) all_52_1 = e2
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | REDUCE: (11), (48) imply:
% 142.80/21.41 | | | | | | (49) op(e2, e3) = e2
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | REF_CLOSE: (23), (32), (41), (46), (49) are inconsistent by
% 142.80/21.41 | | | | | | sub-proof #978.
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | Case 2:
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | (50) all_54_4 = e1 | all_54_4 = e0
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | REF_CLOSE: (8), (9), (28), (50) are inconsistent by sub-proof #793.
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | End of split
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | Case 2:
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | (51) op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 &
% 142.80/21.41 | | | | | op(e3, e2) = e3) | ( ~ (all_56_9 = e2) & op(e3, e3) =
% 142.80/21.41 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 & op(e1, e2) =
% 142.80/21.41 | | | | | e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.80/21.41 | | | | | $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.80/21.41 | | | | | (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.80/21.41 | | | | | ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) &
% 142.80/21.41 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 =
% 142.80/21.41 | | | | | e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) =
% 142.80/21.41 | | | | | all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0)
% 142.80/21.41 | | | | | = e2) | ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 &
% 142.80/21.41 | | | | | $i(all_56_12)))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | ALPHA: (51) implies:
% 142.80/21.41 | | | | | (52) (all_56_15 = e2 & op(e0, e0) = e2) | ( ~ (all_56_12 = e0) &
% 142.80/21.41 | | | | | op(e0, e2) = all_56_12 & $i(all_56_12))
% 142.80/21.41 | | | | | (53) (all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) &
% 142.80/21.41 | | | | | op(e0, e0) = all_56_15 & $i(all_56_15))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | REF_CLOSE: (4), (21), (23), (27), (52), (53) are inconsistent by
% 142.80/21.41 | | | | | sub-proof #975.
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | End of split
% 142.80/21.41 | | | |
% 142.80/21.41 | | | Case 2:
% 142.80/21.41 | | | |
% 142.80/21.41 | | | | (54) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 142.80/21.41 | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.80/21.41 | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) =
% 142.80/21.41 | | | | e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 142.80/21.41 | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 142.80/21.41 | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 142.80/21.41 | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 142.80/21.41 | | | | op(e2, e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0
% 142.80/21.41 | | | | & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.80/21.41 | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.80/21.41 | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.80/21.41 | | | | all_56_14 & $i(all_56_14)))) | (op(e0, e0) = all_56_15 &
% 142.80/21.41 | | | | $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~
% 142.80/21.41 | | | | (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9))) &
% 142.80/21.41 | | | | ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 142.80/21.41 | | | | op(e2, e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1
% 142.80/21.41 | | | | & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) =
% 142.80/21.41 | | | | all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3)
% 142.80/21.41 | | | | = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 142.80/21.41 | | | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 142.80/21.41 | | | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 142.80/21.41 | | | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) &
% 142.80/21.41 | | | | op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.80/21.41 | | | |
% 142.80/21.41 | | | | BETA: splitting (54) gives:
% 142.80/21.41 | | | |
% 142.80/21.41 | | | | Case 1:
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | (55) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 &
% 142.80/21.41 | | | | | op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.80/21.41 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) =
% 142.80/21.41 | | | | | e2) | ( ~ (all_56_11 = e1) & op(e2, e2) = all_56_11 &
% 142.80/21.41 | | | | | $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~
% 142.80/21.41 | | | | | (all_56_1 = e3) & op(e3, e1) = all_56_1 & $i(all_56_1))) &
% 142.80/21.41 | | | | | ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 142.80/21.41 | | | | | op(e2, e1) = all_56_4 & $i(all_56_4))) & ((all_56_14 = e0
% 142.80/21.41 | | | | | & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0) =
% 142.80/21.41 | | | | | all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.80/21.41 | | | | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) =
% 142.80/21.41 | | | | | all_56_14 & $i(all_56_14)))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | ALPHA: (55) implies:
% 142.80/21.41 | | | | | (56) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) &
% 142.80/21.41 | | | | | op(e2, e1) = all_56_4 & $i(all_56_4))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | BETA: splitting (33) gives:
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | Case 1:
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | (57) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3,
% 142.80/21.41 | | | | | | e2) = e0)
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | REF_CLOSE: (2), (13), (15), (20), (23), (57) are inconsistent by
% 142.80/21.41 | | | | | | sub-proof #819.
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | Case 2:
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | (58) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3,
% 142.80/21.41 | | | | | | e0) = e0)
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | BETA: splitting (58) gives:
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | | Case 1:
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | (59) all_57_4 = e0 & op(e3, e1) = e0
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | ALPHA: (59) implies:
% 142.80/21.41 | | | | | | | (60) all_57_4 = e0
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | BETA: splitting (22) gives:
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | Case 1:
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | (61) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 &
% 142.80/21.41 | | | | | | | | op(e2, e1) = e2)
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | BETA: splitting (61) gives:
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | Case 1:
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | (62) all_57_4 = e2 & op(e3, e1) = e2
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | ALPHA: (62) implies:
% 142.80/21.41 | | | | | | | | | (63) all_57_4 = e2
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REF_CLOSE: (16), (60), (63) are inconsistent by sub-proof
% 142.80/21.41 | | | | | | | | | #1050.
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | Case 2:
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | (64) all_57_5 = e2 & op(e2, e1) = e2
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | ALPHA: (64) implies:
% 142.80/21.41 | | | | | | | | | (65) op(e2, e1) = e2
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | | REF_CLOSE: (13), (23), (32), (56), (65) are inconsistent by
% 142.80/21.41 | | | | | | | | | sub-proof #950.
% 142.80/21.41 | | | | | | | | |
% 142.80/21.41 | | | | | | | | End of split
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | Case 2:
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | (66) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 &
% 142.80/21.41 | | | | | | | | op(e0, e1) = e2)
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | | REF_CLOSE: (1), (3), (7), (10), (13), (14), (16), (21), (23),
% 142.80/21.41 | | | | | | | | (24), (39), (40), (41), (66) are inconsistent by
% 142.80/21.41 | | | | | | | | sub-proof #799.
% 142.80/21.41 | | | | | | | |
% 142.80/21.41 | | | | | | | End of split
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | Case 2:
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | (67) all_57_9 = e0 & op(e3, e0) = e0
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | ALPHA: (67) implies:
% 142.80/21.41 | | | | | | | (68) op(e3, e0) = e0
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | | REF_CLOSE: (12), (17), (23), (68) are inconsistent by sub-proof
% 142.80/21.41 | | | | | | | #941.
% 142.80/21.41 | | | | | | |
% 142.80/21.41 | | | | | | End of split
% 142.80/21.41 | | | | | |
% 142.80/21.41 | | | | | End of split
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | Case 2:
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | (69) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 &
% 142.80/21.41 | | | | | op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) =
% 142.80/21.41 | | | | | all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) =
% 142.80/21.41 | | | | | e2) | ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 &
% 142.80/21.41 | | | | | $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~
% 142.80/21.41 | | | | | (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.80/21.41 | | | | | $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.80/21.41 | | | | | (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.80/21.41 | | | | | ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) &
% 142.80/21.41 | | | | | op(e2, e0) = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0
% 142.80/21.41 | | | | | & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1, e0) =
% 142.80/21.41 | | | | | all_56_8 & $i(all_56_8)))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | ALPHA: (69) implies:
% 142.80/21.41 | | | | | (70) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) &
% 142.80/21.41 | | | | | op(e2, e2) = all_56_11 & $i(all_56_11))
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | | REF_CLOSE: (23), (26), (32), (34), (70) are inconsistent by sub-proof
% 142.80/21.41 | | | | | #856.
% 142.80/21.41 | | | | |
% 142.80/21.41 | | | | End of split
% 142.80/21.41 | | | |
% 142.80/21.41 | | | End of split
% 142.80/21.41 | | |
% 142.80/21.41 | | End of split
% 142.80/21.41 | |
% 142.80/21.41 | Case 2:
% 142.80/21.41 | |
% 142.80/21.41 | | (71) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (18), (25), (30), (31), (71) are inconsistent by sub-proof #790.
% 142.80/21.41 | |
% 142.80/21.41 | End of split
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #790 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 142.80/21.41 (2) ~ (all_52_2 = e1)
% 142.80/21.41 (3) ~ (all_52_2 = e0)
% 142.80/21.41 (4) all_54_8 = all_52_2
% 142.80/21.41 (5) ~ (all_52_2 = e2)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | BETA: splitting (1) gives:
% 142.80/21.41 |
% 142.80/21.41 | Case 1:
% 142.80/21.41 | |
% 142.80/21.41 | | (6) all_54_8 = e2
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (4), (5), (6) are inconsistent by sub-proof #988.
% 142.80/21.41 | |
% 142.80/21.41 | Case 2:
% 142.80/21.41 | |
% 142.80/21.41 | | (7) all_54_8 = e1 | all_54_8 = e0
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #791.
% 142.80/21.41 | |
% 142.80/21.41 | End of split
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #791 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_8 = e1 | all_54_8 = e0
% 142.80/21.41 (2) all_54_8 = all_52_2
% 142.80/21.41 (3) ~ (all_52_2 = e1)
% 142.80/21.41 (4) ~ (all_52_2 = e0)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | BETA: splitting (1) gives:
% 142.80/21.41 |
% 142.80/21.41 | Case 1:
% 142.80/21.41 | |
% 142.80/21.41 | | (5) all_54_8 = e1
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #987.
% 142.80/21.41 | |
% 142.80/21.41 | Case 2:
% 142.80/21.41 | |
% 142.80/21.41 | | (6) all_54_8 = e0
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #792.
% 142.80/21.41 | |
% 142.80/21.41 | End of split
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #792 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_8 = all_52_2
% 142.80/21.41 (2) all_54_8 = e0
% 142.80/21.41 (3) ~ (all_52_2 = e0)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | COMBINE_EQS: (1), (2) imply:
% 142.80/21.41 | (4) all_52_2 = e0
% 142.80/21.41 |
% 142.80/21.41 | SIMP: (4) implies:
% 142.80/21.41 | (5) all_52_2 = e0
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (3), (5) imply:
% 142.80/21.41 | (6) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (6) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #793 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_4 = e1 | all_54_4 = e0
% 142.80/21.41 (2) all_54_4 = all_52_1
% 142.80/21.41 (3) ~ (all_52_1 = e1)
% 142.80/21.41 (4) ~ (all_52_1 = e0)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | BETA: splitting (1) gives:
% 142.80/21.41 |
% 142.80/21.41 | Case 1:
% 142.80/21.41 | |
% 142.80/21.41 | | (5) all_54_4 = e1
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (2), (3), (5) are inconsistent by sub-proof #795.
% 142.80/21.41 | |
% 142.80/21.41 | Case 2:
% 142.80/21.41 | |
% 142.80/21.41 | | (6) all_54_4 = e0
% 142.80/21.41 | |
% 142.80/21.41 | | REF_CLOSE: (2), (4), (6) are inconsistent by sub-proof #794.
% 142.80/21.41 | |
% 142.80/21.41 | End of split
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #794 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_4 = all_52_1
% 142.80/21.41 (2) all_54_4 = e0
% 142.80/21.41 (3) ~ (all_52_1 = e0)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | COMBINE_EQS: (1), (2) imply:
% 142.80/21.41 | (4) all_52_1 = e0
% 142.80/21.41 |
% 142.80/21.41 | SIMP: (4) implies:
% 142.80/21.41 | (5) all_52_1 = e0
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (3), (5) imply:
% 142.80/21.41 | (6) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (6) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #795 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_4 = all_52_1
% 142.80/21.41 (2) all_54_4 = e1
% 142.80/21.41 (3) ~ (all_52_1 = e1)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | COMBINE_EQS: (1), (2) imply:
% 142.80/21.41 | (4) all_52_1 = e1
% 142.80/21.41 |
% 142.80/21.41 | SIMP: (4) implies:
% 142.80/21.41 | (5) all_52_1 = e1
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (3), (5) imply:
% 142.80/21.41 | (6) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (6) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #796 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_4 = all_52_1
% 142.80/21.41 (2) all_54_4 = e3
% 142.80/21.41 (3) ~ (all_52_1 = e3)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | COMBINE_EQS: (1), (2) imply:
% 142.80/21.41 | (4) all_52_1 = e3
% 142.80/21.41 |
% 142.80/21.41 | SIMP: (4) implies:
% 142.80/21.41 | (5) all_52_1 = e3
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (3), (5) imply:
% 142.80/21.41 | (6) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (6) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #797 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_54_9 = all_18_0
% 142.80/21.41 (2) all_54_9 = e3
% 142.80/21.41 (3) ~ (all_18_0 = e3)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | COMBINE_EQS: (1), (2) imply:
% 142.80/21.41 | (4) all_18_0 = e3
% 142.80/21.41 |
% 142.80/21.41 | SIMP: (4) implies:
% 142.80/21.41 | (5) all_18_0 = e3
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (3), (5) imply:
% 142.80/21.41 | (6) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (6) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #798 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) all_57_12 = e3 & op(e0, e3) = e3
% 142.80/21.41 (2) all_57_12 = e1
% 142.80/21.41 (3) ~ (e3 = e1)
% 142.80/21.41
% 142.80/21.41 Begin of proof
% 142.80/21.41 |
% 142.80/21.41 | ALPHA: (1) implies:
% 142.80/21.41 | (4) all_57_12 = e3
% 142.80/21.41 |
% 142.80/21.41 | COMBINE_EQS: (2), (4) imply:
% 142.80/21.41 | (5) e3 = e1
% 142.80/21.41 |
% 142.80/21.41 | REDUCE: (3), (5) imply:
% 142.80/21.41 | (6) $false
% 142.80/21.41 |
% 142.80/21.41 | CLOSE: (6) is inconsistent.
% 142.80/21.41 |
% 142.80/21.41 End of proof
% 142.80/21.41
% 142.80/21.41 Sub-proof #799 shows that the following formulas are inconsistent:
% 142.80/21.41 ----------------------------------------------------------------
% 142.80/21.41 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.80/21.41 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.80/21.41 (2) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.80/21.41 (3) ~ (e2 = e1)
% 142.80/21.41 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.80/21.41 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.80/21.41 (5) ~ (e3 = e0)
% 142.80/21.41 (6) op(e1, e1) = e1
% 142.80/21.41 (7) ~ (e1 = e0)
% 142.80/21.41 (8) all_57_13 = e1
% 142.80/21.41 (9) ~ (e2 = e0)
% 142.80/21.41 (10) ~ (e3 = e2)
% 142.80/21.41 (11) op(e0, e0) = e2
% 142.80/21.41 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.80/21.41 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.41 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.41 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.41 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.41 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.41 (14) ~ (e3 = e1)
% 142.81/21.41
% 142.81/21.41 Begin of proof
% 142.81/21.41 |
% 142.81/21.41 | BETA: splitting (2) gives:
% 142.81/21.41 |
% 142.81/21.41 | Case 1:
% 142.81/21.41 | |
% 142.81/21.41 | | (15) all_57_8 = e2 & op(e1, e1) = e2
% 142.81/21.41 | |
% 142.81/21.41 | | ALPHA: (15) implies:
% 142.81/21.41 | | (16) op(e1, e1) = e2
% 142.81/21.41 | |
% 142.81/21.41 | | REF_CLOSE: (3), (6), (12), (16) are inconsistent by sub-proof #1085.
% 142.81/21.41 | |
% 142.81/21.41 | Case 2:
% 142.81/21.41 | |
% 142.81/21.41 | | (17) all_57_14 = e2 & op(e0, e1) = e2
% 142.81/21.41 | |
% 142.81/21.41 | | ALPHA: (17) implies:
% 142.81/21.41 | | (18) all_57_14 = e2
% 142.81/21.41 | |
% 142.81/21.41 | | REF_CLOSE: (1), (3), (4), (5), (7), (8), (9), (10), (11), (12), (13), (14),
% 142.81/21.41 | | (18) are inconsistent by sub-proof #800.
% 142.81/21.41 | |
% 142.81/21.41 | End of split
% 142.81/21.41 |
% 142.81/21.41 End of proof
% 142.81/21.41
% 142.81/21.41 Sub-proof #800 shows that the following formulas are inconsistent:
% 142.81/21.41 ----------------------------------------------------------------
% 142.81/21.41 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.41 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.41 (2) ~ (e2 = e1)
% 142.81/21.41 (3) all_57_14 = e2
% 142.81/21.41 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.41 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.41 (5) ~ (e3 = e0)
% 142.81/21.41 (6) ~ (e1 = e0)
% 142.81/21.41 (7) all_57_13 = e1
% 142.81/21.41 (8) ~ (e2 = e0)
% 142.81/21.41 (9) ~ (e3 = e2)
% 142.81/21.41 (10) op(e0, e0) = e2
% 142.81/21.42 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.42 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.42 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.42 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.42 (13) ~ (e3 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (12) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (14) all_57_15 = e0 & op(e0, e0) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (14) implies:
% 142.81/21.42 | | (15) op(e0, e0) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (8), (10), (11), (15) are inconsistent by sub-proof #1094.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (16) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.81/21.42 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.81/21.42 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.81/21.42 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (16) implies:
% 142.81/21.42 | | (17) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.81/21.42 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (17) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (18) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (18) implies:
% 142.81/21.42 | | | (19) all_57_12 = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | BETA: splitting (1) gives:
% 142.81/21.42 | | |
% 142.81/21.42 | | | Case 1:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (20) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 142.81/21.42 | | | | e2) = e3)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | BETA: splitting (20) gives:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | Case 1:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (21) all_57_12 = e3 & op(e0, e3) = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | ALPHA: (21) implies:
% 142.81/21.42 | | | | | (22) all_57_12 = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (5), (19), (22) are inconsistent by sub-proof #828.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | Case 2:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (23) all_57_13 = e3 & op(e0, e2) = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | ALPHA: (23) implies:
% 142.81/21.42 | | | | | (24) all_57_13 = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (7), (13), (24) are inconsistent by sub-proof #1001.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | End of split
% 142.81/21.42 | | | |
% 142.81/21.42 | | | Case 2:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (25) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 142.81/21.42 | | | | e0) = e3)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | REF_CLOSE: (3), (9), (10), (11), (25) are inconsistent by sub-proof
% 142.81/21.42 | | | | #889.
% 142.81/21.42 | | | |
% 142.81/21.42 | | | End of split
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (26) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 142.81/21.42 | | | = e0)
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (8), (9), (10), (11), (13), (26)
% 142.81/21.42 | | | are inconsistent by sub-proof #801.
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #801 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.42 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.42 (2) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.42 (3) ~ (e2 = e1)
% 142.81/21.42 (4) all_57_14 = e2
% 142.81/21.42 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.42 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.42 (6) ~ (e3 = e0)
% 142.81/21.42 (7) ~ (e1 = e0)
% 142.81/21.42 (8) ~ (e2 = e0)
% 142.81/21.42 (9) ~ (e3 = e2)
% 142.81/21.42 (10) op(e0, e0) = e2
% 142.81/21.42 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (12) ~ (e3 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (2) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (13) all_57_13 = e0 & op(e0, e2) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (13) implies:
% 142.81/21.42 | | (14) all_57_13 = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (12), (14) are
% 142.81/21.42 | | inconsistent by sub-proof #802.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (15) all_57_14 = e0 & op(e0, e1) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (4), (8), (15) are inconsistent by sub-proof #920.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #802 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.42 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.42 (2) ~ (e2 = e1)
% 142.81/21.42 (3) all_57_14 = e2
% 142.81/21.42 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.42 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.42 (5) all_57_13 = e0
% 142.81/21.42 (6) ~ (e3 = e0)
% 142.81/21.42 (7) ~ (e1 = e0)
% 142.81/21.42 (8) ~ (e3 = e2)
% 142.81/21.42 (9) op(e0, e0) = e2
% 142.81/21.42 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (11) ~ (e3 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (1) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (12) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) =
% 142.81/21.42 | | e3)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (12) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (13) all_57_12 = e3 & op(e0, e3) = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (13) implies:
% 142.81/21.42 | | | (14) all_57_12 = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | BETA: splitting (4) gives:
% 142.81/21.42 | | |
% 142.81/21.42 | | | Case 1:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (15) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0,
% 142.81/21.42 | | | | e2) = e1)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | BETA: splitting (15) gives:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | Case 1:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (16) all_57_12 = e1 & op(e0, e3) = e1
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | ALPHA: (16) implies:
% 142.81/21.42 | | | | | (17) all_57_12 = e1
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (11), (14), (17) are inconsistent by sub-proof #834.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | Case 2:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (18) all_57_13 = e1 & op(e0, e2) = e1
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (5), (7), (18) are inconsistent by sub-proof #805.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | End of split
% 142.81/21.42 | | | |
% 142.81/21.42 | | | Case 2:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (19) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0,
% 142.81/21.42 | | | | e0) = e1)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | REF_CLOSE: (2), (3), (9), (10), (19) are inconsistent by sub-proof #888.
% 142.81/21.42 | | | |
% 142.81/21.42 | | | End of split
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (20) all_57_13 = e3 & op(e0, e2) = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (20) implies:
% 142.81/21.42 | | | (21) all_57_13 = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (5), (6), (21) are inconsistent by sub-proof #804.
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (22) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 142.81/21.42 | | e3)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (22) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (23) all_57_14 = e3 & op(e0, e1) = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (3), (8), (23) are inconsistent by sub-proof #803.
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (24) all_57_15 = e3 & op(e0, e0) = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (24) implies:
% 142.81/21.42 | | | (25) op(e0, e0) = e3
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (8), (9), (10), (25) are inconsistent by sub-proof #1066.
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #803 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_14 = e3 & op(e0, e1) = e3
% 142.81/21.42 (2) all_57_14 = e2
% 142.81/21.42 (3) ~ (e3 = e2)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | ALPHA: (1) implies:
% 142.81/21.42 | (4) all_57_14 = e3
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.42 | (5) e3 = e2
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #804 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_13 = e3
% 142.81/21.42 (2) all_57_13 = e0
% 142.81/21.42 (3) ~ (e3 = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.42 | (4) e3 = e0
% 142.81/21.42 |
% 142.81/21.42 | SIMP: (4) implies:
% 142.81/21.42 | (5) e3 = e0
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #805 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_13 = e1 & op(e0, e2) = e1
% 142.81/21.42 (2) all_57_13 = e0
% 142.81/21.42 (3) ~ (e1 = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | ALPHA: (1) implies:
% 142.81/21.42 | (4) all_57_13 = e1
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.42 | (5) e1 = e0
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #806 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) op(e1, e2) = all_52_6
% 142.81/21.42 (2) ~ (e2 = e1)
% 142.81/21.42 (3) ~ (e3 = e0)
% 142.81/21.42 (4) op(e1, e1) = e1
% 142.81/21.42 (5) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.42 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.42 (6) ~ (e1 = e0)
% 142.81/21.42 (7) ~ (e2 = e0)
% 142.81/21.42 (8) ~ (e3 = e2)
% 142.81/21.42 (9) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.42 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.42 (10) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.42 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.42 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (12) ~ (e3 = e1)
% 142.81/21.42 (13) ~ (all_52_6 = e0)
% 142.81/21.42 (14) all_57_11 = e1
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (5) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (15) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) =
% 142.81/21.42 | | e0)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (15) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (16) all_57_6 = e0 & op(e1, e3) = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (16) implies:
% 142.81/21.42 | | | (17) all_57_6 = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | BETA: splitting (10) gives:
% 142.81/21.42 | | |
% 142.81/21.42 | | | Case 1:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (18) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 142.81/21.42 | | | | = e2)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | BETA: splitting (18) gives:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | Case 1:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (19) all_57_6 = e2 & op(e1, e3) = e2
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | ALPHA: (19) implies:
% 142.81/21.42 | | | | | (20) all_57_6 = e2
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (7), (17), (20) are inconsistent by sub-proof #811.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | Case 2:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (21) all_57_7 = e2 & op(e1, e2) = e2
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | ALPHA: (21) implies:
% 142.81/21.42 | | | | | (22) all_57_7 = e2
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (3), (4), (8), (9), (11), (12), (14), (17), (22) are
% 142.81/21.42 | | | | | inconsistent by sub-proof #866.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | End of split
% 142.81/21.42 | | | |
% 142.81/21.42 | | | Case 2:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (23) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 142.81/21.42 | | | | = e2)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | REF_CLOSE: (2), (4), (11), (14), (23) are inconsistent by sub-proof
% 142.81/21.42 | | | | #809.
% 142.81/21.42 | | | |
% 142.81/21.42 | | | End of split
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (24) all_57_7 = e0 & op(e1, e2) = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (24) implies:
% 142.81/21.42 | | | (25) op(e1, e2) = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (1), (11), (13), (25) are inconsistent by sub-proof #999.
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (26) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.81/21.42 | | e0)
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (4), (6), (11), (14), (26) are inconsistent by sub-proof #807.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #807 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.42 (2) op(e1, e1) = e1
% 142.81/21.42 (3) ~ (e1 = e0)
% 142.81/21.42 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (5) all_57_11 = e1
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (1) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (6) all_57_8 = e0 & op(e1, e1) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (6) implies:
% 142.81/21.42 | | (7) op(e1, e1) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1089.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (8) all_57_11 = e0 & op(e1, e0) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (3), (5), (8) are inconsistent by sub-proof #808.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #808 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_11 = e0 & op(e1, e0) = e0
% 142.81/21.42 (2) all_57_11 = e1
% 142.81/21.42 (3) ~ (e1 = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | ALPHA: (1) implies:
% 142.81/21.42 | (4) all_57_11 = e0
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.42 | (5) e1 = e0
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #809 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) ~ (e2 = e1)
% 142.81/21.42 (2) op(e1, e1) = e1
% 142.81/21.42 (3) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.42 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (5) all_57_11 = e1
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (3) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (6) all_57_8 = e2 & op(e1, e1) = e2
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (6) implies:
% 142.81/21.42 | | (7) op(e1, e1) = e2
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (1), (2), (4), (7) are inconsistent by sub-proof #1085.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (8) all_57_11 = e2 & op(e1, e0) = e2
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (8) implies:
% 142.81/21.42 | | (9) all_57_11 = e2
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (1), (5), (9) are inconsistent by sub-proof #810.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #810 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_11 = e2
% 142.81/21.42 (2) all_57_11 = e1
% 142.81/21.42 (3) ~ (e2 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.42 | (4) e2 = e1
% 142.81/21.42 |
% 142.81/21.42 | SIMP: (4) implies:
% 142.81/21.42 | (5) e2 = e1
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #811 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_6 = e2
% 142.81/21.42 (2) all_57_6 = e0
% 142.81/21.42 (3) ~ (e2 = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.42 | (4) e2 = e0
% 142.81/21.42 |
% 142.81/21.42 | SIMP: (4) implies:
% 142.81/21.42 | (5) e2 = e0
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #812 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.81/21.42 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.81/21.42 (2) ~ (all_52_4 = e0)
% 142.81/21.42 (3) ~ (e2 = e1)
% 142.81/21.42 (4) all_57_9 = e1
% 142.81/21.42 (5) ~ (e3 = e0)
% 142.81/21.42 (6) ~ (e1 = e0)
% 142.81/21.42 (7) op(e3, e2) = all_52_4
% 142.81/21.42 (8) ~ (e2 = e0)
% 142.81/21.42 (9) ~ (e3 = e2)
% 142.81/21.42 (10) op(e3, e3) = e1
% 142.81/21.42 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (12) ~ (e3 = e1)
% 142.81/21.42 (13) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.42 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.42 (14) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.81/21.42 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (14) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (15) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 142.81/21.42 | | e0)
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (2), (6), (7), (10), (11), (15) are inconsistent by sub-proof
% 142.81/21.42 | | #819.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 142.81/21.42 | | e0)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (16) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (17) all_57_4 = e0 & op(e3, e1) = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (17) implies:
% 142.81/21.42 | | | (18) all_57_4 = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (1), (3), (4), (5), (8), (9), (10), (11), (12), (13), (18) are
% 142.81/21.42 | | | inconsistent by sub-proof #814.
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (19) all_57_9 = e0 & op(e3, e0) = e0
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (4), (6), (19) are inconsistent by sub-proof #813.
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #813 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_9 = e0 & op(e3, e0) = e0
% 142.81/21.42 (2) all_57_9 = e1
% 142.81/21.42 (3) ~ (e1 = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | ALPHA: (1) implies:
% 142.81/21.42 | (4) all_57_9 = e0
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.42 | (5) e1 = e0
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #814 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.81/21.42 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.81/21.42 (2) ~ (e2 = e1)
% 142.81/21.42 (3) all_57_4 = e0
% 142.81/21.42 (4) all_57_9 = e1
% 142.81/21.42 (5) ~ (e3 = e0)
% 142.81/21.42 (6) ~ (e2 = e0)
% 142.81/21.42 (7) ~ (e3 = e2)
% 142.81/21.42 (8) op(e3, e3) = e1
% 142.81/21.42 (9) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (10) ~ (e3 = e1)
% 142.81/21.42 (11) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.42 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (1) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (12) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) =
% 142.81/21.42 | | e2)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (12) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (13) all_57_0 = e2 & op(e3, e3) = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (13) implies:
% 142.81/21.42 | | | (14) op(e3, e3) = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (2), (8), (9), (14) are inconsistent by sub-proof #818.
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (15) all_57_1 = e2 & op(e3, e2) = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (15) implies:
% 142.81/21.42 | | | (16) all_57_1 = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | BETA: splitting (11) gives:
% 142.81/21.42 | | |
% 142.81/21.42 | | | Case 1:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (17) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2)
% 142.81/21.42 | | | | = e3)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | REF_CLOSE: (7), (8), (9), (10), (16), (17) are inconsistent by sub-proof
% 142.81/21.42 | | | | #817.
% 142.81/21.42 | | | |
% 142.81/21.42 | | | Case 2:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | (18) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0)
% 142.81/21.42 | | | | = e3)
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | BETA: splitting (18) gives:
% 142.81/21.42 | | | |
% 142.81/21.42 | | | | Case 1:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (19) all_57_4 = e3 & op(e3, e1) = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | ALPHA: (19) implies:
% 142.81/21.42 | | | | | (20) all_57_4 = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (3), (5), (20) are inconsistent by sub-proof #831.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | Case 2:
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | (21) all_57_9 = e3 & op(e3, e0) = e3
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | | REF_CLOSE: (4), (10), (21) are inconsistent by sub-proof #816.
% 142.81/21.42 | | | | |
% 142.81/21.42 | | | | End of split
% 142.81/21.42 | | | |
% 142.81/21.42 | | | End of split
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (22) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) =
% 142.81/21.42 | | e2)
% 142.81/21.42 | |
% 142.81/21.42 | | BETA: splitting (22) gives:
% 142.81/21.42 | |
% 142.81/21.42 | | Case 1:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (23) all_57_4 = e2 & op(e3, e1) = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (23) implies:
% 142.81/21.42 | | | (24) all_57_4 = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (3), (6), (24) are inconsistent by sub-proof #1050.
% 142.81/21.42 | | |
% 142.81/21.42 | | Case 2:
% 142.81/21.42 | | |
% 142.81/21.42 | | | (25) all_57_9 = e2 & op(e3, e0) = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | ALPHA: (25) implies:
% 142.81/21.42 | | | (26) all_57_9 = e2
% 142.81/21.42 | | |
% 142.81/21.42 | | | REF_CLOSE: (2), (4), (26) are inconsistent by sub-proof #815.
% 142.81/21.42 | | |
% 142.81/21.42 | | End of split
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #815 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_9 = e2
% 142.81/21.42 (2) all_57_9 = e1
% 142.81/21.42 (3) ~ (e2 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.42 | (4) e2 = e1
% 142.81/21.42 |
% 142.81/21.42 | SIMP: (4) implies:
% 142.81/21.42 | (5) e2 = e1
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #816 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_9 = e3 & op(e3, e0) = e3
% 142.81/21.42 (2) all_57_9 = e1
% 142.81/21.42 (3) ~ (e3 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | ALPHA: (1) implies:
% 142.81/21.42 | (4) all_57_9 = e3
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.42 | (5) e3 = e1
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #817 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3)
% 142.81/21.42 (2) ~ (e3 = e2)
% 142.81/21.42 (3) op(e3, e3) = e1
% 142.81/21.42 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (5) ~ (e3 = e1)
% 142.81/21.42 (6) all_57_1 = e2
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (1) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (7) all_57_0 = e3 & op(e3, e3) = e3
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (7) implies:
% 142.81/21.42 | | (8) op(e3, e3) = e3
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (3), (4), (5), (8) are inconsistent by sub-proof #838.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (9) all_57_1 = e3 & op(e3, e2) = e3
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (2), (6), (9) are inconsistent by sub-proof #842.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #818 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (2) op(e3, e3) = e2
% 142.81/21.42 (3) op(e3, e3) = e1
% 142.81/21.42 (4) ~ (e2 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | GROUND_INST: instantiating (1) with e1, e2, e3, e3, simplifying with (2), (3)
% 142.81/21.42 | gives:
% 142.81/21.42 | (5) e2 = e1
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (4), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #819 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) ~ (all_52_4 = e0)
% 142.81/21.42 (2) ~ (e1 = e0)
% 142.81/21.42 (3) op(e3, e2) = all_52_4
% 142.81/21.42 (4) op(e3, e3) = e1
% 142.81/21.42 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (6) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (7) implies:
% 142.81/21.42 | | (8) op(e3, e3) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (2), (4), (5), (8) are inconsistent by sub-proof #840.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (9) all_57_1 = e0 & op(e3, e2) = e0
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (1), (3), (5), (9) are inconsistent by sub-proof #1102.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #820 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_4 = e2
% 142.81/21.42 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3)
% 142.81/21.42 (3) all_57_5 = e1
% 142.81/21.42 (4) ~ (e3 = e2)
% 142.81/21.42 (5) ~ (e3 = e1)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (2) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (6) all_57_4 = e3 & op(e3, e1) = e3
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (6) implies:
% 142.81/21.42 | | (7) all_57_4 = e3
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (1), (4), (7) are inconsistent by sub-proof #821.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (8) all_57_5 = e3 & op(e2, e1) = e3
% 142.81/21.42 | |
% 142.81/21.42 | | ALPHA: (8) implies:
% 142.81/21.42 | | (9) all_57_5 = e3
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (3), (5), (9) are inconsistent by sub-proof #1035.
% 142.81/21.42 | |
% 142.81/21.42 | End of split
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #821 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) all_57_4 = e3
% 142.81/21.42 (2) all_57_4 = e2
% 142.81/21.42 (3) ~ (e3 = e2)
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.42 | (4) e3 = e2
% 142.81/21.42 |
% 142.81/21.42 | SIMP: (4) implies:
% 142.81/21.42 | (5) e3 = e2
% 142.81/21.42 |
% 142.81/21.42 | REDUCE: (3), (5) imply:
% 142.81/21.42 | (6) $false
% 142.81/21.42 |
% 142.81/21.42 | CLOSE: (6) is inconsistent.
% 142.81/21.42 |
% 142.81/21.42 End of proof
% 142.81/21.42
% 142.81/21.42 Sub-proof #822 shows that the following formulas are inconsistent:
% 142.81/21.42 ----------------------------------------------------------------
% 142.81/21.42 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.81/21.42 (2) ~ (e3 = e0)
% 142.81/21.42 (3) ~ (e3 = e2)
% 142.81/21.42 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.42 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.42 (5) op(e2, e2) = e0
% 142.81/21.42 (6) all_57_2 = e2
% 142.81/21.42
% 142.81/21.42 Begin of proof
% 142.81/21.42 |
% 142.81/21.42 | BETA: splitting (1) gives:
% 142.81/21.42 |
% 142.81/21.42 | Case 1:
% 142.81/21.42 | |
% 142.81/21.42 | | (7) all_57_2 = e3 & op(e2, e3) = e3
% 142.81/21.42 | |
% 142.81/21.42 | | REF_CLOSE: (3), (6), (7) are inconsistent by sub-proof #823.
% 142.81/21.42 | |
% 142.81/21.42 | Case 2:
% 142.81/21.42 | |
% 142.81/21.42 | | (8) all_57_3 = e3 & op(e2, e2) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (8) implies:
% 142.81/21.43 | | (9) op(e2, e2) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (2), (4), (5), (9) are inconsistent by sub-proof #1119.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #823 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) all_57_2 = e3 & op(e2, e3) = e3
% 142.81/21.43 (2) all_57_2 = e2
% 142.81/21.43 (3) ~ (e3 = e2)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | ALPHA: (1) implies:
% 142.81/21.43 | (4) all_57_2 = e3
% 142.81/21.43 |
% 142.81/21.43 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.43 | (5) e3 = e2
% 142.81/21.43 |
% 142.81/21.43 | SIMP: (5) implies:
% 142.81/21.43 | (6) e3 = e2
% 142.81/21.43 |
% 142.81/21.43 | REDUCE: (3), (6) imply:
% 142.81/21.43 | (7) $false
% 142.81/21.43 |
% 142.81/21.43 | CLOSE: (7) is inconsistent.
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #824 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.43 (2) ~ (e2 = e1)
% 142.81/21.43 (3) all_57_5 = e1
% 142.81/21.43 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (5) ~ (all_52_13 = e2)
% 142.81/21.43 (6) op(e2, e0) = all_52_13
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (1) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (7) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #1012.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (8) all_57_10 = e2 & op(e2, e0) = e2
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (8) implies:
% 142.81/21.43 | | (9) op(e2, e0) = e2
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1030.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #825 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.43 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.43 (2) all_57_13 = e2 & op(e0, e2) = e2
% 142.81/21.43 (3) ~ (e2 = e1)
% 142.81/21.43 (4) ~ (all_52_7 = e0)
% 142.81/21.43 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.43 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.43 (6) ~ (e3 = e0)
% 142.81/21.43 (7) ~ (e1 = e0)
% 142.81/21.43 (8) ~ (e2 = e0)
% 142.81/21.43 (9) ~ (e3 = e2)
% 142.81/21.43 (10) op(e0, e0) = e2
% 142.81/21.43 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.43 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.43 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.43 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.43 (13) ~ (e3 = e1)
% 142.81/21.43 (14) op(e0, e2) = all_52_7
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | ALPHA: (2) implies:
% 142.81/21.43 | (15) all_57_13 = e2
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (5) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (16) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) =
% 142.81/21.43 | | e1)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (16) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (17) all_57_12 = e1 & op(e0, e3) = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (17) implies:
% 142.81/21.43 | | | (18) all_57_12 = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.81/21.43 | | | (14), (15), (18) are inconsistent by sub-proof #835.
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (19) all_57_13 = e1 & op(e0, e2) = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (3), (15), (19) are inconsistent by sub-proof #1072.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (20) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.81/21.43 | | e1)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (20) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (21) all_57_14 = e1 & op(e0, e1) = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (21) implies:
% 142.81/21.43 | | | (22) all_57_14 = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | BETA: splitting (12) gives:
% 142.81/21.43 | | |
% 142.81/21.43 | | | Case 1:
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | (23) all_57_15 = e0 & op(e0, e0) = e0
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | ALPHA: (23) implies:
% 142.81/21.43 | | | | (24) op(e0, e0) = e0
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | REF_CLOSE: (8), (10), (11), (24) are inconsistent by sub-proof #1094.
% 142.81/21.43 | | | |
% 142.81/21.43 | | | Case 2:
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | (25) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2,
% 142.81/21.43 | | | | e0) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)) &
% 142.81/21.43 | | | | ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.81/21.43 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | ALPHA: (25) implies:
% 142.81/21.43 | | | | (26) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0,
% 142.81/21.43 | | | | e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | BETA: splitting (26) gives:
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | Case 1:
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | (27) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | ALPHA: (27) implies:
% 142.81/21.43 | | | | | (28) all_57_12 = e0
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | BETA: splitting (1) gives:
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | Case 1:
% 142.81/21.43 | | | | | |
% 142.81/21.43 | | | | | | (29) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 &
% 142.81/21.43 | | | | | | op(e0, e2) = e3)
% 142.81/21.43 | | | | | |
% 142.81/21.43 | | | | | | REF_CLOSE: (6), (9), (15), (28), (29) are inconsistent by sub-proof
% 142.81/21.43 | | | | | | #827.
% 142.81/21.43 | | | | | |
% 142.81/21.43 | | | | | Case 2:
% 142.81/21.43 | | | | | |
% 142.81/21.43 | | | | | | (30) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 &
% 142.81/21.43 | | | | | | op(e0, e0) = e3)
% 142.81/21.43 | | | | | |
% 142.81/21.43 | | | | | | REF_CLOSE: (9), (10), (11), (13), (22), (30) are inconsistent by
% 142.81/21.43 | | | | | | sub-proof #826.
% 142.81/21.43 | | | | | |
% 142.81/21.43 | | | | | End of split
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | Case 2:
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | (31) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0,
% 142.81/21.43 | | | | | e1) = e0)
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 142.81/21.43 | | | | | (15), (31) are inconsistent by sub-proof #836.
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | End of split
% 142.81/21.43 | | | |
% 142.81/21.43 | | | End of split
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (32) all_57_15 = e1 & op(e0, e0) = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (32) implies:
% 142.81/21.43 | | | (33) op(e0, e0) = e1
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (3), (10), (11), (33) are inconsistent by sub-proof #1070.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #826 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) all_57_14 = e1
% 142.81/21.43 (2) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.43 (3) ~ (e3 = e2)
% 142.81/21.43 (4) op(e0, e0) = e2
% 142.81/21.43 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (6) ~ (e3 = e1)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (2) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (7) all_57_14 = e3 & op(e0, e1) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (7) implies:
% 142.81/21.43 | | (8) all_57_14 = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (1), (6), (8) are inconsistent by sub-proof #1045.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (9) all_57_15 = e3 & op(e0, e0) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (9) implies:
% 142.81/21.43 | | (10) op(e0, e0) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #1066.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #827 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.43 (2) ~ (e3 = e0)
% 142.81/21.43 (3) all_57_13 = e2
% 142.81/21.43 (4) ~ (e3 = e2)
% 142.81/21.43 (5) all_57_12 = e0
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (1) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (6) all_57_12 = e3 & op(e0, e3) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (6) implies:
% 142.81/21.43 | | (7) all_57_12 = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (2), (5), (7) are inconsistent by sub-proof #828.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (8) all_57_13 = e3 & op(e0, e2) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (8) implies:
% 142.81/21.43 | | (9) all_57_13 = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (3), (4), (9) are inconsistent by sub-proof #1068.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #828 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) all_57_12 = e3
% 142.81/21.43 (2) all_57_12 = e0
% 142.81/21.43 (3) ~ (e3 = e0)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.43 | (4) e3 = e0
% 142.81/21.43 |
% 142.81/21.43 | SIMP: (4) implies:
% 142.81/21.43 | (5) e3 = e0
% 142.81/21.43 |
% 142.81/21.43 | REDUCE: (3), (5) imply:
% 142.81/21.43 | (6) $false
% 142.81/21.43 |
% 142.81/21.43 | CLOSE: (6) is inconsistent.
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #829 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.43 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.43 (2) ~ (e2 = e1)
% 142.81/21.43 (3) all_57_5 = e1
% 142.81/21.43 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.43 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.43 (5) ~ (e3 = e0)
% 142.81/21.43 (6) op(e1, e1) = e1
% 142.81/21.43 (7) all_57_14 = e1
% 142.81/21.43 (8) ~ (e1 = e0)
% 142.81/21.43 (9) ~ (e2 = e0)
% 142.81/21.43 (10) ~ (e3 = e2)
% 142.81/21.43 (11) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.43 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.43 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (13) ~ (e3 = e1)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (4) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (14) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 142.81/21.43 | | e0)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (14) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (15) all_57_4 = e0 & op(e3, e1) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (15) implies:
% 142.81/21.43 | | | (16) all_57_4 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (16) are
% 142.81/21.43 | | | inconsistent by sub-proof #830.
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (17) all_57_5 = e0 & op(e2, e1) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (17) implies:
% 142.81/21.43 | | | (18) all_57_5 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (18) are
% 142.81/21.43 | | | inconsistent by sub-proof #1040.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (19) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.81/21.43 | | e0)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (19) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (20) all_57_8 = e0 & op(e1, e1) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (20) implies:
% 142.81/21.43 | | | (21) op(e1, e1) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (6), (8), (12), (21) are inconsistent by sub-proof #1089.
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (22) all_57_14 = e0 & op(e0, e1) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (22) implies:
% 142.81/21.43 | | | (23) all_57_14 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | COMBINE_EQS: (7), (23) imply:
% 142.81/21.43 | | | (24) e1 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | COMBINE_EQS: (3), (24) imply:
% 142.81/21.43 | | | (25) all_57_5 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (1), (2), (5), (6), (7), (9), (10), (11), (12), (13), (25) are
% 142.81/21.43 | | | inconsistent by sub-proof #1040.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #830 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.43 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.43 (2) ~ (e2 = e1)
% 142.81/21.43 (3) all_57_4 = e0
% 142.81/21.43 (4) ~ (e3 = e0)
% 142.81/21.43 (5) op(e1, e1) = e1
% 142.81/21.43 (6) all_57_14 = e1
% 142.81/21.43 (7) ~ (e2 = e0)
% 142.81/21.43 (8) ~ (e3 = e2)
% 142.81/21.43 (9) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.43 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.43 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (11) ~ (e3 = e1)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (1) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (12) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) =
% 142.81/21.43 | | e3)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (12) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (13) all_57_4 = e3 & op(e3, e1) = e3
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (13) implies:
% 142.81/21.43 | | | (14) all_57_4 = e3
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (3), (4), (14) are inconsistent by sub-proof #831.
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (15) all_57_5 = e3 & op(e2, e1) = e3
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (2), (3), (5), (6), (7), (8), (9), (10), (15) are inconsistent
% 142.81/21.43 | | | by sub-proof #1046.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (16) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) =
% 142.81/21.43 | | e3)
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (5), (6), (10), (11), (16) are inconsistent by sub-proof #1044.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #831 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) all_57_4 = e3
% 142.81/21.43 (2) all_57_4 = e0
% 142.81/21.43 (3) ~ (e3 = e0)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.43 | (4) e3 = e0
% 142.81/21.43 |
% 142.81/21.43 | SIMP: (4) implies:
% 142.81/21.43 | (5) e3 = e0
% 142.81/21.43 |
% 142.81/21.43 | REDUCE: (3), (5) imply:
% 142.81/21.43 | (6) $false
% 142.81/21.43 |
% 142.81/21.43 | CLOSE: (6) is inconsistent.
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #832 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.43 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.43 (2) ~ (e2 = e1)
% 142.81/21.43 (3) ~ (all_52_7 = e0)
% 142.81/21.43 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.43 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.43 (5) ~ (all_52_1 = e0)
% 142.81/21.43 (6) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.43 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.43 (7) ~ (e3 = e0)
% 142.81/21.43 (8) op(e2, e3) = all_52_1
% 142.81/21.43 (9) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3) = e3) |
% 142.81/21.43 (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.81/21.43 (10) ~ (e1 = e0)
% 142.81/21.43 (11) ~ (e2 = e0)
% 142.81/21.43 (12) ~ (e3 = e2)
% 142.81/21.43 (13) op(e3, e3) = e1
% 142.81/21.43 (14) op(e0, e0) = e2
% 142.81/21.43 (15) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (16) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.43 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.43 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.43 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.43 (17) ~ (e3 = e1)
% 142.81/21.43 (18) all_57_13 = e3
% 142.81/21.43 (19) op(e0, e2) = all_52_7
% 142.81/21.43 (20) all_57_2 = e2
% 142.81/21.43 (21) all_57_12 = e1
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (6) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (22) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 142.81/21.43 | | e0)
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (5), (8), (10), (13), (15), (22) are inconsistent by sub-proof
% 142.81/21.43 | | #839.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (23) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 142.81/21.43 | | e0)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (23) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (24) all_57_6 = e0 & op(e1, e3) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (24) implies:
% 142.81/21.43 | | | (25) all_57_6 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | BETA: splitting (9) gives:
% 142.81/21.43 | | |
% 142.81/21.43 | | | Case 1:
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_2 = e3 & op(e2, e3)
% 142.81/21.43 | | | | = e3)
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | BETA: splitting (26) gives:
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | Case 1:
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | (27) all_57_0 = e3 & op(e3, e3) = e3
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | ALPHA: (27) implies:
% 142.81/21.43 | | | | | (28) op(e3, e3) = e3
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | REF_CLOSE: (13), (15), (17), (28) are inconsistent by sub-proof #838.
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | Case 2:
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | (29) all_57_2 = e3 & op(e2, e3) = e3
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | ALPHA: (29) implies:
% 142.81/21.43 | | | | | (30) all_57_2 = e3
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | COMBINE_EQS: (20), (30) imply:
% 142.81/21.43 | | | | | (31) e3 = e2
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | SIMP: (31) implies:
% 142.81/21.43 | | | | | (32) e3 = e2
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | COMBINE_EQS: (18), (32) imply:
% 142.81/21.43 | | | | | (33) all_57_13 = e2
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | | REF_CLOSE: (1), (2), (3), (4), (7), (10), (11), (12), (14), (15),
% 142.81/21.43 | | | | | (16), (17), (19), (21), (33) are inconsistent by sub-proof
% 142.81/21.43 | | | | | #835.
% 142.81/21.43 | | | | |
% 142.81/21.43 | | | | End of split
% 142.81/21.43 | | | |
% 142.81/21.43 | | | Case 2:
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | (34) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3)
% 142.81/21.43 | | | | = e3)
% 142.81/21.43 | | | |
% 142.81/21.43 | | | | REF_CLOSE: (7), (17), (21), (25), (34) are inconsistent by sub-proof
% 142.81/21.43 | | | | #833.
% 142.81/21.43 | | | |
% 142.81/21.43 | | | End of split
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (35) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | ALPHA: (35) implies:
% 142.81/21.43 | | | (36) all_57_12 = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (10), (21), (36) are inconsistent by sub-proof #1002.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #833 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_12 = e3 & op(e0, e3) = e3)
% 142.81/21.43 (2) ~ (e3 = e0)
% 142.81/21.43 (3) all_57_6 = e0
% 142.81/21.43 (4) ~ (e3 = e1)
% 142.81/21.43 (5) all_57_12 = e1
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (1) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (6) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (6) implies:
% 142.81/21.43 | | (7) all_57_6 = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (2), (3), (7) are inconsistent by sub-proof #873.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (8) all_57_12 = e3 & op(e0, e3) = e3
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (8) implies:
% 142.81/21.43 | | (9) all_57_12 = e3
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #834.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #834 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) all_57_12 = e3
% 142.81/21.43 (2) all_57_12 = e1
% 142.81/21.43 (3) ~ (e3 = e1)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.43 | (4) e3 = e1
% 142.81/21.43 |
% 142.81/21.43 | SIMP: (4) implies:
% 142.81/21.43 | (5) e3 = e1
% 142.81/21.43 |
% 142.81/21.43 | REDUCE: (3), (5) imply:
% 142.81/21.43 | (6) $false
% 142.81/21.43 |
% 142.81/21.43 | CLOSE: (6) is inconsistent.
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #835 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.43 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.43 (2) ~ (e2 = e1)
% 142.81/21.43 (3) ~ (all_52_7 = e0)
% 142.81/21.43 (4) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.43 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.43 (5) ~ (e3 = e0)
% 142.81/21.43 (6) all_57_13 = e2
% 142.81/21.43 (7) ~ (e1 = e0)
% 142.81/21.43 (8) ~ (e2 = e0)
% 142.81/21.43 (9) ~ (e3 = e2)
% 142.81/21.43 (10) op(e0, e0) = e2
% 142.81/21.43 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (12) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.43 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.43 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.43 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.43 (13) ~ (e3 = e1)
% 142.81/21.43 (14) op(e0, e2) = all_52_7
% 142.81/21.43 (15) all_57_12 = e1
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (12) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (16) all_57_15 = e0 & op(e0, e0) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (16) implies:
% 142.81/21.43 | | (17) op(e0, e0) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (8), (10), (11), (17) are inconsistent by sub-proof #1094.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (18) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.81/21.43 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.81/21.43 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.81/21.43 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (18) implies:
% 142.81/21.43 | | (19) (all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) =
% 142.81/21.43 | | e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.43 | |
% 142.81/21.43 | | BETA: splitting (19) gives:
% 142.81/21.43 | |
% 142.81/21.43 | | Case 1:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (20) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (7), (15), (20) are inconsistent by sub-proof #837.
% 142.81/21.43 | | |
% 142.81/21.43 | | Case 2:
% 142.81/21.43 | | |
% 142.81/21.43 | | | (21) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1)
% 142.81/21.43 | | | = e0)
% 142.81/21.43 | | |
% 142.81/21.43 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (10), (11), (13), (14),
% 142.81/21.43 | | | (21) are inconsistent by sub-proof #836.
% 142.81/21.43 | | |
% 142.81/21.43 | | End of split
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #836 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.43 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.43 (2) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.43 (3) ~ (e2 = e1)
% 142.81/21.43 (4) ~ (all_52_7 = e0)
% 142.81/21.43 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.43 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.43 (6) ~ (e3 = e0)
% 142.81/21.43 (7) all_57_13 = e2
% 142.81/21.43 (8) ~ (e1 = e0)
% 142.81/21.43 (9) ~ (e3 = e2)
% 142.81/21.43 (10) op(e0, e0) = e2
% 142.81/21.43 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (12) ~ (e3 = e1)
% 142.81/21.43 (13) op(e0, e2) = all_52_7
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (2) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (14) all_57_13 = e0 & op(e0, e2) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (14) implies:
% 142.81/21.43 | | (15) op(e0, e2) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (4), (11), (13), (15) are inconsistent by sub-proof #977.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (16) all_57_14 = e0 & op(e0, e1) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (16) implies:
% 142.81/21.43 | | (17) all_57_14 = e0
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (10), (11), (12), (17) are
% 142.81/21.43 | | inconsistent by sub-proof #1064.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #837 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.43 (2) all_57_12 = e1
% 142.81/21.43 (3) ~ (e1 = e0)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | ALPHA: (1) implies:
% 142.81/21.43 | (4) all_57_12 = e0
% 142.81/21.43 |
% 142.81/21.43 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.43 | (5) e1 = e0
% 142.81/21.43 |
% 142.81/21.43 | REDUCE: (3), (5) imply:
% 142.81/21.43 | (6) $false
% 142.81/21.43 |
% 142.81/21.43 | CLOSE: (6) is inconsistent.
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #838 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (2) op(e3, e3) = e3
% 142.81/21.43 (3) op(e3, e3) = e1
% 142.81/21.43 (4) ~ (e3 = e1)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | GROUND_INST: instantiating (1) with e1, e3, e3, e3, simplifying with (2), (3)
% 142.81/21.43 | gives:
% 142.81/21.43 | (5) e3 = e1
% 142.81/21.43 |
% 142.81/21.43 | REDUCE: (4), (5) imply:
% 142.81/21.43 | (6) $false
% 142.81/21.43 |
% 142.81/21.43 | CLOSE: (6) is inconsistent.
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #839 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 142.81/21.43 (2) ~ (all_52_1 = e0)
% 142.81/21.43 (3) op(e2, e3) = all_52_1
% 142.81/21.43 (4) ~ (e1 = e0)
% 142.81/21.43 (5) op(e3, e3) = e1
% 142.81/21.43 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | BETA: splitting (1) gives:
% 142.81/21.43 |
% 142.81/21.43 | Case 1:
% 142.81/21.43 | |
% 142.81/21.43 | | (7) all_57_0 = e0 & op(e3, e3) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | ALPHA: (7) implies:
% 142.81/21.43 | | (8) op(e3, e3) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (4), (5), (6), (8) are inconsistent by sub-proof #840.
% 142.81/21.43 | |
% 142.81/21.43 | Case 2:
% 142.81/21.43 | |
% 142.81/21.43 | | (9) all_57_2 = e0 & op(e2, e3) = e0
% 142.81/21.43 | |
% 142.81/21.43 | | REF_CLOSE: (2), (3), (6), (9) are inconsistent by sub-proof #1028.
% 142.81/21.43 | |
% 142.81/21.43 | End of split
% 142.81/21.43 |
% 142.81/21.43 End of proof
% 142.81/21.43
% 142.81/21.43 Sub-proof #840 shows that the following formulas are inconsistent:
% 142.81/21.43 ----------------------------------------------------------------
% 142.81/21.43 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.43 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.43 (2) op(e3, e3) = e1
% 142.81/21.43 (3) op(e3, e3) = e0
% 142.81/21.43 (4) ~ (e1 = e0)
% 142.81/21.43
% 142.81/21.43 Begin of proof
% 142.81/21.43 |
% 142.81/21.43 | GROUND_INST: instantiating (1) with e0, e1, e3, e3, simplifying with (2), (3)
% 142.81/21.44 | gives:
% 142.81/21.44 | (5) e1 = e0
% 142.81/21.44 |
% 142.81/21.44 | REDUCE: (4), (5) imply:
% 142.81/21.44 | (6) $false
% 142.81/21.44 |
% 142.81/21.44 | CLOSE: (6) is inconsistent.
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #841 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3)
% 142.81/21.44 (2) ~ (e3 = e0)
% 142.81/21.44 (3) ~ (e3 = e2)
% 142.81/21.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (5) all_57_1 = e2
% 142.81/21.44 (6) op(e2, e2) = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (1) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (7) all_57_1 = e3 & op(e3, e2) = e3
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (3), (5), (7) are inconsistent by sub-proof #842.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (8) all_57_3 = e3 & op(e2, e2) = e3
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (8) implies:
% 142.81/21.44 | | (9) op(e2, e2) = e3
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (2), (4), (6), (9) are inconsistent by sub-proof #1119.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #842 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) all_57_1 = e3 & op(e3, e2) = e3
% 142.81/21.44 (2) all_57_1 = e2
% 142.81/21.44 (3) ~ (e3 = e2)
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | ALPHA: (1) implies:
% 142.81/21.44 | (4) all_57_1 = e3
% 142.81/21.44 |
% 142.81/21.44 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.44 | (5) e3 = e2
% 142.81/21.44 |
% 142.81/21.44 | SIMP: (5) implies:
% 142.81/21.44 | (6) e3 = e2
% 142.81/21.44 |
% 142.81/21.44 | REDUCE: (3), (6) imply:
% 142.81/21.44 | (7) $false
% 142.81/21.44 |
% 142.81/21.44 | CLOSE: (7) is inconsistent.
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #843 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) ~ (all_52_4 = e1)
% 142.81/21.44 (2) ~ (e1 = e0)
% 142.81/21.44 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 142.81/21.44 (4) op(e3, e2) = all_52_4
% 142.81/21.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (6) op(e2, e2) = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (3) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (7) all_57_1 = e1 & op(e3, e2) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (4), (5), (7) are inconsistent by sub-proof #844.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (8) implies:
% 142.81/21.44 | | (9) op(e2, e2) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (2), (5), (6), (9) are inconsistent by sub-proof #1117.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #844 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) all_57_1 = e1 & op(e3, e2) = e1
% 142.81/21.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (3) op(e3, e2) = all_52_4
% 142.81/21.44 (4) ~ (all_52_4 = e1)
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | ALPHA: (1) implies:
% 142.81/21.44 | (5) op(e3, e2) = e1
% 142.81/21.44 |
% 142.81/21.44 | GROUND_INST: instantiating (2) with all_52_4, e1, e2, e3, simplifying with
% 142.81/21.44 | (3), (5) gives:
% 142.81/21.44 | (6) all_52_4 = e1
% 142.81/21.44 |
% 142.81/21.44 | REDUCE: (4), (6) imply:
% 142.81/21.44 | (7) $false
% 142.81/21.44 |
% 142.81/21.44 | CLOSE: (7) is inconsistent.
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #845 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1)
% 142.81/21.44 (2) ~ (all_52_1 = e1)
% 142.81/21.44 (3) op(e2, e3) = all_52_1
% 142.81/21.44 (4) ~ (e1 = e0)
% 142.81/21.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (6) op(e2, e2) = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (1) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (7) all_57_2 = e1 & op(e2, e3) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #846.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (8) all_57_3 = e1 & op(e2, e2) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (8) implies:
% 142.81/21.44 | | (9) op(e2, e2) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1117.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #846 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) all_57_2 = e1 & op(e2, e3) = e1
% 142.81/21.44 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (3) op(e2, e3) = all_52_1
% 142.81/21.44 (4) ~ (all_52_1 = e1)
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | ALPHA: (1) implies:
% 142.81/21.44 | (5) op(e2, e3) = e1
% 142.81/21.44 |
% 142.81/21.44 | GROUND_INST: instantiating (2) with all_52_1, e1, e3, e2, simplifying with
% 142.81/21.44 | (3), (5) gives:
% 142.81/21.44 | (6) all_52_1 = e1
% 142.81/21.44 |
% 142.81/21.44 | REDUCE: (4), (6) imply:
% 142.81/21.44 | (7) $false
% 142.81/21.44 |
% 142.81/21.44 | CLOSE: (7) is inconsistent.
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #847 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) all_57_14 = e0
% 142.81/21.44 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.44 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.44 (3) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.44 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.44 (4) op(e1, e2) = all_52_6
% 142.81/21.44 (5) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.44 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.44 (6) ~ (e2 = e1)
% 142.81/21.44 (7) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 142.81/21.44 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 142.81/21.44 (8) op(e2, e1) = e2
% 142.81/21.44 (9) ~ (all_52_7 = e0)
% 142.81/21.44 (10) all_57_7 = e2
% 142.81/21.44 (11) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.44 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.44 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.44 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.44 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.81/21.44 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.81/21.44 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.81/21.44 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.81/21.44 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.81/21.44 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.81/21.44 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.81/21.44 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.81/21.44 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.81/21.44 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.81/21.44 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.81/21.44 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.81/21.44 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.81/21.44 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.81/21.44 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.81/21.44 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.81/21.44 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.44 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.44 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.44 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.44 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.44 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.44 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.44 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.44 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.81/21.44 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.81/21.44 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.81/21.44 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.81/21.44 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.81/21.44 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.81/21.44 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.44 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.81/21.44 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.81/21.44 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.44 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.44 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.81/21.44 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.44 (12) op(e3, e3) = e2
% 142.81/21.44 (13) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.44 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.44 (14) ~ (e3 = e0)
% 142.81/21.44 (15) op(e1, e1) = all_4_2
% 142.81/21.44 (16) all_57_6 = e0
% 142.81/21.44 (17) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.44 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.44 (18) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.81/21.44 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.44 (19) ~ (all_4_2 = e3)
% 142.81/21.44 (20) ~ (e1 = e0)
% 142.81/21.44 (21) all_57_13 = e1
% 142.81/21.44 (22) ~ (e2 = e0)
% 142.81/21.44 (23) ~ (e3 = e2)
% 142.81/21.44 (24) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.44 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.44 (25) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.81/21.44 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.44 (26) op(e0, e0) = e2
% 142.81/21.44 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (28) all_57_5 = e2
% 142.81/21.44 (29) ~ (all_52_13 = e2)
% 142.81/21.44 (30) ~ (e3 = e1)
% 142.81/21.44 (31) op(e0, e2) = all_52_7
% 142.81/21.44 (32) op(e2, e2) = e0
% 142.81/21.44 (33) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.44 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.44 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.44 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.44 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.44 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.44 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.44 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.44 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.44 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.44 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.44 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.44 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.44 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.44 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.44 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.44 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.44 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.44 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.44 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.44 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.44 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.44 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.44 $i(all_56_14))))
% 142.81/21.44 (34) ~ (all_52_6 = e0)
% 142.81/21.44 (35) op(e2, e0) = all_52_13
% 142.81/21.44 (36) all_57_12 = e2
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (24) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (37) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.81/21.44 | | e3)
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (10), (14), (16), (23), (37) are inconsistent by sub-proof #867.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (38) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.81/21.44 | | e3)
% 142.81/21.44 | |
% 142.81/21.44 | | BETA: splitting (38) gives:
% 142.81/21.44 | |
% 142.81/21.44 | | Case 1:
% 142.81/21.44 | | |
% 142.81/21.44 | | | (39) all_57_8 = e3 & op(e1, e1) = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | ALPHA: (39) implies:
% 142.81/21.44 | | | (40) op(e1, e1) = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | REF_CLOSE: (15), (19), (27), (40) are inconsistent by sub-proof #1127.
% 142.81/21.44 | | |
% 142.81/21.44 | | Case 2:
% 142.81/21.44 | | |
% 142.81/21.44 | | | (41) all_57_11 = e3 & op(e1, e0) = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | ALPHA: (41) implies:
% 142.81/21.44 | | | (42) all_57_11 = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | BETA: splitting (3) gives:
% 142.81/21.44 | | |
% 142.81/21.44 | | | Case 1:
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | (43) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0,
% 142.81/21.44 | | | | e2) = e3)
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | BETA: splitting (43) gives:
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | Case 1:
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | (44) all_57_12 = e3 & op(e0, e3) = e3
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | ALPHA: (44) implies:
% 142.81/21.44 | | | | | (45) all_57_12 = e3
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | COMBINE_EQS: (36), (45) imply:
% 142.81/21.44 | | | | | (46) e3 = e2
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | SIMP: (46) implies:
% 142.81/21.44 | | | | | (47) e3 = e2
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | COMBINE_EQS: (42), (47) imply:
% 142.81/21.44 | | | | | (48) all_57_11 = e2
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | REF_CLOSE: (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.81/21.44 | | | | | (14), (15), (17), (18), (19), (20), (22), (23), (24), (25),
% 142.81/21.44 | | | | | (26), (27), (28), (29), (30), (31), (32), (33), (34), (35),
% 142.81/21.44 | | | | | (48) are inconsistent by sub-proof #860.
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | Case 2:
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | (49) all_57_13 = e3 & op(e0, e2) = e3
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | ALPHA: (49) implies:
% 142.81/21.44 | | | | | (50) all_57_13 = e3
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | | REF_CLOSE: (21), (30), (50) are inconsistent by sub-proof #1001.
% 142.81/21.44 | | | | |
% 142.81/21.44 | | | | End of split
% 142.81/21.44 | | | |
% 142.81/21.44 | | | Case 2:
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | (51) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0,
% 142.81/21.44 | | | | e0) = e3)
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | REF_CLOSE: (1), (14), (23), (26), (27), (51) are inconsistent by
% 142.81/21.44 | | | | sub-proof #1065.
% 142.81/21.44 | | | |
% 142.81/21.44 | | | End of split
% 142.81/21.44 | | |
% 142.81/21.44 | | End of split
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #848 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) all_57_12 = e1 & op(e0, e3) = e1
% 142.81/21.44 (2) all_57_12 = e2
% 142.81/21.44 (3) ~ (e2 = e1)
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | ALPHA: (1) implies:
% 142.81/21.44 | (4) all_57_12 = e1
% 142.81/21.44 |
% 142.81/21.44 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.44 | (5) e2 = e1
% 142.81/21.44 |
% 142.81/21.44 | REDUCE: (3), (5) imply:
% 142.81/21.44 | (6) $false
% 142.81/21.44 |
% 142.81/21.44 | CLOSE: (6) is inconsistent.
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #849 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.44 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.44 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.44 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.44 (3) ~ (e2 = e1)
% 142.81/21.44 (4) ~ (e3 = e0)
% 142.81/21.44 (5) all_57_11 = e2
% 142.81/21.44 (6) ~ (e1 = e0)
% 142.81/21.44 (7) ~ (e2 = e0)
% 142.81/21.44 (8) ~ (e3 = e2)
% 142.81/21.44 (9) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.81/21.44 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.44 (10) op(e0, e0) = e2
% 142.81/21.44 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (12) all_57_5 = e2
% 142.81/21.44 (13) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.44 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.44 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.44 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.44 (14) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.44 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.44 (15) ~ (e3 = e1)
% 142.81/21.44 (16) op(e2, e2) = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (13) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (17) all_57_15 = e0 & op(e0, e0) = e0
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (17) implies:
% 142.81/21.44 | | (18) op(e0, e0) = e0
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (7), (10), (11), (18) are inconsistent by sub-proof #1094.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (19) ((all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.81/21.44 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)) & ((all_57_12 = e0 &
% 142.81/21.44 | | op(e0, e3) = e0) | (all_57_13 = e0 & op(e0, e2) = e0) |
% 142.81/21.44 | | (all_57_14 = e0 & op(e0, e1) = e0))
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (19) implies:
% 142.81/21.44 | | (20) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) =
% 142.81/21.44 | | e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.81/21.44 | | (14), (15), (16), (20) are inconsistent by sub-proof #850.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #850 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.44 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.44 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.44 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.44 (3) ~ (e2 = e1)
% 142.81/21.44 (4) ~ (e3 = e0)
% 142.81/21.44 (5) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.81/21.44 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.44 (6) all_57_11 = e2
% 142.81/21.44 (7) ~ (e1 = e0)
% 142.81/21.44 (8) ~ (e2 = e0)
% 142.81/21.44 (9) ~ (e3 = e2)
% 142.81/21.44 (10) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.81/21.44 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.44 (11) op(e0, e0) = e2
% 142.81/21.44 (12) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (13) all_57_5 = e2
% 142.81/21.44 (14) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.44 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.44 (15) ~ (e3 = e1)
% 142.81/21.44 (16) op(e2, e2) = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (5) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (17) all_57_9 = e0 & op(e3, e0) = e0
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (17) implies:
% 142.81/21.44 | | (18) all_57_9 = e0
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (3), (4), (6), (7), (9), (10), (11), (12), (14), (15), (18) are
% 142.81/21.44 | | inconsistent by sub-proof #851.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (19) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0) =
% 142.81/21.44 | | e0)
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (2), (3), (4), (6), (7), (8), (9), (12), (13), (15), (16),
% 142.81/21.44 | | (19) are inconsistent by sub-proof #933.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #851 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) ~ (e2 = e1)
% 142.81/21.44 (2) ~ (e3 = e0)
% 142.81/21.44 (3) all_57_11 = e2
% 142.81/21.44 (4) ~ (e1 = e0)
% 142.81/21.44 (5) ~ (e3 = e2)
% 142.81/21.44 (6) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.81/21.44 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.44 (7) op(e0, e0) = e2
% 142.81/21.44 (8) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (9) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.44 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.44 (10) ~ (e3 = e1)
% 142.81/21.44 (11) all_57_9 = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (6) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (12) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 142.81/21.44 | | e3)
% 142.81/21.44 | |
% 142.81/21.44 | | BETA: splitting (12) gives:
% 142.81/21.44 | |
% 142.81/21.44 | | Case 1:
% 142.81/21.44 | | |
% 142.81/21.44 | | | (13) all_57_9 = e3 & op(e3, e0) = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | ALPHA: (13) implies:
% 142.81/21.44 | | | (14) all_57_9 = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | REF_CLOSE: (2), (11), (14) are inconsistent by sub-proof #863.
% 142.81/21.44 | | |
% 142.81/21.44 | | Case 2:
% 142.81/21.44 | | |
% 142.81/21.44 | | | (15) all_57_10 = e3 & op(e2, e0) = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | ALPHA: (15) implies:
% 142.81/21.44 | | | (16) all_57_10 = e3
% 142.81/21.44 | | |
% 142.81/21.44 | | | BETA: splitting (9) gives:
% 142.81/21.44 | | |
% 142.81/21.44 | | | Case 1:
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | (17) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0)
% 142.81/21.44 | | | | = e1)
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | REF_CLOSE: (4), (10), (11), (16), (17) are inconsistent by sub-proof
% 142.81/21.44 | | | | #854.
% 142.81/21.44 | | | |
% 142.81/21.44 | | | Case 2:
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | (18) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0,
% 142.81/21.44 | | | | e0) = e1)
% 142.81/21.44 | | | |
% 142.81/21.44 | | | | REF_CLOSE: (1), (3), (7), (8), (18) are inconsistent by sub-proof #853.
% 142.81/21.44 | | | |
% 142.81/21.44 | | | End of split
% 142.81/21.44 | | |
% 142.81/21.44 | | End of split
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (19) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) =
% 142.81/21.44 | | e3)
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (3), (5), (7), (8), (19) are inconsistent by sub-proof #852.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #852 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) all_57_11 = e2
% 142.81/21.44 (2) ~ (e3 = e2)
% 142.81/21.44 (3) op(e0, e0) = e2
% 142.81/21.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (5) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (5) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (6) all_57_11 = e3 & op(e1, e0) = e3
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (6) implies:
% 142.81/21.44 | | (7) all_57_11 = e3
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1055.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (8) implies:
% 142.81/21.44 | | (9) op(e0, e0) = e3
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (2), (3), (4), (9) are inconsistent by sub-proof #1066.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #853 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) ~ (e2 = e1)
% 142.81/21.44 (2) (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.44 (3) all_57_11 = e2
% 142.81/21.44 (4) op(e0, e0) = e2
% 142.81/21.44 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (2) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (6) all_57_11 = e1 & op(e1, e0) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (3), (6) are inconsistent by sub-proof #862.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (7) all_57_15 = e1 & op(e0, e0) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (7) implies:
% 142.81/21.44 | | (8) op(e0, e0) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (4), (5), (8) are inconsistent by sub-proof #1070.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #854 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) ~ (e1 = e0)
% 142.81/21.44 (2) all_57_10 = e3
% 142.81/21.44 (3) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.44 (4) ~ (e3 = e1)
% 142.81/21.44 (5) all_57_9 = e0
% 142.81/21.44
% 142.81/21.44 Begin of proof
% 142.81/21.44 |
% 142.81/21.44 | BETA: splitting (3) gives:
% 142.81/21.44 |
% 142.81/21.44 | Case 1:
% 142.81/21.44 | |
% 142.81/21.44 | | (6) all_57_9 = e1 & op(e3, e0) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | ALPHA: (6) implies:
% 142.81/21.44 | | (7) all_57_9 = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (1), (5), (7) are inconsistent by sub-proof #1079.
% 142.81/21.44 | |
% 142.81/21.44 | Case 2:
% 142.81/21.44 | |
% 142.81/21.44 | | (8) all_57_10 = e1 & op(e2, e0) = e1
% 142.81/21.44 | |
% 142.81/21.44 | | REF_CLOSE: (2), (4), (8) are inconsistent by sub-proof #929.
% 142.81/21.44 | |
% 142.81/21.44 | End of split
% 142.81/21.44 |
% 142.81/21.44 End of proof
% 142.81/21.44
% 142.81/21.44 Sub-proof #855 shows that the following formulas are inconsistent:
% 142.81/21.44 ----------------------------------------------------------------
% 142.81/21.44 (1) (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.44 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.44 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.44 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.44 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.44 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.44 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.44 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 142.81/21.44 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 142.81/21.44 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 142.81/21.44 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.81/21.44 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.44 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.81/21.44 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 142.81/21.44 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.81/21.44 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.81/21.44 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.44 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.44 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.81/21.44 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.44 (2) op(e2, e1) = e2
% 142.81/21.44 (3) ~ (e1 = e0)
% 142.81/21.44 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.44 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.44 (5) ~ (all_52_13 = e2)
% 142.81/21.44 (6) op(e2, e2) = e0
% 142.81/21.45 (7) op(e2, e0) = all_52_13
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (1) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (8) op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1)
% 142.81/21.45 | | = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 &
% 142.81/21.45 | | $i(all_56_9))) & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~
% 142.81/21.45 | | (all_56_11 = e1) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.45 | | ((all_56_9 = e1 & op(e3, e3) = e1) | ( ~ (all_56_1 = e3) & op(e3, e1)
% 142.81/21.45 | | = all_56_1 & $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1)
% 142.81/21.45 | | | ( ~ (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.45 | | ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.81/21.45 | | e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.81/21.45 | | e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.81/21.45 | | $i(all_56_14)))
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (8) implies:
% 142.81/21.45 | | (9) (all_56_11 = e1 & op(e2, e2) = e1) | ( ~ (all_56_4 = e2) & op(e2, e1)
% 142.81/21.45 | | = all_56_4 & $i(all_56_4))
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (2), (3), (4), (6), (9) are inconsistent by sub-proof #950.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (10) op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3,
% 142.81/21.45 | | e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 &
% 142.81/21.45 | | $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~
% 142.81/21.45 | | (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.45 | | ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1,
% 142.81/21.45 | | e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3,
% 142.81/21.45 | | e3) = e0) | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 &
% 142.81/21.45 | | $i(all_56_2))) & ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~
% 142.81/21.45 | | (all_56_5 = e2) & op(e2, e0) = all_56_5 & $i(all_56_5))) &
% 142.81/21.45 | | ((all_56_13 = e0 & op(e1, e1) = e0) | ( ~ (all_56_8 = e1) & op(e1,
% 142.81/21.45 | | e0) = all_56_8 & $i(all_56_8)))
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (10) implies:
% 142.81/21.45 | | (11) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.81/21.45 | | e2) = all_56_11 & $i(all_56_11))
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (4), (5), (6), (7), (11) are inconsistent by sub-proof #856.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #856 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) (all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2, e2) =
% 142.81/21.45 all_56_11 & $i(all_56_11))
% 142.81/21.45 (2) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45 (3) ~ (all_52_13 = e2)
% 142.81/21.45 (4) op(e2, e2) = e0
% 142.81/21.45 (5) op(e2, e0) = all_52_13
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (1) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (6) all_56_5 = e2 & op(e2, e0) = e2
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (6) implies:
% 142.81/21.45 | | (7) op(e2, e0) = e2
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (2), (3), (5), (7) are inconsistent by sub-proof #1030.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (8) ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11)
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (8) implies:
% 142.81/21.45 | | (9) ~ (all_56_11 = e0)
% 142.81/21.45 | | (10) op(e2, e2) = all_56_11
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (2), (4), (9), (10) are inconsistent by sub-proof #857.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #857 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45 (2) op(e2, e2) = all_56_11
% 142.81/21.45 (3) op(e2, e2) = e0
% 142.81/21.45 (4) ~ (all_56_11 = e0)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | GROUND_INST: instantiating (1) with e0, all_56_11, e2, e2, simplifying with
% 142.81/21.45 | (2), (3) gives:
% 142.81/21.45 | (5) all_56_11 = e0
% 142.81/21.45 |
% 142.81/21.45 | REDUCE: (4), (5) imply:
% 142.81/21.45 | (6) $false
% 142.81/21.45 |
% 142.81/21.45 | CLOSE: (6) is inconsistent.
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #858 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_11 = e3
% 142.81/21.45 (2) all_57_11 = e0
% 142.81/21.45 (3) ~ (e3 = e0)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.45 | (4) e3 = e0
% 142.81/21.45 |
% 142.81/21.45 | SIMP: (4) implies:
% 142.81/21.45 | (5) e3 = e0
% 142.81/21.45 |
% 142.81/21.45 | REDUCE: (3), (5) imply:
% 142.81/21.45 | (6) $false
% 142.81/21.45 |
% 142.81/21.45 | CLOSE: (6) is inconsistent.
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #859 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_14 = e0
% 142.81/21.45 (2) ~ (e3 = e0)
% 142.81/21.45 (3) op(e1, e1) = e1
% 142.81/21.45 (4) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.45 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45 (6) ~ (e3 = e1)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (4) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (7) implies:
% 142.81/21.45 | | (8) op(e1, e1) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (3), (5), (6), (8) are inconsistent by sub-proof #1096.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (9) all_57_14 = e3 & op(e0, e1) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (9) implies:
% 142.81/21.45 | | (10) all_57_14 = e3
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (1), (2), (10) are inconsistent by sub-proof #1067.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #860 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.45 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.45 (2) op(e1, e2) = all_52_6
% 142.81/21.45 (3) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.45 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.45 (4) ~ (e2 = e1)
% 142.81/21.45 (5) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1, e2) = e1) |
% 142.81/21.45 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1, e0) = e1)
% 142.81/21.45 (6) op(e2, e1) = e2
% 142.81/21.45 (7) ~ (all_52_7 = e0)
% 142.81/21.45 (8) all_57_7 = e2
% 142.81/21.45 (9) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.45 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.45 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.45 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.45 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.81/21.45 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 142.81/21.45 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 142.81/21.45 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 142.81/21.45 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 142.81/21.45 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 142.81/21.45 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 142.81/21.45 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.45 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 142.81/21.45 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 142.81/21.45 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.81/21.45 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 142.81/21.45 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 142.81/21.45 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 142.81/21.45 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 142.81/21.45 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.45 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.45 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.45 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.45 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.45 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.45 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.45 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.45 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 142.81/21.45 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 142.81/21.45 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 142.81/21.45 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.81/21.45 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.45 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.81/21.45 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 142.81/21.45 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.81/21.45 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.81/21.45 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.45 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.45 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.81/21.45 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.45 (10) op(e3, e3) = e2
% 142.81/21.45 (11) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.45 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.45 (12) ~ (e3 = e0)
% 142.81/21.45 (13) op(e1, e1) = all_4_2
% 142.81/21.45 (14) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.45 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.45 (15) (all_57_9 = e0 & op(e3, e0) = e0) | (all_57_10 = e0 & op(e2, e0) = e0) |
% 142.81/21.45 (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.45 (16) ~ (all_4_2 = e3)
% 142.81/21.45 (17) all_57_11 = e2
% 142.81/21.45 (18) ~ (e1 = e0)
% 142.81/21.45 (19) ~ (e2 = e0)
% 142.81/21.45 (20) ~ (e3 = e2)
% 142.81/21.45 (21) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.45 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.45 (22) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.81/21.45 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.45 (23) op(e0, e0) = e2
% 142.81/21.45 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45 (25) all_57_5 = e2
% 142.81/21.45 (26) ~ (all_52_13 = e2)
% 142.81/21.45 (27) ~ (e3 = e1)
% 142.81/21.45 (28) op(e0, e2) = all_52_7
% 142.81/21.45 (29) op(e2, e2) = e0
% 142.81/21.45 (30) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.45 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.45 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.45 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.45 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.45 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.45 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.45 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.45 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.45 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.45 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.45 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.45 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.45 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.45 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.45 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.45 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.45 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.45 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.45 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.45 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.45 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.45 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.45 $i(all_56_14))))
% 142.81/21.45 (31) ~ (all_52_6 = e0)
% 142.81/21.45 (32) op(e2, e0) = all_52_13
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (21) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (33) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.81/21.45 | | e3)
% 142.81/21.45 | |
% 142.81/21.45 | | BETA: splitting (33) gives:
% 142.81/21.45 | |
% 142.81/21.45 | | Case 1:
% 142.81/21.45 | | |
% 142.81/21.45 | | | (34) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.45 | | |
% 142.81/21.45 | | | ALPHA: (34) implies:
% 142.81/21.45 | | | (35) all_57_6 = e3
% 142.81/21.45 | | |
% 142.81/21.45 | | | BETA: splitting (15) gives:
% 142.81/21.45 | | |
% 142.81/21.45 | | | Case 1:
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | (36) all_57_9 = e0 & op(e3, e0) = e0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | ALPHA: (36) implies:
% 142.81/21.45 | | | | (37) all_57_9 = e0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | BETA: splitting (5) gives:
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | Case 1:
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | | (38) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_7 = e1 & op(e1,
% 142.81/21.45 | | | | | e2) = e1)
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | | BETA: splitting (38) gives:
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | | Case 1:
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | (39) all_57_6 = e1 & op(e1, e3) = e1
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | REF_CLOSE: (27), (35), (39) are inconsistent by sub-proof #865.
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | Case 2:
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | (40) all_57_7 = e1 & op(e1, e2) = e1
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | REF_CLOSE: (4), (8), (40) are inconsistent by sub-proof #864.
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | End of split
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | Case 2:
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | | (41) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_11 = e1 & op(e1,
% 142.81/21.45 | | | | | e0) = e1)
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | | BETA: splitting (41) gives:
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | | Case 1:
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | (42) all_57_8 = e1 & op(e1, e1) = e1
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | ALPHA: (42) implies:
% 142.81/21.45 | | | | | | (43) op(e1, e1) = e1
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | BETA: splitting (22) gives:
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | Case 1:
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | | (44) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 &
% 142.81/21.45 | | | | | | | op(e2, e0) = e3)
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | | BETA: splitting (44) gives:
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | | Case 1:
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | (45) all_57_9 = e3 & op(e3, e0) = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | ALPHA: (45) implies:
% 142.81/21.45 | | | | | | | | (46) all_57_9 = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | REF_CLOSE: (12), (37), (46) are inconsistent by sub-proof #863.
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | Case 2:
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | (47) all_57_10 = e3 & op(e2, e0) = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | ALPHA: (47) implies:
% 142.81/21.45 | | | | | | | | (48) all_57_10 = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | BETA: splitting (11) gives:
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | Case 1:
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | | (49) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 &
% 142.81/21.45 | | | | | | | | | op(e2, e3) = e0)
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | | BETA: splitting (49) gives:
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | | Case 1:
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | (50) all_57_0 = e0 & op(e3, e3) = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | ALPHA: (50) implies:
% 142.81/21.45 | | | | | | | | | | (51) op(e3, e3) = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | REF_CLOSE: (10), (19), (24), (51) are inconsistent by
% 142.81/21.45 | | | | | | | | | | sub-proof #880.
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | Case 2:
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | (52) all_57_2 = e0 & op(e2, e3) = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | ALPHA: (52) implies:
% 142.81/21.45 | | | | | | | | | | (53) all_57_2 = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | REF_CLOSE: (3), (4), (18), (24), (25), (27), (29), (48), (53)
% 142.81/21.45 | | | | | | | | | | are inconsistent by sub-proof #876.
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | End of split
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | Case 2:
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | | (54) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 &
% 142.81/21.45 | | | | | | | | | op(e0, e3) = e0)
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | | BETA: splitting (54) gives:
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | | Case 1:
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | (55) all_57_6 = e0 & op(e1, e3) = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | ALPHA: (55) implies:
% 142.81/21.45 | | | | | | | | | | (56) all_57_6 = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | COMBINE_EQS: (35), (56) imply:
% 142.81/21.45 | | | | | | | | | | (57) e3 = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | COMBINE_EQS: (48), (57) imply:
% 142.81/21.45 | | | | | | | | | | (58) all_57_10 = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | REF_CLOSE: (1), (3), (4), (12), (18), (20), (24), (25), (27),
% 142.81/21.45 | | | | | | | | | | (29), (58) are inconsistent by sub-proof #934.
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | Case 2:
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | (59) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | ALPHA: (59) implies:
% 142.81/21.45 | | | | | | | | | | (60) op(e0, e3) = e0
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | | REF_CLOSE: (4), (6), (7), (9), (12), (13), (16), (18), (20),
% 142.81/21.45 | | | | | | | | | | (23), (24), (26), (28), (29), (30), (32), (60) are
% 142.81/21.45 | | | | | | | | | | inconsistent by sub-proof #945.
% 142.81/21.45 | | | | | | | | | |
% 142.81/21.45 | | | | | | | | | End of split
% 142.81/21.45 | | | | | | | | |
% 142.81/21.45 | | | | | | | | End of split
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | End of split
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | Case 2:
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | | (61) (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 &
% 142.81/21.45 | | | | | | | op(e0, e0) = e3)
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | | BETA: splitting (61) gives:
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | | Case 1:
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | (62) all_57_11 = e3 & op(e1, e0) = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | ALPHA: (62) implies:
% 142.81/21.45 | | | | | | | | (63) all_57_11 = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | COMBINE_EQS: (17), (63) imply:
% 142.81/21.45 | | | | | | | | (64) e3 = e2
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | SIMP: (64) implies:
% 142.81/21.45 | | | | | | | | (65) e3 = e2
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | COMBINE_EQS: (35), (65) imply:
% 142.81/21.45 | | | | | | | | (66) all_57_6 = e2
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | REF_CLOSE: (2), (14), (17), (18), (19), (24), (31), (43), (66)
% 142.81/21.45 | | | | | | | | are inconsistent by sub-proof #990.
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | Case 2:
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | (67) all_57_15 = e3 & op(e0, e0) = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | ALPHA: (67) implies:
% 142.81/21.45 | | | | | | | | (68) op(e0, e0) = e3
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | | REF_CLOSE: (20), (23), (24), (68) are inconsistent by sub-proof
% 142.81/21.45 | | | | | | | | #1066.
% 142.81/21.45 | | | | | | | |
% 142.81/21.45 | | | | | | | End of split
% 142.81/21.45 | | | | | | |
% 142.81/21.45 | | | | | | End of split
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | Case 2:
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | (69) all_57_11 = e1 & op(e1, e0) = e1
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | | REF_CLOSE: (4), (17), (69) are inconsistent by sub-proof #862.
% 142.81/21.45 | | | | | |
% 142.81/21.45 | | | | | End of split
% 142.81/21.45 | | | | |
% 142.81/21.45 | | | | End of split
% 142.81/21.45 | | | |
% 142.81/21.45 | | | Case 2:
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | (70) (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1,
% 142.81/21.45 | | | | e0) = e0)
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | REF_CLOSE: (1), (3), (4), (12), (17), (18), (19), (20), (24), (25),
% 142.81/21.45 | | | | (27), (29), (70) are inconsistent by sub-proof #933.
% 142.81/21.45 | | | |
% 142.81/21.45 | | | End of split
% 142.81/21.45 | | |
% 142.81/21.45 | | Case 2:
% 142.81/21.45 | | |
% 142.81/21.45 | | | (71) all_57_7 = e3 & op(e1, e2) = e3
% 142.81/21.45 | | |
% 142.81/21.45 | | | ALPHA: (71) implies:
% 142.81/21.45 | | | (72) all_57_7 = e3
% 142.81/21.45 | | |
% 142.81/21.45 | | | REF_CLOSE: (8), (20), (72) are inconsistent by sub-proof #1098.
% 142.81/21.45 | | |
% 142.81/21.45 | | End of split
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (73) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.81/21.45 | | e3)
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (13), (16), (17), (20), (24), (73) are inconsistent by sub-proof
% 142.81/21.45 | | #861.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #861 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.45 (2) op(e1, e1) = all_4_2
% 142.81/21.45 (3) ~ (all_4_2 = e3)
% 142.81/21.45 (4) all_57_11 = e2
% 142.81/21.45 (5) ~ (e3 = e2)
% 142.81/21.45 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (1) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (7) all_57_8 = e3 & op(e1, e1) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (7) implies:
% 142.81/21.45 | | (8) op(e1, e1) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (2), (3), (6), (8) are inconsistent by sub-proof #1127.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (9) all_57_11 = e3 & op(e1, e0) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (9) implies:
% 142.81/21.45 | | (10) all_57_11 = e3
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (4), (5), (10) are inconsistent by sub-proof #1055.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #862 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_11 = e1 & op(e1, e0) = e1
% 142.81/21.45 (2) all_57_11 = e2
% 142.81/21.45 (3) ~ (e2 = e1)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | ALPHA: (1) implies:
% 142.81/21.45 | (4) all_57_11 = e1
% 142.81/21.45 |
% 142.81/21.45 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.45 | (5) e2 = e1
% 142.81/21.45 |
% 142.81/21.45 | REDUCE: (3), (5) imply:
% 142.81/21.45 | (6) $false
% 142.81/21.45 |
% 142.81/21.45 | CLOSE: (6) is inconsistent.
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #863 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_9 = e3
% 142.81/21.45 (2) all_57_9 = e0
% 142.81/21.45 (3) ~ (e3 = e0)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.45 | (4) e3 = e0
% 142.81/21.45 |
% 142.81/21.45 | SIMP: (4) implies:
% 142.81/21.45 | (5) e3 = e0
% 142.81/21.45 |
% 142.81/21.45 | REDUCE: (3), (5) imply:
% 142.81/21.45 | (6) $false
% 142.81/21.45 |
% 142.81/21.45 | CLOSE: (6) is inconsistent.
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #864 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_7 = e1 & op(e1, e2) = e1
% 142.81/21.45 (2) all_57_7 = e2
% 142.81/21.45 (3) ~ (e2 = e1)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | ALPHA: (1) implies:
% 142.81/21.45 | (4) all_57_7 = e1
% 142.81/21.45 |
% 142.81/21.45 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.45 | (5) e2 = e1
% 142.81/21.45 |
% 142.81/21.45 | REDUCE: (3), (5) imply:
% 142.81/21.45 | (6) $false
% 142.81/21.45 |
% 142.81/21.45 | CLOSE: (6) is inconsistent.
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #865 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_6 = e1 & op(e1, e3) = e1
% 142.81/21.45 (2) all_57_6 = e3
% 142.81/21.45 (3) ~ (e3 = e1)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | ALPHA: (1) implies:
% 142.81/21.45 | (4) all_57_6 = e1
% 142.81/21.45 |
% 142.81/21.45 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.45 | (5) e3 = e1
% 142.81/21.45 |
% 142.81/21.45 | REDUCE: (3), (5) imply:
% 142.81/21.45 | (6) $false
% 142.81/21.45 |
% 142.81/21.45 | CLOSE: (6) is inconsistent.
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #866 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) all_57_7 = e2
% 142.81/21.45 (2) ~ (e3 = e0)
% 142.81/21.45 (3) op(e1, e1) = e1
% 142.81/21.45 (4) all_57_6 = e0
% 142.81/21.45 (5) ~ (e3 = e2)
% 142.81/21.45 (6) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.45 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.45 (7) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45 (8) ~ (e3 = e1)
% 142.81/21.45 (9) all_57_11 = e1
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (6) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (10) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.81/21.45 | | e3)
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (1), (2), (4), (5), (10) are inconsistent by sub-proof #867.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (11) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.81/21.45 | | e3)
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (3), (7), (8), (9), (11) are inconsistent by sub-proof #911.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #867 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3)
% 142.81/21.45 (2) all_57_7 = e2
% 142.81/21.45 (3) ~ (e3 = e0)
% 142.81/21.45 (4) all_57_6 = e0
% 142.81/21.45 (5) ~ (e3 = e2)
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (1) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (6) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (6) implies:
% 142.81/21.45 | | (7) all_57_6 = e3
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (3), (4), (7) are inconsistent by sub-proof #873.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (8) all_57_7 = e3 & op(e1, e2) = e3
% 142.81/21.45 | |
% 142.81/21.45 | | ALPHA: (8) implies:
% 142.81/21.45 | | (9) all_57_7 = e3
% 142.81/21.45 | |
% 142.81/21.45 | | REF_CLOSE: (2), (5), (9) are inconsistent by sub-proof #1098.
% 142.81/21.45 | |
% 142.81/21.45 | End of split
% 142.81/21.45 |
% 142.81/21.45 End of proof
% 142.81/21.45
% 142.81/21.45 Sub-proof #868 shows that the following formulas are inconsistent:
% 142.81/21.45 ----------------------------------------------------------------
% 142.81/21.45 (1) ~ (all_44_2 = e2) | ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 &
% 142.81/21.45 op(e3, e2) = all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 =
% 142.81/21.45 e0) & op(e3, e2) = all_44_1 & $i(all_44_1))
% 142.81/21.45 (2) all_44_2 = e2
% 142.81/21.45 (3) ( ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) = all_36_1
% 142.81/21.45 & $i(all_36_0) & $i(all_36_1)) | ( ~ (all_36_1 = e1) & op(e3, e2) =
% 142.81/21.45 all_36_1 & $i(all_36_1))
% 142.81/21.45 (4) op(e3, e2) = e1
% 142.81/21.45 (5) op(e1, e3) = e0
% 142.81/21.45 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.45 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.45
% 142.81/21.45 Begin of proof
% 142.81/21.45 |
% 142.81/21.45 | BETA: splitting (1) gives:
% 142.81/21.45 |
% 142.81/21.45 | Case 1:
% 142.81/21.45 | |
% 142.81/21.45 | | (7) ~ (all_44_2 = e2)
% 142.81/21.45 | |
% 142.81/21.45 | | REDUCE: (2), (7) imply:
% 142.81/21.45 | | (8) $false
% 142.81/21.45 | |
% 142.81/21.45 | | CLOSE: (8) is inconsistent.
% 142.81/21.45 | |
% 142.81/21.45 | Case 2:
% 142.81/21.45 | |
% 142.81/21.45 | | (9) ( ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 142.81/21.45 | | all_44_1 & $i(all_44_0) & $i(all_44_1)) | ( ~ (all_44_1 = e0) &
% 142.81/21.45 | | op(e3, e2) = all_44_1 & $i(all_44_1))
% 142.81/21.45 | |
% 142.81/21.45 | | BETA: splitting (9) gives:
% 142.81/21.45 | |
% 142.81/21.45 | | Case 1:
% 142.81/21.45 | | |
% 142.81/21.45 | | | (10) ~ (all_44_0 = e1) & op(all_44_1, e3) = all_44_0 & op(e3, e2) =
% 142.81/21.45 | | | all_44_1 & $i(all_44_0) & $i(all_44_1)
% 142.81/21.45 | | |
% 142.81/21.45 | | | ALPHA: (10) implies:
% 142.81/21.45 | | | (11) op(e3, e2) = all_44_1
% 142.81/21.45 | | | (12) op(all_44_1, e3) = all_44_0
% 142.81/21.45 | | |
% 142.81/21.45 | | | BETA: splitting (3) gives:
% 142.81/21.45 | | |
% 142.81/21.45 | | | Case 1:
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | (13) ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 142.81/21.45 | | | | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | ALPHA: (13) implies:
% 142.81/21.45 | | | | (14) ~ (all_36_0 = e0)
% 142.81/21.45 | | | | (15) op(e3, e2) = all_36_1
% 142.81/21.45 | | | | (16) op(all_36_1, e3) = all_36_0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | GROUND_INST: instantiating (6) with e1, all_44_1, e2, e3, simplifying
% 142.81/21.45 | | | | with (4), (11) gives:
% 142.81/21.45 | | | | (17) all_44_1 = e1
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | GROUND_INST: instantiating (6) with all_36_1, all_44_1, e2, e3,
% 142.81/21.45 | | | | simplifying with (11), (15) gives:
% 142.81/21.45 | | | | (18) all_44_1 = all_36_1
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | COMBINE_EQS: (17), (18) imply:
% 142.81/21.45 | | | | (19) all_36_1 = e1
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | SIMP: (19) implies:
% 142.81/21.45 | | | | (20) all_36_1 = e1
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | REDUCE: (12), (17) imply:
% 142.81/21.45 | | | | (21) op(e1, e3) = all_44_0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | REDUCE: (16), (20) imply:
% 142.81/21.45 | | | | (22) op(e1, e3) = all_36_0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | GROUND_INST: instantiating (6) with e0, all_44_0, e3, e1, simplifying
% 142.81/21.45 | | | | with (5), (21) gives:
% 142.81/21.45 | | | | (23) all_44_0 = e0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | GROUND_INST: instantiating (6) with all_36_0, all_44_0, e3, e1,
% 142.81/21.45 | | | | simplifying with (21), (22) gives:
% 142.81/21.45 | | | | (24) all_44_0 = all_36_0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | COMBINE_EQS: (23), (24) imply:
% 142.81/21.45 | | | | (25) all_36_0 = e0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | SIMP: (25) implies:
% 142.81/21.45 | | | | (26) all_36_0 = e0
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | REDUCE: (14), (26) imply:
% 142.81/21.45 | | | | (27) $false
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | CLOSE: (27) is inconsistent.
% 142.81/21.45 | | | |
% 142.81/21.45 | | | Case 2:
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | (28) ~ (all_36_1 = e1) & op(e3, e2) = all_36_1 & $i(all_36_1)
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | ALPHA: (28) implies:
% 142.81/21.45 | | | | (29) ~ (all_36_1 = e1)
% 142.81/21.45 | | | | (30) op(e3, e2) = all_36_1
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | REF_CLOSE: (4), (6), (11), (29), (30) are inconsistent by sub-proof
% 142.81/21.45 | | | | #869.
% 142.81/21.45 | | | |
% 142.81/21.45 | | | End of split
% 142.81/21.45 | | |
% 142.81/21.45 | | Case 2:
% 142.81/21.45 | | |
% 142.81/21.45 | | | (31) ~ (all_44_1 = e0) & op(e3, e2) = all_44_1 & $i(all_44_1)
% 142.81/21.45 | | |
% 142.81/21.45 | | | ALPHA: (31) implies:
% 142.81/21.45 | | | (32) op(e3, e2) = all_44_1
% 142.81/21.45 | | |
% 142.81/21.45 | | | BETA: splitting (3) gives:
% 142.81/21.45 | | |
% 142.81/21.45 | | | Case 1:
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | (33) ~ (all_36_0 = e0) & op(all_36_1, e3) = all_36_0 & op(e3, e2) =
% 142.81/21.45 | | | | all_36_1 & $i(all_36_0) & $i(all_36_1)
% 142.81/21.45 | | | |
% 142.81/21.45 | | | | ALPHA: (33) implies:
% 142.81/21.45 | | | | (34) ~ (all_36_0 = e0)
% 142.81/21.46 | | | | (35) op(e3, e2) = all_36_1
% 142.81/21.46 | | | | (36) op(all_36_1, e3) = all_36_0
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | GROUND_INST: instantiating (6) with e1, all_44_1, e2, e3, simplifying
% 142.81/21.46 | | | | with (4), (32) gives:
% 142.81/21.46 | | | | (37) all_44_1 = e1
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | GROUND_INST: instantiating (6) with all_36_1, all_44_1, e2, e3,
% 142.81/21.46 | | | | simplifying with (32), (35) gives:
% 142.81/21.46 | | | | (38) all_44_1 = all_36_1
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | COMBINE_EQS: (37), (38) imply:
% 142.81/21.46 | | | | (39) all_36_1 = e1
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | SIMP: (39) implies:
% 142.81/21.46 | | | | (40) all_36_1 = e1
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REDUCE: (36), (40) imply:
% 142.81/21.46 | | | | (41) op(e1, e3) = all_36_0
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | GROUND_INST: instantiating (6) with e0, all_36_0, e3, e1, simplifying
% 142.81/21.46 | | | | with (5), (41) gives:
% 142.81/21.46 | | | | (42) all_36_0 = e0
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REDUCE: (34), (42) imply:
% 142.81/21.46 | | | | (43) $false
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | CLOSE: (43) is inconsistent.
% 142.81/21.46 | | | |
% 142.81/21.46 | | | Case 2:
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | (44) ~ (all_36_1 = e1) & op(e3, e2) = all_36_1 & $i(all_36_1)
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | ALPHA: (44) implies:
% 142.81/21.46 | | | | (45) ~ (all_36_1 = e1)
% 142.81/21.46 | | | | (46) op(e3, e2) = all_36_1
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REF_CLOSE: (4), (6), (32), (45), (46) are inconsistent by sub-proof
% 142.81/21.46 | | | | #869.
% 142.81/21.46 | | | |
% 142.81/21.46 | | | End of split
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #869 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) op(e3, e2) = all_44_1
% 142.81/21.46 (2) ~ (all_36_1 = e1)
% 142.81/21.46 (3) op(e3, e2) = e1
% 142.81/21.46 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (5) op(e3, e2) = all_36_1
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | GROUND_INST: instantiating (4) with e1, all_44_1, e2, e3, simplifying with
% 142.81/21.46 | (1), (3) gives:
% 142.81/21.46 | (6) all_44_1 = e1
% 142.81/21.46 |
% 142.81/21.46 | GROUND_INST: instantiating (4) with all_36_1, all_44_1, e2, e3, simplifying
% 142.81/21.46 | with (1), (5) gives:
% 142.81/21.46 | (7) all_44_1 = all_36_1
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (6), (7) imply:
% 142.81/21.46 | (8) all_36_1 = e1
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (8) implies:
% 142.81/21.46 | (9) all_36_1 = e1
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (2), (9) imply:
% 142.81/21.46 | (10) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (10) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #870 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_14 = e0
% 142.81/21.46 (2) ~ (e2 = e1)
% 142.81/21.46 (3) all_57_5 = e1
% 142.81/21.46 (4) all_57_4 = e3
% 142.81/21.46 (5) ~ (e2 = e0)
% 142.81/21.46 (6) ~ (e3 = e2)
% 142.81/21.46 (7) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.46 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.46 (8) all_57_8 = e1
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (7) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (9) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2)
% 142.81/21.46 | |
% 142.81/21.46 | | BETA: splitting (9) gives:
% 142.81/21.46 | |
% 142.81/21.46 | | Case 1:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (10) all_57_4 = e2 & op(e3, e1) = e2
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (4), (6), (10) are inconsistent by sub-proof #1043.
% 142.81/21.46 | | |
% 142.81/21.46 | | Case 2:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (11) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (2), (3), (11) are inconsistent by sub-proof #1012.
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (12) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.81/21.46 | | e2)
% 142.81/21.46 | |
% 142.81/21.46 | | BETA: splitting (12) gives:
% 142.81/21.46 | |
% 142.81/21.46 | | Case 1:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (13) all_57_8 = e2 & op(e1, e1) = e2
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (2), (8), (13) are inconsistent by sub-proof #871.
% 142.81/21.46 | | |
% 142.81/21.46 | | Case 2:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (14) all_57_14 = e2 & op(e0, e1) = e2
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (1), (5), (14) are inconsistent by sub-proof #932.
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #871 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_8 = e2 & op(e1, e1) = e2
% 142.81/21.46 (2) all_57_8 = e1
% 142.81/21.46 (3) ~ (e2 = e1)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | ALPHA: (1) implies:
% 142.81/21.46 | (4) all_57_8 = e2
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.46 | (5) e2 = e1
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (5) implies:
% 142.81/21.46 | (6) e2 = e1
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (3), (6) imply:
% 142.81/21.46 | (7) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (7) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #872 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_7 = e2
% 142.81/21.46 (2) all_57_7 = e1
% 142.81/21.46 (3) ~ (e2 = e1)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.46 | (4) e2 = e1
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (4) implies:
% 142.81/21.46 | (5) e2 = e1
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (3), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #873 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_6 = e3
% 142.81/21.46 (2) all_57_6 = e0
% 142.81/21.46 (3) ~ (e3 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.46 | (4) e3 = e0
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (4) implies:
% 142.81/21.46 | (5) e3 = e0
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (3), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #874 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.46 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.46 (2) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.46 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.46 (3) ~ (e2 = e1)
% 142.81/21.46 (4) op(e2, e1) = e2
% 142.81/21.46 (5) ~ (all_52_7 = e0)
% 142.81/21.46 (6) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.46 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.46 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.46 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.46 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.81/21.46 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 142.81/21.46 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 142.81/21.46 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 142.81/21.46 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 142.81/21.46 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 142.81/21.46 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 142.81/21.46 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.46 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 142.81/21.46 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 142.81/21.46 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.81/21.46 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 142.81/21.46 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 142.81/21.46 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 142.81/21.46 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 142.81/21.46 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.46 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.46 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.46 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.46 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.46 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.46 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.46 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.46 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 142.81/21.46 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 142.81/21.46 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 142.81/21.46 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.81/21.46 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.46 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.81/21.46 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 142.81/21.46 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.81/21.46 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.81/21.46 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.46 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.46 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.81/21.46 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.46 (7) op(e3, e3) = e2
% 142.81/21.46 (8) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.46 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.46 (9) ~ (e3 = e0)
% 142.81/21.46 (10) op(e1, e1) = all_4_2
% 142.81/21.46 (11) all_57_6 = e2 & op(e1, e3) = e2
% 142.81/21.46 (12) ~ (all_4_2 = e3)
% 142.81/21.46 (13) ~ (e1 = e0)
% 142.81/21.46 (14) ~ (e2 = e0)
% 142.81/21.46 (15) ~ (e3 = e2)
% 142.81/21.46 (16) op(e0, e0) = e2
% 142.81/21.46 (17) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (18) all_57_5 = e2
% 142.81/21.46 (19) ~ (all_52_13 = e2)
% 142.81/21.46 (20) ~ (e3 = e1)
% 142.81/21.46 (21) op(e0, e2) = all_52_7
% 142.81/21.46 (22) op(e2, e2) = e0
% 142.81/21.46 (23) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.46 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.46 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.46 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.46 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.46 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.46 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.46 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.46 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.46 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.46 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.46 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.46 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.46 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.46 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.46 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.46 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.46 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.46 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.46 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.46 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.46 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.46 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.46 $i(all_56_14))))
% 142.81/21.46 (24) op(e2, e0) = all_52_13
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | ALPHA: (11) implies:
% 142.81/21.46 | (25) all_57_6 = e2
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (8) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (26) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) =
% 142.81/21.46 | | e0)
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (1), (2), (3), (7), (9), (13), (14), (15), (17), (18), (20),
% 142.81/21.46 | | (22), (26) are inconsistent by sub-proof #875.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (27) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) =
% 142.81/21.46 | | e0)
% 142.81/21.46 | |
% 142.81/21.46 | | BETA: splitting (27) gives:
% 142.81/21.46 | |
% 142.81/21.46 | | Case 1:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (28) all_57_6 = e0 & op(e1, e3) = e0
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (14), (25), (28) are inconsistent by sub-proof #994.
% 142.81/21.46 | | |
% 142.81/21.46 | | Case 2:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (29) all_57_12 = e0 & op(e0, e3) = e0
% 142.81/21.46 | | |
% 142.81/21.46 | | | ALPHA: (29) implies:
% 142.81/21.46 | | | (30) op(e0, e3) = e0
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (3), (4), (5), (6), (9), (10), (12), (13), (15), (16), (17),
% 142.81/21.46 | | | (19), (21), (22), (23), (24), (30) are inconsistent by
% 142.81/21.46 | | | sub-proof #945.
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #875 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.46 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.46 (2) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0)
% 142.81/21.46 (3) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.46 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.46 (4) ~ (e2 = e1)
% 142.81/21.46 (5) op(e3, e3) = e2
% 142.81/21.46 (6) ~ (e3 = e0)
% 142.81/21.46 (7) ~ (e1 = e0)
% 142.81/21.46 (8) ~ (e2 = e0)
% 142.81/21.46 (9) ~ (e3 = e2)
% 142.81/21.46 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (11) all_57_5 = e2
% 142.81/21.46 (12) ~ (e3 = e1)
% 142.81/21.46 (13) op(e2, e2) = e0
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (2) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (14) all_57_0 = e0 & op(e3, e3) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (14) implies:
% 142.81/21.46 | | (15) op(e3, e3) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (5), (8), (10), (15) are inconsistent by sub-proof #880.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (16) all_57_2 = e0 & op(e2, e3) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (16) implies:
% 142.81/21.46 | | (17) all_57_2 = e0
% 142.81/21.46 | |
% 142.81/21.46 | | BETA: splitting (1) gives:
% 142.81/21.46 | |
% 142.81/21.46 | | Case 1:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (18) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) =
% 142.81/21.46 | | | e3)
% 142.81/21.46 | | |
% 142.81/21.46 | | | BETA: splitting (18) gives:
% 142.81/21.46 | | |
% 142.81/21.46 | | | Case 1:
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | (19) all_57_2 = e3 & op(e2, e3) = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | ALPHA: (19) implies:
% 142.81/21.46 | | | | (20) all_57_2 = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REF_CLOSE: (6), (17), (20) are inconsistent by sub-proof #879.
% 142.81/21.46 | | | |
% 142.81/21.46 | | | Case 2:
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | (21) all_57_3 = e3 & op(e2, e2) = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | ALPHA: (21) implies:
% 142.81/21.46 | | | | (22) op(e2, e2) = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REF_CLOSE: (6), (10), (13), (22) are inconsistent by sub-proof #1119.
% 142.81/21.46 | | | |
% 142.81/21.46 | | | End of split
% 142.81/21.46 | | |
% 142.81/21.46 | | Case 2:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (23) (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) =
% 142.81/21.46 | | | e3)
% 142.81/21.46 | | |
% 142.81/21.46 | | | BETA: splitting (23) gives:
% 142.81/21.46 | | |
% 142.81/21.46 | | | Case 1:
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | (24) all_57_5 = e3 & op(e2, e1) = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | ALPHA: (24) implies:
% 142.81/21.46 | | | | (25) all_57_5 = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REF_CLOSE: (9), (11), (25) are inconsistent by sub-proof #936.
% 142.81/21.46 | | | |
% 142.81/21.46 | | | Case 2:
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | (26) all_57_10 = e3 & op(e2, e0) = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | ALPHA: (26) implies:
% 142.81/21.46 | | | | (27) all_57_10 = e3
% 142.81/21.46 | | | |
% 142.81/21.46 | | | | REF_CLOSE: (3), (4), (7), (10), (11), (12), (13), (17), (27) are
% 142.81/21.46 | | | | inconsistent by sub-proof #876.
% 142.81/21.46 | | | |
% 142.81/21.46 | | | End of split
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #876 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.46 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.46 (2) ~ (e2 = e1)
% 142.81/21.46 (3) ~ (e1 = e0)
% 142.81/21.46 (4) all_57_10 = e3
% 142.81/21.46 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (6) all_57_5 = e2
% 142.81/21.46 (7) ~ (e3 = e1)
% 142.81/21.46 (8) op(e2, e2) = e0
% 142.81/21.46 (9) all_57_2 = e0
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (1) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (10) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) =
% 142.81/21.46 | | e1)
% 142.81/21.46 | |
% 142.81/21.46 | | BETA: splitting (10) gives:
% 142.81/21.46 | |
% 142.81/21.46 | | Case 1:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (11) all_57_2 = e1 & op(e2, e3) = e1
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (3), (9), (11) are inconsistent by sub-proof #878.
% 142.81/21.46 | | |
% 142.81/21.46 | | Case 2:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (12) all_57_3 = e1 & op(e2, e2) = e1
% 142.81/21.46 | | |
% 142.81/21.46 | | | ALPHA: (12) implies:
% 142.81/21.46 | | | (13) op(e2, e2) = e1
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (3), (5), (8), (13) are inconsistent by sub-proof #1117.
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (14) (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) =
% 142.81/21.46 | | e1)
% 142.81/21.46 | |
% 142.81/21.46 | | BETA: splitting (14) gives:
% 142.81/21.46 | |
% 142.81/21.46 | | Case 1:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (15) all_57_5 = e1 & op(e2, e1) = e1
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (2), (6), (15) are inconsistent by sub-proof #938.
% 142.81/21.46 | | |
% 142.81/21.46 | | Case 2:
% 142.81/21.46 | | |
% 142.81/21.46 | | | (16) all_57_10 = e1 & op(e2, e0) = e1
% 142.81/21.46 | | |
% 142.81/21.46 | | | ALPHA: (16) implies:
% 142.81/21.46 | | | (17) all_57_10 = e1
% 142.81/21.46 | | |
% 142.81/21.46 | | | REF_CLOSE: (4), (7), (17) are inconsistent by sub-proof #877.
% 142.81/21.46 | | |
% 142.81/21.46 | | End of split
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #877 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_10 = e3
% 142.81/21.46 (2) all_57_10 = e1
% 142.81/21.46 (3) ~ (e3 = e1)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.46 | (4) e3 = e1
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (4) implies:
% 142.81/21.46 | (5) e3 = e1
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (3), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #878 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_2 = e1 & op(e2, e3) = e1
% 142.81/21.46 (2) all_57_2 = e0
% 142.81/21.46 (3) ~ (e1 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | ALPHA: (1) implies:
% 142.81/21.46 | (4) all_57_2 = e1
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.46 | (5) e1 = e0
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (5) implies:
% 142.81/21.46 | (6) e1 = e0
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (3), (6) imply:
% 142.81/21.46 | (7) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (7) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #879 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_2 = e3
% 142.81/21.46 (2) all_57_2 = e0
% 142.81/21.46 (3) ~ (e3 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.46 | (4) e3 = e0
% 142.81/21.46 |
% 142.81/21.46 | SIMP: (4) implies:
% 142.81/21.46 | (5) e3 = e0
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (3), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #880 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (2) op(e3, e3) = e2
% 142.81/21.46 (3) op(e3, e3) = e0
% 142.81/21.46 (4) ~ (e2 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | GROUND_INST: instantiating (1) with e0, e2, e3, e3, simplifying with (2), (3)
% 142.81/21.46 | gives:
% 142.81/21.46 | (5) e2 = e0
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (4), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #881 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) ~ (all_52_1 = e2)
% 142.81/21.46 (2) op(e2, e3) = all_52_1
% 142.81/21.46 (3) ~ (e2 = e0)
% 142.81/21.46 (4) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2)
% 142.81/21.46 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (6) op(e2, e2) = e0
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (4) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (7) all_57_2 = e2 & op(e2, e3) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (7) implies:
% 142.81/21.46 | | (8) op(e2, e3) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (1), (2), (5), (8) are inconsistent by sub-proof #882.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (9) all_57_3 = e2 & op(e2, e2) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (9) implies:
% 142.81/21.46 | | (10) op(e2, e2) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (3), (5), (6), (10) are inconsistent by sub-proof #1076.
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #882 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (2) op(e2, e3) = all_52_1
% 142.81/21.46 (3) op(e2, e3) = e2
% 142.81/21.46 (4) ~ (all_52_1 = e2)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | GROUND_INST: instantiating (1) with all_52_1, e2, e3, e2, simplifying with
% 142.81/21.46 | (2), (3) gives:
% 142.81/21.46 | (5) all_52_1 = e2
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (4), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #883 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) ~ (all_14_2 = e2)
% 142.81/21.46 (2) all_54_0 = e2 | all_54_0 = e1 | all_54_0 = e0
% 142.81/21.46 (3) all_54_0 = all_14_2
% 142.81/21.46 (4) ~ (all_14_2 = e1)
% 142.81/21.46 (5) ~ (all_14_2 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (2) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (6) all_54_0 = e2
% 142.81/21.46 | |
% 142.81/21.46 | | COMBINE_EQS: (3), (6) imply:
% 142.81/21.46 | | (7) all_14_2 = e2
% 142.81/21.46 | |
% 142.81/21.46 | | SIMP: (7) implies:
% 142.81/21.46 | | (8) all_14_2 = e2
% 142.81/21.46 | |
% 142.81/21.46 | | REDUCE: (1), (8) imply:
% 142.81/21.46 | | (9) $false
% 142.81/21.46 | |
% 142.81/21.46 | | CLOSE: (9) is inconsistent.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (10) all_54_0 = e1 | all_54_0 = e0
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #884.
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #884 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_54_0 = e1 | all_54_0 = e0
% 142.81/21.46 (2) all_54_0 = all_14_2
% 142.81/21.46 (3) ~ (all_14_2 = e1)
% 142.81/21.46 (4) ~ (all_14_2 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (1) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (5) all_54_0 = e1
% 142.81/21.46 | |
% 142.81/21.46 | | COMBINE_EQS: (2), (5) imply:
% 142.81/21.46 | | (6) all_14_2 = e1
% 142.81/21.46 | |
% 142.81/21.46 | | SIMP: (6) implies:
% 142.81/21.46 | | (7) all_14_2 = e1
% 142.81/21.46 | |
% 142.81/21.46 | | REDUCE: (3), (7) imply:
% 142.81/21.46 | | (8) $false
% 142.81/21.46 | |
% 142.81/21.46 | | CLOSE: (8) is inconsistent.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (9) all_54_0 = e0
% 142.81/21.46 | |
% 142.81/21.46 | | COMBINE_EQS: (2), (9) imply:
% 142.81/21.46 | | (10) all_14_2 = e0
% 142.81/21.46 | |
% 142.81/21.46 | | SIMP: (10) implies:
% 142.81/21.46 | | (11) all_14_2 = e0
% 142.81/21.46 | |
% 142.81/21.46 | | REDUCE: (4), (11) imply:
% 142.81/21.46 | | (12) $false
% 142.81/21.46 | |
% 142.81/21.46 | | CLOSE: (12) is inconsistent.
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #885 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) (all_57_13 = e0 & op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.46 (2) ~ (all_52_7 = e0)
% 142.81/21.46 (3) ~ (all_52_11 = e0)
% 142.81/21.46 (4) op(e0, e1) = all_52_11
% 142.81/21.46 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (6) op(e0, e2) = all_52_7
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (1) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (7) all_57_13 = e0 & op(e0, e2) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (7) implies:
% 142.81/21.46 | | (8) op(e0, e2) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (2), (5), (6), (8) are inconsistent by sub-proof #977.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (9) all_57_14 = e0 & op(e0, e1) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (9) implies:
% 142.81/21.46 | | (10) op(e0, e1) = e0
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (3), (4), (5), (10) are inconsistent by sub-proof #886.
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #886 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (2) op(e0, e1) = all_52_11
% 142.81/21.46 (3) op(e0, e1) = e0
% 142.81/21.46 (4) ~ (all_52_11 = e0)
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | GROUND_INST: instantiating (1) with all_52_11, e0, e1, e0, simplifying with
% 142.81/21.46 | (2), (3) gives:
% 142.81/21.46 | (5) all_52_11 = e0
% 142.81/21.46 |
% 142.81/21.46 | REDUCE: (4), (5) imply:
% 142.81/21.46 | (6) $false
% 142.81/21.46 |
% 142.81/21.46 | CLOSE: (6) is inconsistent.
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #887 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.46 (2) ~ (all_52_9 = e2)
% 142.81/21.46 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46 (4) ~ (all_52_13 = e2)
% 142.81/21.46 (5) op(e2, e1) = all_52_9
% 142.81/21.46 (6) op(e2, e0) = all_52_13
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (1) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (7) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (7) implies:
% 142.81/21.46 | | (8) op(e2, e1) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (2), (3), (5), (8) are inconsistent by sub-proof #890.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (9) all_57_10 = e2 & op(e2, e0) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (9) implies:
% 142.81/21.46 | | (10) op(e2, e0) = e2
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (3), (4), (6), (10) are inconsistent by sub-proof #1030.
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #888 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) ~ (e2 = e1)
% 142.81/21.46 (2) all_57_14 = e2
% 142.81/21.46 (3) (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.46 (4) op(e0, e0) = e2
% 142.81/21.46 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.46 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.46
% 142.81/21.46 Begin of proof
% 142.81/21.46 |
% 142.81/21.46 | BETA: splitting (3) gives:
% 142.81/21.46 |
% 142.81/21.46 | Case 1:
% 142.81/21.46 | |
% 142.81/21.46 | | (6) all_57_14 = e1 & op(e0, e1) = e1
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (6) implies:
% 142.81/21.46 | | (7) all_57_14 = e1
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (1), (2), (7) are inconsistent by sub-proof #1048.
% 142.81/21.46 | |
% 142.81/21.46 | Case 2:
% 142.81/21.46 | |
% 142.81/21.46 | | (8) all_57_15 = e1 & op(e0, e0) = e1
% 142.81/21.46 | |
% 142.81/21.46 | | ALPHA: (8) implies:
% 142.81/21.46 | | (9) op(e0, e0) = e1
% 142.81/21.46 | |
% 142.81/21.46 | | REF_CLOSE: (1), (4), (5), (9) are inconsistent by sub-proof #1070.
% 142.81/21.46 | |
% 142.81/21.46 | End of split
% 142.81/21.46 |
% 142.81/21.46 End of proof
% 142.81/21.46
% 142.81/21.46 Sub-proof #889 shows that the following formulas are inconsistent:
% 142.81/21.46 ----------------------------------------------------------------
% 142.81/21.46 (1) all_57_14 = e2
% 142.81/21.46 (2) (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.46 (3) ~ (e3 = e2)
% 142.81/21.46 (4) op(e0, e0) = e2
% 142.81/21.47 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | BETA: splitting (2) gives:
% 142.81/21.47 |
% 142.81/21.47 | Case 1:
% 142.81/21.47 | |
% 142.81/21.47 | | (6) all_57_14 = e3 & op(e0, e1) = e3
% 142.81/21.47 | |
% 142.81/21.47 | | ALPHA: (6) implies:
% 142.81/21.47 | | (7) all_57_14 = e3
% 142.81/21.47 | |
% 142.81/21.47 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #1011.
% 142.81/21.47 | |
% 142.81/21.47 | Case 2:
% 142.81/21.47 | |
% 142.81/21.47 | | (8) all_57_15 = e3 & op(e0, e0) = e3
% 142.81/21.47 | |
% 142.81/21.47 | | ALPHA: (8) implies:
% 142.81/21.47 | | (9) op(e0, e0) = e3
% 142.81/21.47 | |
% 142.81/21.47 | | REF_CLOSE: (3), (4), (5), (9) are inconsistent by sub-proof #1066.
% 142.81/21.47 | |
% 142.81/21.47 | End of split
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #890 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (2) op(e2, e1) = all_52_9
% 142.81/21.47 (3) op(e2, e1) = e2
% 142.81/21.47 (4) ~ (all_52_9 = e2)
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | GROUND_INST: instantiating (1) with all_52_9, e2, e1, e2, simplifying with
% 142.81/21.47 | (2), (3) gives:
% 142.81/21.47 | (5) all_52_9 = e2
% 142.81/21.47 |
% 142.81/21.47 | REDUCE: (4), (5) imply:
% 142.81/21.47 | (6) $false
% 142.81/21.47 |
% 142.81/21.47 | CLOSE: (6) is inconsistent.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #891 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) all_57_4 = e1 & op(e3, e1) = e1
% 142.81/21.47 (2) all_57_4 = e2
% 142.81/21.47 (3) ~ (e2 = e1)
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | ALPHA: (1) implies:
% 142.81/21.47 | (4) all_57_4 = e1
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.47 | (5) e2 = e1
% 142.81/21.47 |
% 142.81/21.47 | REDUCE: (3), (5) imply:
% 142.81/21.47 | (6) $false
% 142.81/21.47 |
% 142.81/21.47 | CLOSE: (6) is inconsistent.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #892 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) ~ (all_52_12 = e3)
% 142.81/21.47 (2) ~ (all_52_8 = e3)
% 142.81/21.47 (3) all_57_12 = e3
% 142.81/21.47 (4) ~ (e3 = e0)
% 142.81/21.47 (5) ~ (all_52_4 = e3)
% 142.81/21.47 (6) op(e3, e1) = all_52_8
% 142.81/21.47 (7) op(e3, e2) = all_52_4
% 142.81/21.47 (8) all_57_0 = e3
% 142.81/21.47 (9) op(e3, e0) = all_52_12
% 142.81/21.47 (10) all_57_12 = e0
% 142.81/21.47 (11) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (12) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.47 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (3), (10) imply:
% 142.81/21.47 | (13) e3 = e0
% 142.81/21.47 |
% 142.81/21.47 | SIMP: (13) implies:
% 142.81/21.47 | (14) e3 = e0
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (8), (14) imply:
% 142.81/21.47 | (15) all_57_0 = e0
% 142.81/21.47 |
% 142.81/21.47 | REF_CLOSE: (1), (2), (4), (5), (6), (7), (9), (11), (12), (15) are
% 142.81/21.47 | inconsistent by sub-proof #1103.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #893 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) ~ (all_50_2 = e0) | ( ~ (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 &
% 142.81/21.47 op(e1, e0) = all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 =
% 142.81/21.47 e3) & op(e1, e0) = all_50_1 & $i(all_50_1))
% 142.81/21.47 (2) op(e3, e1) = e2
% 142.81/21.47 (3) op(e3, e1) = all_52_8
% 142.81/21.47 (4) op(e1, e0) = e3
% 142.81/21.47 (5) all_50_2 = e0
% 142.81/21.47 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (7) op(e1, e0) = all_52_14
% 142.81/21.47 (8) ( ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) = all_48_1
% 142.81/21.47 & $i(all_48_0) & $i(all_48_1)) | ( ~ (all_48_1 = e2) & op(e1, e0) =
% 142.81/21.47 all_48_1 & $i(all_48_1))
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | GROUND_INST: instantiating (6) with all_52_14, e3, e0, e1, simplifying with
% 142.81/21.47 | (4), (7) gives:
% 142.81/21.47 | (9) all_52_14 = e3
% 142.81/21.47 |
% 142.81/21.47 | GROUND_INST: instantiating (6) with all_52_8, e2, e1, e3, simplifying with
% 142.81/21.47 | (2), (3) gives:
% 142.81/21.47 | (10) all_52_8 = e2
% 142.81/21.47 |
% 142.81/21.47 | BETA: splitting (1) gives:
% 142.81/21.47 |
% 142.81/21.47 | Case 1:
% 142.81/21.47 | |
% 142.81/21.47 | | (11) ~ (all_50_2 = e0)
% 142.81/21.47 | |
% 142.81/21.47 | | REDUCE: (5), (11) imply:
% 142.81/21.47 | | (12) $false
% 142.81/21.47 | |
% 142.81/21.47 | | CLOSE: (12) is inconsistent.
% 142.81/21.47 | |
% 142.81/21.47 | Case 2:
% 142.81/21.47 | |
% 142.81/21.47 | | (13) ( ~ (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 & op(e1, e0) =
% 142.81/21.47 | | all_50_1 & $i(all_50_0) & $i(all_50_1)) | ( ~ (all_50_1 = e3) &
% 142.81/21.47 | | op(e1, e0) = all_50_1 & $i(all_50_1))
% 142.81/21.47 | |
% 142.81/21.47 | | BETA: splitting (13) gives:
% 142.81/21.47 | |
% 142.81/21.47 | | Case 1:
% 142.81/21.47 | | |
% 142.81/21.47 | | | (14) ~ (all_50_0 = e2) & op(all_50_1, e1) = all_50_0 & op(e1, e0) =
% 142.81/21.47 | | | all_50_1 & $i(all_50_0) & $i(all_50_1)
% 142.81/21.47 | | |
% 142.81/21.47 | | | ALPHA: (14) implies:
% 142.81/21.47 | | | (15) ~ (all_50_0 = e2)
% 142.81/21.47 | | | (16) op(e1, e0) = all_50_1
% 142.81/21.47 | | | (17) op(all_50_1, e1) = all_50_0
% 142.81/21.47 | | |
% 142.81/21.47 | | | BETA: splitting (8) gives:
% 142.81/21.47 | | |
% 142.81/21.47 | | | Case 1:
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | (18) ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 142.81/21.47 | | | | all_48_1 & $i(all_48_0) & $i(all_48_1)
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | ALPHA: (18) implies:
% 142.81/21.47 | | | | (19) op(e1, e0) = all_48_1
% 142.81/21.47 | | | | (20) op(all_48_1, e1) = all_48_0
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with e3, all_50_1, e0, e1, simplifying
% 142.81/21.47 | | | | with (4), (16) gives:
% 142.81/21.47 | | | | (21) all_50_1 = e3
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with all_48_1, all_50_1, e0, e1,
% 142.81/21.47 | | | | simplifying with (16), (19) gives:
% 142.81/21.47 | | | | (22) all_50_1 = all_48_1
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | COMBINE_EQS: (21), (22) imply:
% 142.81/21.47 | | | | (23) all_48_1 = e3
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REDUCE: (17), (21) imply:
% 142.81/21.47 | | | | (24) op(e3, e1) = all_50_0
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REDUCE: (20), (23) imply:
% 142.81/21.47 | | | | (25) op(e3, e1) = all_48_0
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with e2, all_50_0, e1, e3, simplifying
% 142.81/21.47 | | | | with (2), (24) gives:
% 142.81/21.47 | | | | (26) all_50_0 = e2
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with all_48_0, all_50_0, e1, e3,
% 142.81/21.47 | | | | simplifying with (24), (25) gives:
% 142.81/21.47 | | | | (27) all_50_0 = all_48_0
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | COMBINE_EQS: (26), (27) imply:
% 142.81/21.47 | | | | (28) all_48_0 = e2
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REDUCE: (15), (26) imply:
% 142.81/21.47 | | | | (29) $false
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | CLOSE: (29) is inconsistent.
% 142.81/21.47 | | | |
% 142.81/21.47 | | | Case 2:
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | (30) ~ (all_48_1 = e2) & op(e1, e0) = all_48_1 & $i(all_48_1)
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | ALPHA: (30) implies:
% 142.81/21.47 | | | | (31) op(e1, e0) = all_48_1
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with e3, all_50_1, e0, e1, simplifying
% 142.81/21.47 | | | | with (4), (16) gives:
% 142.81/21.47 | | | | (32) all_50_1 = e3
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with all_48_1, all_50_1, e0, e1,
% 142.81/21.47 | | | | simplifying with (16), (31) gives:
% 142.81/21.47 | | | | (33) all_50_1 = all_48_1
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | COMBINE_EQS: (32), (33) imply:
% 142.81/21.47 | | | | (34) all_48_1 = e3
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REDUCE: (17), (32) imply:
% 142.81/21.47 | | | | (35) op(e3, e1) = all_50_0
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | GROUND_INST: instantiating (6) with e2, all_50_0, e1, e3, simplifying
% 142.81/21.47 | | | | with (2), (35) gives:
% 142.81/21.47 | | | | (36) all_50_0 = e2
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REDUCE: (15), (36) imply:
% 142.81/21.47 | | | | (37) $false
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | CLOSE: (37) is inconsistent.
% 142.81/21.47 | | | |
% 142.81/21.47 | | | End of split
% 142.81/21.47 | | |
% 142.81/21.47 | | Case 2:
% 142.81/21.47 | | |
% 142.81/21.47 | | | (38) ~ (all_50_1 = e3) & op(e1, e0) = all_50_1 & $i(all_50_1)
% 142.81/21.47 | | |
% 142.81/21.47 | | | ALPHA: (38) implies:
% 142.81/21.47 | | | (39) ~ (all_50_1 = e3)
% 142.81/21.47 | | | (40) op(e1, e0) = all_50_1
% 142.81/21.47 | | |
% 142.81/21.47 | | | BETA: splitting (8) gives:
% 142.81/21.47 | | |
% 142.81/21.47 | | | Case 1:
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | (41) ~ (all_48_0 = e3) & op(all_48_1, e1) = all_48_0 & op(e1, e0) =
% 142.81/21.47 | | | | all_48_1 & $i(all_48_0) & $i(all_48_1)
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | ALPHA: (41) implies:
% 142.81/21.47 | | | | (42) op(e1, e0) = all_48_1
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REF_CLOSE: (4), (6), (39), (40), (42) are inconsistent by sub-proof
% 142.81/21.47 | | | | #894.
% 142.81/21.47 | | | |
% 142.81/21.47 | | | Case 2:
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | (43) ~ (all_48_1 = e2) & op(e1, e0) = all_48_1 & $i(all_48_1)
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | ALPHA: (43) implies:
% 142.81/21.47 | | | | (44) op(e1, e0) = all_48_1
% 142.81/21.47 | | | |
% 142.81/21.47 | | | | REF_CLOSE: (4), (6), (39), (40), (44) are inconsistent by sub-proof
% 142.81/21.47 | | | | #894.
% 142.81/21.47 | | | |
% 142.81/21.47 | | | End of split
% 142.81/21.47 | | |
% 142.81/21.47 | | End of split
% 142.81/21.47 | |
% 142.81/21.47 | End of split
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #894 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) op(e1, e0) = all_50_1
% 142.81/21.47 (2) op(e1, e0) = e3
% 142.81/21.47 (3) ~ (all_50_1 = e3)
% 142.81/21.47 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (5) op(e1, e0) = all_48_1
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | GROUND_INST: instantiating (4) with e3, all_50_1, e0, e1, simplifying with
% 142.81/21.47 | (1), (2) gives:
% 142.81/21.47 | (6) all_50_1 = e3
% 142.81/21.47 |
% 142.81/21.47 | GROUND_INST: instantiating (4) with all_48_1, all_50_1, e0, e1, simplifying
% 142.81/21.47 | with (1), (5) gives:
% 142.81/21.47 | (7) all_50_1 = all_48_1
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (6), (7) imply:
% 142.81/21.47 | (8) all_48_1 = e3
% 142.81/21.47 |
% 142.81/21.47 | REDUCE: (3), (6) imply:
% 142.81/21.47 | (9) $false
% 142.81/21.47 |
% 142.81/21.47 | CLOSE: (9) is inconsistent.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #895 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) ~ (all_52_8 = e3)
% 142.81/21.47 (2) ~ (e2 = e1)
% 142.81/21.47 (3) all_56_9 = e3
% 142.81/21.47 (4) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.47 (5) op(e3, e1) = all_52_8
% 142.81/21.47 (6) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) = e1) |
% 142.81/21.47 (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) = e1)
% 142.81/21.47 (7) ~ (e1 = e0)
% 142.81/21.47 (8) all_57_0 = e3
% 142.81/21.47 (9) all_57_12 = e0
% 142.81/21.47 (10) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (11) all_57_2 = e2
% 142.81/21.47 (12) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.81/21.47 all_56_9 & $i(all_56_9))
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | ALPHA: (4) implies:
% 142.81/21.47 | (13) all_57_6 = e3
% 142.81/21.47 |
% 142.81/21.47 | BETA: splitting (6) gives:
% 142.81/21.47 |
% 142.81/21.47 | Case 1:
% 142.81/21.47 | |
% 142.81/21.47 | | (14) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_2 = e1 & op(e2, e3) =
% 142.81/21.47 | | e1)
% 142.81/21.47 | |
% 142.81/21.47 | | BETA: splitting (14) gives:
% 142.81/21.47 | |
% 142.81/21.47 | | Case 1:
% 142.81/21.47 | | |
% 142.81/21.47 | | | (15) all_57_0 = e1 & op(e3, e3) = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | REF_CLOSE: (1), (3), (5), (8), (10), (12), (15) are inconsistent by
% 142.81/21.47 | | | sub-proof #897.
% 142.81/21.47 | | |
% 142.81/21.47 | | Case 2:
% 142.81/21.47 | | |
% 142.81/21.47 | | | (16) all_57_2 = e1 & op(e2, e3) = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | ALPHA: (16) implies:
% 142.81/21.47 | | | (17) all_57_2 = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | REF_CLOSE: (2), (11), (17) are inconsistent by sub-proof #943.
% 142.81/21.47 | | |
% 142.81/21.47 | | End of split
% 142.81/21.47 | |
% 142.81/21.47 | Case 2:
% 142.81/21.47 | |
% 142.81/21.47 | | (18) (all_57_6 = e1 & op(e1, e3) = e1) | (all_57_12 = e1 & op(e0, e3) =
% 142.81/21.47 | | e1)
% 142.81/21.47 | |
% 142.81/21.47 | | BETA: splitting (18) gives:
% 142.81/21.47 | |
% 142.81/21.47 | | Case 1:
% 142.81/21.47 | | |
% 142.81/21.47 | | | (19) all_57_6 = e1 & op(e1, e3) = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | ALPHA: (19) implies:
% 142.81/21.47 | | | (20) all_57_6 = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | COMBINE_EQS: (13), (20) imply:
% 142.81/21.47 | | | (21) e3 = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | SIMP: (21) implies:
% 142.81/21.47 | | | (22) e3 = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | COMBINE_EQS: (3), (22) imply:
% 142.81/21.47 | | | (23) all_56_9 = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | REF_CLOSE: (1), (5), (10), (12), (23) are inconsistent by sub-proof #898.
% 142.81/21.47 | | |
% 142.81/21.47 | | Case 2:
% 142.81/21.47 | | |
% 142.81/21.47 | | | (24) all_57_12 = e1 & op(e0, e3) = e1
% 142.81/21.47 | | |
% 142.81/21.47 | | | REF_CLOSE: (7), (9), (24) are inconsistent by sub-proof #896.
% 142.81/21.47 | | |
% 142.81/21.47 | | End of split
% 142.81/21.47 | |
% 142.81/21.47 | End of split
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #896 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) all_57_12 = e1 & op(e0, e3) = e1
% 142.81/21.47 (2) all_57_12 = e0
% 142.81/21.47 (3) ~ (e1 = e0)
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | ALPHA: (1) implies:
% 142.81/21.47 | (4) all_57_12 = e1
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.47 | (5) e1 = e0
% 142.81/21.47 |
% 142.81/21.47 | REDUCE: (3), (5) imply:
% 142.81/21.47 | (6) $false
% 142.81/21.47 |
% 142.81/21.47 | CLOSE: (6) is inconsistent.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #897 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) ~ (all_52_8 = e3)
% 142.81/21.47 (2) all_56_9 = e3
% 142.81/21.47 (3) all_57_0 = e1 & op(e3, e3) = e1
% 142.81/21.47 (4) op(e3, e1) = all_52_8
% 142.81/21.47 (5) all_57_0 = e3
% 142.81/21.47 (6) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (7) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.81/21.47 all_56_9 & $i(all_56_9))
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | ALPHA: (3) implies:
% 142.81/21.47 | (8) all_57_0 = e1
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (5), (8) imply:
% 142.81/21.47 | (9) e3 = e1
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (2), (9) imply:
% 142.81/21.47 | (10) all_56_9 = e1
% 142.81/21.47 |
% 142.81/21.47 | REF_CLOSE: (1), (4), (6), (7), (10) are inconsistent by sub-proof #898.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #898 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) all_56_9 = e1
% 142.81/21.47 (2) ~ (all_52_8 = e3)
% 142.81/21.47 (3) op(e3, e1) = all_52_8
% 142.81/21.47 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (5) (all_56_1 = e3 & op(e3, e1) = e3) | ( ~ (all_56_9 = e1) & op(e3, e3) =
% 142.81/21.47 all_56_9 & $i(all_56_9))
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | BETA: splitting (5) gives:
% 142.81/21.47 |
% 142.81/21.47 | Case 1:
% 142.81/21.47 | |
% 142.81/21.47 | | (6) all_56_1 = e3 & op(e3, e1) = e3
% 142.81/21.47 | |
% 142.81/21.47 | | ALPHA: (6) implies:
% 142.81/21.47 | | (7) op(e3, e1) = e3
% 142.81/21.47 | |
% 142.81/21.47 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1106.
% 142.81/21.47 | |
% 142.81/21.47 | Case 2:
% 142.81/21.47 | |
% 142.81/21.47 | | (8) ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)
% 142.81/21.47 | |
% 142.81/21.47 | | ALPHA: (8) implies:
% 142.81/21.47 | | (9) ~ (all_56_9 = e1)
% 142.81/21.47 | |
% 142.81/21.47 | | REDUCE: (1), (9) imply:
% 142.81/21.47 | | (10) $false
% 142.81/21.47 | |
% 142.81/21.47 | | CLOSE: (10) is inconsistent.
% 142.81/21.47 | |
% 142.81/21.47 | End of split
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #899 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) all_54_10 = all_4_2
% 142.81/21.47 (2) all_54_10 = e0
% 142.81/21.47 (3) ~ (all_4_2 = e0)
% 142.81/21.47
% 142.81/21.47 Begin of proof
% 142.81/21.47 |
% 142.81/21.47 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.47 | (4) all_4_2 = e0
% 142.81/21.47 |
% 142.81/21.47 | SIMP: (4) implies:
% 142.81/21.47 | (5) all_4_2 = e0
% 142.81/21.47 |
% 142.81/21.47 | REDUCE: (3), (5) imply:
% 142.81/21.47 | (6) $false
% 142.81/21.47 |
% 142.81/21.47 | CLOSE: (6) is inconsistent.
% 142.81/21.47 |
% 142.81/21.47 End of proof
% 142.81/21.47
% 142.81/21.47 Sub-proof #900 shows that the following formulas are inconsistent:
% 142.81/21.47 ----------------------------------------------------------------
% 142.81/21.47 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.81/21.47 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.81/21.47 (2) ~ (all_52_14 = e2)
% 142.81/21.47 (3) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.47 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.47 (4) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.47 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.47 (5) ~ (all_52_13 = e0)
% 142.81/21.47 (6) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.47 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.47 (7) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.47 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.47 (8) ~ (all_52_14 = e1)
% 142.81/21.47 (9) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.47 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.47 (10) ~ (all_52_12 = e3)
% 142.81/21.47 (11) op(e1, e2) = all_52_6
% 142.81/21.47 (12) ~ (all_52_6 = e1)
% 142.81/21.47 (13) (all_57_2 = e1 & op(e2, e3) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.47 (all_57_5 = e1 & op(e2, e1) = e1) | (all_57_10 = e1 & op(e2, e0) = e1)
% 142.81/21.47 (14) ~ (all_52_8 = e3)
% 142.81/21.47 (15) ~ (all_52_2 = all_52_14)
% 142.81/21.47 (16) ~ (all_52_4 = e0)
% 142.81/21.47 (17) ~ (e2 = e1)
% 142.81/21.47 (18) all_54_11 = all_52_14
% 142.81/21.47 (19) all_54_7 = all_52_13
% 142.81/21.47 (20) ~ (all_52_7 = e0)
% 142.81/21.47 (21) ( ~ (all_16_0 = e1) & op(all_16_1, e2) = all_16_0 & op(e2, e0) =
% 142.81/21.47 all_16_1 & $i(all_16_0) & $i(all_16_1)) | ( ~ (all_16_1 = e3) & op(e2,
% 142.81/21.47 e0) = all_16_1 & $i(all_16_1))
% 142.81/21.47 (22) ( ~ (all_18_0 = e3) & op(all_18_1, e2) = all_18_0 & op(e2, e0) =
% 142.81/21.47 all_18_1 & $i(all_18_0) & $i(all_18_1)) | ( ~ (all_18_1 = e1) & op(e2,
% 142.81/21.47 e0) = all_18_1 & $i(all_18_1))
% 142.81/21.47 (23) all_54_3 = all_52_12
% 142.81/21.47 (24) ~ (all_52_2 = all_52_6)
% 142.81/21.47 (25) op(e0, e3) = all_52_3
% 142.81/21.47 (26) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.47 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.47 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.47 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.47 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.81/21.47 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.81/21.47 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.81/21.47 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.81/21.47 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.81/21.47 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.81/21.47 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.81/21.47 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.81/21.47 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.81/21.47 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.81/21.47 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.81/21.47 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.81/21.47 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.81/21.47 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.81/21.47 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.81/21.47 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.81/21.47 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.47 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.47 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.47 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.47 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.47 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.47 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.47 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.47 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.81/21.47 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.81/21.47 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.81/21.47 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.81/21.47 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.81/21.47 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.81/21.47 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.47 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.81/21.47 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.81/21.47 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.47 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.47 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.81/21.47 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.47 (27) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.47 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.47 (28) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.47 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.81/21.47 e1)
% 142.81/21.47 (29) ~ (all_52_1 = e0)
% 142.81/21.47 (30) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.47 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.81/21.47 (31) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.47 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.47 (32) ~ (e3 = e0)
% 142.81/21.47 (33) op(e1, e1) = e1
% 142.81/21.47 (34) op(e1, e1) = all_4_2
% 142.81/21.47 (35) ~ (all_52_4 = e3)
% 142.81/21.47 (36) op(e3, e1) = all_52_8
% 142.81/21.47 (37) ~ (all_52_12 = all_52_14)
% 142.81/21.47 (38) all_54_9 = all_52_6
% 142.81/21.47 (39) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.47 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.47 (40) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) = e1) |
% 142.81/21.47 (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) = e1)
% 142.81/21.47 (41) (all_57_12 = e2 & op(e0, e3) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.81/21.47 | (all_57_14 = e2 & op(e0, e1) = e2) | (all_57_15 = e2 & op(e0, e0) =
% 142.81/21.47 e2)
% 142.81/21.47 (42) op(e2, e3) = all_52_1
% 142.81/21.47 (43) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.81/21.47 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.81/21.47 (44) ~ (all_52_6 = all_52_14)
% 142.81/21.47 (45) ~ (all_52_13 = all_52_14)
% 142.81/21.47 (46) all_54_11 = e3 | all_54_11 = e2 | all_54_11 = e1 | all_54_11 = e0
% 142.81/21.47 (47) ~ (all_4_2 = e3)
% 142.81/21.47 (48) ~ (all_52_8 = all_52_12)
% 142.81/21.47 (49) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.81/21.47 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.81/21.47 (50) ~ (e1 = e0)
% 142.81/21.47 (51) all_54_9 = e3 | all_54_9 = e2 | all_54_9 = e1 | all_54_9 = e0
% 142.81/21.47 (52) op(e3, e2) = all_52_4
% 142.81/21.47 (53) ~ (e2 = e0)
% 142.81/21.47 (54) ~ (e3 = e2)
% 142.81/21.47 (55) all_57_0 = e3
% 142.81/21.47 (56) op(e3, e0) = all_52_12
% 142.81/21.47 (57) ~ (all_52_2 = e1)
% 142.81/21.47 (58) all_54_3 = e3 | all_54_3 = e2 | all_54_3 = e1 | all_54_3 = e0
% 142.81/21.47 (59) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.47 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.47 (60) ~ (all_52_1 = all_52_2)
% 142.81/21.47 (61) (all_57_9 = e3 & op(e3, e0) = e3) | (all_57_10 = e3 & op(e2, e0) = e3) |
% 142.81/21.47 (all_57_11 = e3 & op(e1, e0) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.47 (62) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.47 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.47 (63) op(e0, e0) = e2
% 142.81/21.47 (64) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.47 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.47 (65) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.47 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.47 (66) ~ (all_52_12 = all_52_13)
% 142.81/21.47 (67) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.47 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.47 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.47 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.47 (68) ~ (all_52_13 = e2)
% 142.81/21.47 (69) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.47 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.47 (70) all_54_7 = e3 | all_54_7 = e2 | all_54_7 = e1 | all_54_7 = e0
% 142.81/21.47 (71) ~ (e3 = e1)
% 142.81/21.47 (72) op(e0, e2) = all_52_7
% 142.81/21.47 (73) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.47 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.47 (74) ~ (all_52_12 = e2)
% 142.81/21.47 (75) ~ (all_52_2 = all_52_3)
% 142.81/21.47 (76) all_54_8 = e3 | all_54_8 = e2 | all_54_8 = e1 | all_54_8 = e0
% 142.81/21.47 (77) all_54_8 = all_52_2
% 142.81/21.47 (78) op(e2, e2) = e0
% 142.81/21.47 (79) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.47 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.47 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.47 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.48 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.48 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.48 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.48 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.48 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.48 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.48 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.48 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.48 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.48 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.48 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.48 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.48 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.48 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.48 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.48 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.48 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.48 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.48 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.48 $i(all_56_14))))
% 142.81/21.48 (80) ~ (all_52_6 = e0)
% 142.81/21.48 (81) all_57_11 = e1
% 142.81/21.48 (82) op(e2, e1) = all_52_9
% 142.81/21.48 (83) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_2 = e2 & op(e2, e3) = e2) |
% 142.81/21.48 (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_12 = e2 & op(e0, e3) = e2)
% 142.81/21.48 (84) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.81/21.48 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.48 (85) ~ (all_52_4 = all_52_12)
% 142.81/21.48 (86) op(e2, e0) = all_52_13
% 142.81/21.48 (87) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.48 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.48 (88) ~ (all_52_9 = e0)
% 142.81/21.48
% 142.81/21.48 Begin of proof
% 142.81/21.48 |
% 142.81/21.48 | BETA: splitting (40) gives:
% 142.81/21.48 |
% 142.81/21.48 | Case 1:
% 142.81/21.48 | |
% 142.81/21.48 | | (89) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_5 = e1 & op(e2, e1) =
% 142.81/21.48 | | e1)
% 142.81/21.48 | |
% 142.81/21.48 | | BETA: splitting (89) gives:
% 142.81/21.48 | |
% 142.81/21.48 | | Case 1:
% 142.81/21.48 | | |
% 142.81/21.48 | | | (90) all_57_4 = e1 & op(e3, e1) = e1
% 142.81/21.48 | | |
% 142.81/21.48 | | | ALPHA: (90) implies:
% 142.81/21.48 | | | (91) all_57_4 = e1
% 142.81/21.48 | | |
% 142.81/21.48 | | | REF_CLOSE: (6), (7), (10), (14), (17), (27), (28), (32), (33), (35), (36),
% 142.81/21.48 | | | (50), (52), (53), (54), (55), (56), (59), (62), (63), (64),
% 142.81/21.48 | | | (65), (71), (73), (78), (81), (82), (87), (88), (91) are
% 142.81/21.48 | | | inconsistent by sub-proof #909.
% 142.81/21.48 | | |
% 142.81/21.48 | | Case 2:
% 142.81/21.48 | | |
% 142.81/21.48 | | | (92) all_57_5 = e1 & op(e2, e1) = e1
% 142.81/21.48 | | |
% 142.81/21.48 | | | ALPHA: (92) implies:
% 142.81/21.48 | | | (93) all_57_5 = e1
% 142.81/21.48 | | |
% 142.81/21.48 | | | REF_CLOSE: (1), (3), (4), (5), (6), (7), (9), (10), (11), (14), (16),
% 142.81/21.48 | | | (17), (20), (26), (27), (28), (29), (30), (31), (32), (33),
% 142.81/21.48 | | | (34), (35), (36), (39), (42), (43), (47), (49), (50), (52),
% 142.81/21.48 | | | (53), (54), (55), (56), (59), (62), (63), (64), (65), (67),
% 142.81/21.48 | | | (68), (69), (71), (72), (73), (78), (79), (80), (81), (82),
% 142.81/21.48 | | | (84), (86), (87), (88), (93) are inconsistent by sub-proof
% 142.81/21.48 | | | #902.
% 142.81/21.48 | | |
% 142.81/21.48 | | End of split
% 142.81/21.48 | |
% 142.81/21.48 | Case 2:
% 142.81/21.48 | |
% 142.81/21.48 | | (94) (all_57_8 = e1 & op(e1, e1) = e1) | (all_57_14 = e1 & op(e0, e1) =
% 142.81/21.48 | | e1)
% 142.81/21.48 | |
% 142.81/21.48 | | REF_CLOSE: (2), (3), (5), (7), (8), (9), (10), (11), (12), (13), (14), (15),
% 142.81/21.48 | | (16), (17), (18), (19), (20), (21), (22), (23), (24), (25), (26),
% 142.81/21.48 | | (27), (28), (29), (31), (32), (33), (34), (35), (36), (37), (38),
% 142.81/21.48 | | (39), (41), (42), (44), (45), (46), (47), (48), (49), (50), (51),
% 142.81/21.48 | | (52), (53), (54), (55), (56), (57), (58), (59), (60), (61), (62),
% 142.81/21.48 | | (63), (64), (65), (66), (67), (68), (70), (71), (72), (73), (74),
% 142.81/21.48 | | (75), (76), (77), (78), (79), (80), (82), (83), (84), (85), (86),
% 142.81/21.48 | | (87), (88), (94) are inconsistent by sub-proof #927.
% 142.81/21.48 | |
% 142.81/21.48 | End of split
% 142.81/21.48 |
% 142.81/21.48 End of proof
% 142.81/21.48
% 142.81/21.48 Sub-proof #901 shows that the following formulas are inconsistent:
% 142.81/21.48 ----------------------------------------------------------------
% 142.81/21.48 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.81/21.48 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.81/21.48 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.48 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.48 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.48 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.48 (4) ~ (all_52_13 = e0)
% 142.81/21.48 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.48 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.48 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.48 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.48 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.48 (8) ~ (all_52_12 = e3)
% 142.81/21.48 (9) op(e1, e2) = all_52_6
% 142.81/21.48 (10) ~ (all_52_8 = e3)
% 142.81/21.48 (11) ~ (all_52_4 = e0)
% 142.81/21.48 (12) ~ (e2 = e1)
% 142.81/21.48 (13) all_57_5 = e1
% 142.81/21.48 (14) ~ (all_52_7 = e0)
% 142.81/21.48 (15) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.48 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.48 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.48 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.48 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.81/21.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.81/21.48 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.81/21.48 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.81/21.48 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.81/21.48 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.81/21.48 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.81/21.48 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.81/21.48 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.81/21.48 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.81/21.48 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.81/21.48 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.81/21.48 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.81/21.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.81/21.48 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.81/21.48 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.81/21.48 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.48 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.48 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.48 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.48 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.48 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.48 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.48 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.48 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.81/21.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.81/21.48 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.81/21.48 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.81/21.48 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.81/21.48 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.81/21.48 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.48 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.81/21.48 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.81/21.48 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.48 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.48 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.81/21.48 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.48 (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.48 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.48 (17) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.48 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.81/21.48 e1)
% 142.81/21.48 (18) ~ (all_52_1 = e0)
% 142.81/21.48 (19) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.48 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.81/21.48 (20) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.48 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.48 (21) ~ (e3 = e0)
% 142.81/21.48 (22) op(e1, e1) = e1
% 142.81/21.48 (23) op(e1, e1) = all_4_2
% 142.81/21.48 (24) ~ (all_52_4 = e3)
% 142.81/21.48 (25) op(e3, e1) = all_52_8
% 142.81/21.48 (26) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.48 (27) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.48 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.48 (28) op(e2, e3) = all_52_1
% 142.81/21.48 (29) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.81/21.48 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.81/21.48 (30) ~ (all_4_2 = e3)
% 142.81/21.48 (31) all_57_11 = e2
% 142.81/21.48 (32) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.81/21.48 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.81/21.48 (33) ~ (e1 = e0)
% 142.81/21.48 (34) op(e3, e2) = all_52_4
% 142.81/21.48 (35) ~ (e2 = e0)
% 142.81/21.48 (36) ~ (e3 = e2)
% 142.81/21.48 (37) all_57_0 = e3
% 142.81/21.48 (38) op(e3, e0) = all_52_12
% 142.81/21.48 (39) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.48 (40) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.48 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.48 (41) op(e0, e0) = e2
% 142.81/21.48 (42) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.48 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.48 (43) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.48 (44) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.48 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.48 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.48 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.48 (45) ~ (all_52_13 = e2)
% 142.81/21.48 (46) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.48 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.48 (47) ~ (e3 = e1)
% 142.81/21.48 (48) op(e0, e2) = all_52_7
% 142.81/21.48 (49) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.48 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.48 (50) op(e2, e2) = e0
% 142.81/21.48 (51) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.48 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.48 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.48 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.48 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.48 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.48 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.48 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.48 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.48 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.48 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.48 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.48 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.48 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.48 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.48 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.48 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.48 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.48 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.48 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.48 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.48 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.48 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.48 $i(all_56_14))))
% 142.81/21.48 (52) ~ (all_52_6 = e0)
% 142.81/21.48 (53) op(e2, e1) = all_52_9
% 142.81/21.48 (54) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.81/21.48 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.48 (55) op(e2, e0) = all_52_13
% 142.81/21.48 (56) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.48 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.48 (57) ~ (all_52_9 = e0)
% 142.81/21.48
% 142.81/21.48 Begin of proof
% 142.81/21.48 |
% 142.81/21.48 | ALPHA: (26) implies:
% 142.81/21.48 | (58) all_57_5 = e2
% 142.81/21.48 |
% 142.81/21.48 | COMBINE_EQS: (13), (58) imply:
% 142.81/21.48 | (59) e2 = e1
% 142.81/21.48 |
% 142.81/21.48 | SIMP: (59) implies:
% 142.81/21.48 | (60) e2 = e1
% 142.81/21.48 |
% 142.81/21.48 | COMBINE_EQS: (31), (60) imply:
% 142.81/21.48 | (61) all_57_11 = e1
% 142.81/21.48 |
% 142.81/21.48 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.81/21.48 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.81/21.48 | (24), (25), (27), (28), (29), (30), (32), (33), (34), (35), (36),
% 142.81/21.48 | (37), (38), (39), (40), (41), (42), (43), (44), (45), (46), (47),
% 142.81/21.48 | (48), (49), (50), (51), (52), (53), (54), (55), (56), (57), (61)
% 142.81/21.48 | are inconsistent by sub-proof #902.
% 142.81/21.48 |
% 142.81/21.48 End of proof
% 142.81/21.48
% 142.81/21.48 Sub-proof #902 shows that the following formulas are inconsistent:
% 142.81/21.48 ----------------------------------------------------------------
% 142.81/21.48 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.81/21.48 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.81/21.48 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.48 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.48 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.48 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.48 (4) ~ (all_52_13 = e0)
% 142.81/21.48 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.48 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.48 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.48 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.48 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.48 (8) ~ (all_52_12 = e3)
% 142.81/21.48 (9) op(e1, e2) = all_52_6
% 142.81/21.48 (10) ~ (all_52_8 = e3)
% 142.81/21.48 (11) ~ (all_52_4 = e0)
% 142.81/21.48 (12) ~ (e2 = e1)
% 142.81/21.48 (13) all_57_5 = e1
% 142.81/21.48 (14) ~ (all_52_7 = e0)
% 142.81/21.48 (15) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.48 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.48 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.48 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.48 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.81/21.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.81/21.48 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.81/21.48 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.81/21.48 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.81/21.48 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.81/21.48 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.81/21.48 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.81/21.48 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.81/21.48 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.81/21.48 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.81/21.48 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.81/21.48 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.81/21.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.81/21.48 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.81/21.48 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.81/21.48 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.48 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.48 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.48 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.48 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.48 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.48 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.48 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.48 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.81/21.48 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.81/21.48 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.81/21.48 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.81/21.48 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.81/21.48 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.81/21.48 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.48 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.81/21.48 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.81/21.48 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.48 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.48 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.81/21.48 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.48 (16) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.48 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.48 (17) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.48 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.81/21.48 e1)
% 142.81/21.48 (18) ~ (all_52_1 = e0)
% 142.81/21.48 (19) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.48 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.81/21.48 (20) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.48 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.48 (21) ~ (e3 = e0)
% 142.81/21.48 (22) op(e1, e1) = e1
% 142.81/21.48 (23) op(e1, e1) = all_4_2
% 142.81/21.48 (24) ~ (all_52_4 = e3)
% 142.81/21.48 (25) op(e3, e1) = all_52_8
% 142.81/21.48 (26) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.48 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.48 (27) op(e2, e3) = all_52_1
% 142.81/21.48 (28) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.81/21.48 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.81/21.48 (29) ~ (all_4_2 = e3)
% 142.81/21.48 (30) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.81/21.48 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.81/21.48 (31) ~ (e1 = e0)
% 142.81/21.48 (32) op(e3, e2) = all_52_4
% 142.81/21.48 (33) ~ (e2 = e0)
% 142.81/21.48 (34) ~ (e3 = e2)
% 142.81/21.48 (35) all_57_0 = e3
% 142.81/21.48 (36) op(e3, e0) = all_52_12
% 142.81/21.48 (37) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.48 (38) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.48 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.48 (39) op(e0, e0) = e2
% 142.81/21.48 (40) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.48 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.48 (41) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.48 (42) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.48 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.48 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.48 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.48 (43) ~ (all_52_13 = e2)
% 142.81/21.48 (44) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.48 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.48 (45) ~ (e3 = e1)
% 142.81/21.48 (46) op(e0, e2) = all_52_7
% 142.81/21.48 (47) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.48 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.48 (48) op(e2, e2) = e0
% 142.81/21.48 (49) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.48 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.48 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.48 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.48 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.48 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.48 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.48 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.48 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.48 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.48 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.48 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.48 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.48 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.48 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.48 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.48 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.48 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.48 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.48 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.48 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.48 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.48 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.48 $i(all_56_14))))
% 142.81/21.48 (50) ~ (all_52_6 = e0)
% 142.81/21.48 (51) all_57_11 = e1
% 142.81/21.48 (52) op(e2, e1) = all_52_9
% 142.81/21.48 (53) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.81/21.48 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.48 (54) op(e2, e0) = all_52_13
% 142.81/21.48 (55) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.48 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.48 (56) ~ (all_52_9 = e0)
% 142.81/21.48
% 142.81/21.48 Begin of proof
% 142.81/21.48 |
% 142.81/21.48 | BETA: splitting (40) gives:
% 142.81/21.48 |
% 142.81/21.48 | Case 1:
% 142.81/21.48 | |
% 142.81/21.48 | | (57) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 142.81/21.48 | | e2)
% 142.81/21.48 | |
% 142.81/21.48 | | BETA: splitting (57) gives:
% 142.81/21.48 | |
% 142.81/21.48 | | Case 1:
% 142.81/21.48 | | |
% 142.81/21.48 | | | (58) all_57_4 = e2 & op(e3, e1) = e2
% 142.81/21.48 | | |
% 142.81/21.48 | | | ALPHA: (58) implies:
% 142.81/21.48 | | | (59) all_57_4 = e2
% 142.81/21.48 | | |
% 142.81/21.48 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.81/21.48 | | | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22),
% 142.81/21.48 | | | (23), (24), (25), (26), (27), (28), (29), (30), (31), (32),
% 142.81/21.48 | | | (33), (34), (35), (36), (37), (38), (39), (40), (41), (42),
% 142.81/21.48 | | | (43), (44), (45), (46), (47), (48), (49), (50), (51), (52),
% 142.81/21.48 | | | (53), (54), (55), (56), (59) are inconsistent by sub-proof
% 142.81/21.48 | | | #905.
% 142.81/21.48 | | |
% 142.81/21.48 | | Case 2:
% 142.81/21.48 | | |
% 142.81/21.48 | | | (60) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.48 | | |
% 142.81/21.48 | | | REF_CLOSE: (12), (13), (60) are inconsistent by sub-proof #1012.
% 142.81/21.48 | | |
% 142.81/21.48 | | End of split
% 142.81/21.48 | |
% 142.81/21.48 | Case 2:
% 142.81/21.48 | |
% 142.81/21.48 | | (61) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.81/21.48 | | e2)
% 142.81/21.48 | |
% 142.81/21.48 | | REF_CLOSE: (6), (10), (12), (13), (22), (25), (34), (41), (45), (61) are
% 142.81/21.48 | | inconsistent by sub-proof #1009.
% 142.81/21.48 | |
% 142.81/21.48 | End of split
% 142.81/21.48 |
% 142.81/21.48 End of proof
% 142.81/21.48
% 142.81/21.48 Sub-proof #903 shows that the following formulas are inconsistent:
% 142.81/21.48 ----------------------------------------------------------------
% 142.81/21.48 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.48 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.48 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.48 (3) ~ (all_52_12 = e3)
% 142.81/21.48 (4) ~ (all_52_8 = e3)
% 142.81/21.48 (5) ~ (e2 = e1)
% 142.81/21.48 (6) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.48 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.48 (7) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.48 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.48 (8) ~ (e3 = e0)
% 142.81/21.48 (9) op(e1, e1) = e1
% 142.81/21.48 (10) ~ (all_52_4 = e3)
% 142.81/21.48 (11) op(e3, e1) = all_52_8
% 142.81/21.48 (12) all_57_11 = e2
% 142.81/21.48 (13) ~ (e1 = e0)
% 142.81/21.48 (14) op(e3, e2) = all_52_4
% 142.81/21.48 (15) ~ (e2 = e0)
% 142.81/21.48 (16) ~ (e3 = e2)
% 142.81/21.48 (17) all_57_0 = e3
% 142.81/21.48 (18) op(e3, e0) = all_52_12
% 142.81/21.48 (19) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.48 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.48 (20) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.48 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.48 (21) op(e0, e0) = e2
% 142.81/21.48 (22) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.48 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.48 (23) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.48 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.48 (24) all_57_4 = e1
% 142.81/21.48 (25) ~ (e3 = e1)
% 142.81/21.48 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.48 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.48 (27) op(e2, e2) = e0
% 142.81/21.48 (28) op(e2, e1) = all_52_9
% 142.81/21.48 (29) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.48 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.48 (30) ~ (all_52_9 = e0)
% 142.81/21.48
% 142.81/21.48 Begin of proof
% 142.81/21.48 |
% 142.81/21.48 | BETA: splitting (22) gives:
% 142.81/21.48 |
% 142.81/21.48 | Case 1:
% 142.81/21.48 | |
% 142.81/21.49 | | (31) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 142.81/21.49 | | e2)
% 142.81/21.49 | |
% 142.81/21.49 | | BETA: splitting (31) gives:
% 142.81/21.49 | |
% 142.81/21.49 | | Case 1:
% 142.81/21.49 | | |
% 142.81/21.49 | | | (32) all_57_4 = e2 & op(e3, e1) = e2
% 142.81/21.49 | | |
% 142.81/21.49 | | | ALPHA: (32) implies:
% 142.81/21.49 | | | (33) all_57_4 = e2
% 142.81/21.49 | | |
% 142.81/21.49 | | | COMBINE_EQS: (24), (33) imply:
% 142.81/21.49 | | | (34) e2 = e1
% 142.81/21.49 | | |
% 142.81/21.49 | | | SIMP: (34) implies:
% 142.81/21.49 | | | (35) e2 = e1
% 142.81/21.49 | | |
% 142.81/21.49 | | | COMBINE_EQS: (12), (35) imply:
% 142.81/21.49 | | | (36) all_57_11 = e1
% 142.81/21.49 | | |
% 142.81/21.49 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 142.81/21.49 | | | (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.81/21.49 | | | (24), (25), (26), (27), (28), (29), (30), (36) are inconsistent
% 142.81/21.49 | | | by sub-proof #909.
% 142.81/21.49 | | |
% 142.81/21.49 | | Case 2:
% 142.81/21.49 | | |
% 142.81/21.49 | | | (37) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.49 | | |
% 142.81/21.49 | | | ALPHA: (37) implies:
% 142.81/21.49 | | | (38) all_57_5 = e2
% 142.81/21.49 | | |
% 142.81/21.49 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (13),
% 142.81/21.49 | | | (14), (16), (17), (18), (21), (23), (24), (25), (26), (27),
% 142.81/21.49 | | | (28), (29), (30), (38) are inconsistent by sub-proof #921.
% 142.81/21.49 | | |
% 142.81/21.49 | | End of split
% 142.81/21.49 | |
% 142.81/21.49 | Case 2:
% 142.81/21.49 | |
% 142.81/21.49 | | (39) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.81/21.49 | | e2)
% 142.81/21.49 | |
% 142.81/21.49 | | REF_CLOSE: (5), (6), (9), (13), (15), (23), (24), (28), (30), (39) are
% 142.81/21.49 | | inconsistent by sub-proof #918.
% 142.81/21.49 | |
% 142.81/21.49 | End of split
% 142.81/21.49 |
% 142.81/21.49 End of proof
% 142.81/21.49
% 142.81/21.49 Sub-proof #904 shows that the following formulas are inconsistent:
% 142.81/21.49 ----------------------------------------------------------------
% 142.81/21.49 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.49 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.49 (2) all_57_4 = e2
% 142.81/21.49 (3) ~ (e2 = e1)
% 142.81/21.49 (4) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.49 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.49 (5) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.49 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.49 (6) ~ (e3 = e0)
% 142.81/21.49 (7) op(e1, e1) = e1
% 142.81/21.49 (8) all_57_13 = e2
% 142.81/21.49 (9) ~ (e1 = e0)
% 142.81/21.49 (10) ~ (e2 = e0)
% 142.81/21.49 (11) ~ (e3 = e2)
% 142.81/21.49 (12) op(e0, e0) = e2
% 142.81/21.49 (13) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.49 (14) ~ (e3 = e1)
% 142.81/21.49 (15) op(e2, e1) = all_52_9
% 142.81/21.49 (16) ~ (all_52_9 = e0)
% 142.81/21.49
% 142.81/21.49 Begin of proof
% 142.81/21.49 |
% 142.81/21.49 | BETA: splitting (4) gives:
% 142.81/21.49 |
% 142.81/21.49 | Case 1:
% 142.81/21.49 | |
% 142.81/21.49 | | (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) =
% 142.81/21.49 | | e0)
% 142.81/21.49 | |
% 142.81/21.49 | | REF_CLOSE: (2), (10), (13), (15), (16), (17) are inconsistent by sub-proof
% 142.81/21.49 | | #914.
% 142.81/21.49 | |
% 142.81/21.49 | Case 2:
% 142.81/21.49 | |
% 142.81/21.49 | | (18) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) =
% 142.81/21.49 | | e0)
% 142.81/21.49 | |
% 142.81/21.49 | | REF_CLOSE: (1), (3), (5), (6), (7), (8), (9), (11), (12), (13), (14), (18)
% 142.81/21.49 | | are inconsistent by sub-proof #1063.
% 142.81/21.49 | |
% 142.81/21.49 | End of split
% 142.81/21.49 |
% 142.81/21.49 End of proof
% 142.81/21.49
% 142.81/21.49 Sub-proof #905 shows that the following formulas are inconsistent:
% 142.81/21.49 ----------------------------------------------------------------
% 142.81/21.49 (1) (all_57_0 = e2 & op(e3, e3) = e2) | (all_57_1 = e2 & op(e3, e2) = e2) |
% 142.81/21.49 (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_9 = e2 & op(e3, e0) = e2)
% 142.81/21.49 (2) (all_57_2 = e3 & op(e2, e3) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.49 (all_57_5 = e3 & op(e2, e1) = e3) | (all_57_10 = e3 & op(e2, e0) = e3)
% 142.81/21.49 (3) (all_57_1 = e1 & op(e3, e2) = e1) | (all_57_3 = e1 & op(e2, e2) = e1) |
% 142.81/21.49 (all_57_7 = e1 & op(e1, e2) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.49 (4) ~ (all_52_13 = e0)
% 142.81/21.49 (5) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.49 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.49 (6) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.49 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.49 (7) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.49 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.49 (8) all_57_4 = e2
% 142.81/21.49 (9) ~ (all_52_12 = e3)
% 142.81/21.49 (10) op(e1, e2) = all_52_6
% 142.81/21.49 (11) ~ (all_52_8 = e3)
% 142.81/21.49 (12) ~ (all_52_4 = e0)
% 142.81/21.49 (13) ~ (e2 = e1)
% 142.81/21.49 (14) all_57_5 = e1
% 142.81/21.49 (15) ~ (all_52_7 = e0)
% 142.81/21.49 (16) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.49 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.49 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.49 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.49 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0,
% 142.81/21.49 e0) = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2,
% 142.81/21.49 e2) = e3) | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 &
% 142.81/21.49 $i(all_56_3))) & ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~
% 142.81/21.49 (all_56_6 = e1) & op(e1, e3) = all_56_6 & $i(all_56_6))) &
% 142.81/21.49 ((all_56_15 = e3 & op(e0, e0) = e3) | ( ~ (all_56_10 = e0) & op(e0,
% 142.81/21.49 e3) = all_56_10 & $i(all_56_10)))) | (op(e2, e2) = all_56_11 &
% 142.81/21.49 $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) = e3) | ( ~ (all_56_9 =
% 142.81/21.49 e2) & op(e3, e3) = all_56_9 & $i(all_56_9))) & ((all_56_7 = e1 &
% 142.81/21.49 op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1, e1) = all_56_13 &
% 142.81/21.49 $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3) = e2) | ( ~
% 142.81/21.49 (all_56_0 = e3) & op(e3, e2) = all_56_0 & $i(all_56_0))) &
% 142.81/21.49 ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~ (all_56_15 = e2) & op(e0,
% 142.81/21.49 e0) = all_56_15 & $i(all_56_15))) & ((all_56_13 = e2 & op(e1,
% 142.81/21.49 e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2) = all_56_7 &
% 142.81/21.49 $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) | ( ~
% 142.81/21.49 (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.49 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.49 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.49 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.49 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.49 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.49 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.49 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.49 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0,
% 142.81/21.49 e0) = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0,
% 142.81/21.49 e0) = e1) | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 &
% 142.81/21.49 $i(all_56_14)))) | (op(e0, e0) = all_56_15 & $i(all_56_15) &
% 142.81/21.49 ((all_56_2 = e3 & op(e3, e0) = e3) | ( ~ (all_56_9 = e0) & op(e3, e3)
% 142.81/21.49 = all_56_9 & $i(all_56_9))) & ((all_56_5 = e2 & op(e2, e0) = e2) |
% 142.81/21.49 ( ~ (all_56_11 = e0) & op(e2, e2) = all_56_11 & $i(all_56_11))) &
% 142.81/21.49 ((all_56_8 = e1 & op(e1, e0) = e1) | ( ~ (all_56_13 = e0) & op(e1, e1)
% 142.81/21.49 = all_56_13 & $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0)
% 142.81/21.49 | ( ~ (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.49 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.49 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0)
% 142.81/21.49 | ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.49 (17) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.49 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.49 (18) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1)
% 142.81/21.49 | (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) =
% 142.81/21.49 e1)
% 142.81/21.49 (19) ~ (all_52_1 = e0)
% 142.81/21.49 (20) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.49 (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 & op(e0, e2) = e2)
% 142.81/21.49 (21) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.49 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.49 (22) ~ (e3 = e0)
% 142.81/21.49 (23) op(e1, e1) = e1
% 142.81/21.49 (24) op(e1, e1) = all_4_2
% 142.81/21.49 (25) ~ (all_52_4 = e3)
% 142.81/21.49 (26) op(e3, e1) = all_52_8
% 142.81/21.49 (27) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.49 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.49 (28) op(e2, e3) = all_52_1
% 142.81/21.49 (29) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1 & op(e3, e2) = e1) |
% 142.81/21.49 (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1 & op(e3, e0) = e1)
% 142.81/21.49 (30) ~ (all_4_2 = e3)
% 142.81/21.49 (31) (all_57_1 = e0 & op(e3, e2) = e0) | (all_57_3 = e0 & op(e2, e2) = e0) |
% 142.81/21.49 (all_57_7 = e0 & op(e1, e2) = e0) | (all_57_13 = e0 & op(e0, e2) = e0)
% 142.81/21.49 (32) ~ (e1 = e0)
% 142.81/21.49 (33) op(e3, e2) = all_52_4
% 142.81/21.49 (34) ~ (e2 = e0)
% 142.81/21.49 (35) ~ (e3 = e2)
% 142.81/21.49 (36) all_57_0 = e3
% 142.81/21.49 (37) op(e3, e0) = all_52_12
% 142.81/21.49 (38) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.49 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.49 (39) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.49 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.49 (40) op(e0, e0) = e2
% 142.81/21.49 (41) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.49 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.49 (42) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.49 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.49 (43) (all_57_15 = e0 & op(e0, e0) = e0) | (((all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.49 | (all_57_10 = e0 & op(e2, e0) = e0) | (all_57_11 = e0 & op(e1, e0)
% 142.81/21.49 = e0)) & ((all_57_12 = e0 & op(e0, e3) = e0) | (all_57_13 = e0 &
% 142.81/21.49 op(e0, e2) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)))
% 142.81/21.49 (44) ~ (all_52_13 = e2)
% 142.81/21.49 (45) (all_57_9 = e1 & op(e3, e0) = e1) | (all_57_10 = e1 & op(e2, e0) = e1) |
% 142.81/21.49 (all_57_11 = e1 & op(e1, e0) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.49 (46) ~ (e3 = e1)
% 142.81/21.49 (47) op(e0, e2) = all_52_7
% 142.81/21.49 (48) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.49 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.49 (49) op(e2, e2) = e0
% 142.81/21.49 (50) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.49 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.49 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.49 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.49 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.49 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.49 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.49 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.49 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.49 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.49 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.49 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.49 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.49 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.49 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.49 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.49 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.49 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.49 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.49 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.49 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.49 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.49 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.49 $i(all_56_14))))
% 142.81/21.49 (51) ~ (all_52_6 = e0)
% 142.81/21.49 (52) all_57_11 = e1
% 142.81/21.49 (53) op(e2, e1) = all_52_9
% 142.81/21.49 (54) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) = e0) |
% 142.81/21.49 (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) = e0)
% 142.81/21.49 (55) op(e2, e0) = all_52_13
% 142.81/21.49 (56) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.49 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.49 (57) ~ (all_52_9 = e0)
% 142.81/21.49
% 142.81/21.49 Begin of proof
% 142.81/21.49 |
% 142.81/21.49 | BETA: splitting (54) gives:
% 142.81/21.49 |
% 142.81/21.49 | Case 1:
% 142.81/21.49 | |
% 142.81/21.49 | | (58) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_1 = e0 & op(e3, e2) =
% 142.81/21.49 | | e0)
% 142.81/21.49 | |
% 142.81/21.49 | | REF_CLOSE: (9), (11), (12), (22), (25), (26), (33), (37), (42), (48), (58)
% 142.81/21.49 | | are inconsistent by sub-proof #1101.
% 142.81/21.49 | |
% 142.81/21.49 | Case 2:
% 142.81/21.49 | |
% 142.81/21.49 | | (59) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_9 = e0 & op(e3, e0) =
% 142.81/21.49 | | e0)
% 142.81/21.49 | |
% 142.81/21.49 | | BETA: splitting (59) gives:
% 142.81/21.49 | |
% 142.81/21.49 | | Case 1:
% 142.81/21.49 | | |
% 142.81/21.49 | | | (60) all_57_4 = e0 & op(e3, e1) = e0
% 142.81/21.49 | | |
% 142.81/21.49 | | | ALPHA: (60) implies:
% 142.81/21.49 | | | (61) all_57_4 = e0
% 142.81/21.49 | | |
% 142.81/21.49 | | | REF_CLOSE: (8), (34), (61) are inconsistent by sub-proof #1050.
% 142.81/21.49 | | |
% 142.81/21.49 | | Case 2:
% 142.81/21.49 | | |
% 142.81/21.49 | | | (62) all_57_9 = e0 & op(e3, e0) = e0
% 142.81/21.49 | | |
% 142.81/21.49 | | | ALPHA: (62) implies:
% 142.81/21.49 | | | (63) all_57_9 = e0
% 142.81/21.49 | | |
% 142.81/21.49 | | | BETA: splitting (38) gives:
% 142.81/21.49 | | |
% 142.81/21.49 | | | Case 1:
% 142.81/21.49 | | | |
% 142.81/21.49 | | | | (64) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2)
% 142.81/21.49 | | | | = e3)
% 142.81/21.49 | | | |
% 142.81/21.49 | | | | BETA: splitting (64) gives:
% 142.81/21.49 | | | |
% 142.81/21.49 | | | | Case 1:
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | (65) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | ALPHA: (65) implies:
% 142.81/21.49 | | | | | (66) all_57_6 = e3
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | BETA: splitting (39) gives:
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | Case 1:
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | (67) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 142.81/21.49 | | | | | | e2) = e2)
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | BETA: splitting (67) gives:
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | Case 1:
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | (68) all_57_6 = e2 & op(e1, e3) = e2
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | REF_CLOSE: (35), (66), (68) are inconsistent by sub-proof #998.
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | Case 2:
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | (69) all_57_7 = e2 & op(e1, e2) = e2
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | ALPHA: (69) implies:
% 142.81/21.49 | | | | | | | (70) all_57_7 = e2
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | BETA: splitting (17) gives:
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | (71) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 &
% 142.81/21.49 | | | | | | | | op(e2, e1) = e0)
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | REF_CLOSE: (8), (34), (42), (53), (57), (71) are inconsistent by
% 142.81/21.49 | | | | | | | | sub-proof #914.
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | (72) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 &
% 142.81/21.49 | | | | | | | | op(e0, e1) = e0)
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | BETA: splitting (72) gives:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | (73) all_57_8 = e0 & op(e1, e1) = e0
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | ALPHA: (73) implies:
% 142.81/21.49 | | | | | | | | | (74) op(e1, e1) = e0
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | REF_CLOSE: (23), (32), (42), (74) are inconsistent by
% 142.81/21.49 | | | | | | | | | sub-proof #1089.
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | (75) all_57_14 = e0 & op(e0, e1) = e0
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | ALPHA: (75) implies:
% 142.81/21.49 | | | | | | | | | (76) all_57_14 = e0
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | BETA: splitting (6) gives:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | (77) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 &
% 142.81/21.49 | | | | | | | | | | op(e2, e1) = e3)
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | BETA: splitting (77) gives:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (78) all_57_4 = e3 & op(e3, e1) = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (78) implies:
% 142.81/21.49 | | | | | | | | | | | (79) op(e3, e1) = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (11), (26), (42), (79) are inconsistent by
% 142.81/21.49 | | | | | | | | | | | sub-proof #1106.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (80) all_57_5 = e3 & op(e2, e1) = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (80) implies:
% 142.81/21.49 | | | | | | | | | | | (81) all_57_5 = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | COMBINE_EQS: (14), (81) imply:
% 142.81/21.49 | | | | | | | | | | | (82) e3 = e1
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | COMBINE_EQS: (66), (82) imply:
% 142.81/21.49 | | | | | | | | | | | (83) all_57_6 = e1
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (9), (11),
% 142.81/21.49 | | | | | | | | | | | (12), (13), (14), (17), (18), (20), (22), (23),
% 142.81/21.49 | | | | | | | | | | | (25), (26), (29), (31), (32), (33), (34), (35),
% 142.81/21.49 | | | | | | | | | | | (36), (37), (38), (39), (40), (41), (42), (43),
% 142.81/21.49 | | | | | | | | | | | (44), (45), (46), (48), (49), (53), (54), (55),
% 142.81/21.49 | | | | | | | | | | | (57), (70), (83) are inconsistent by sub-proof
% 142.81/21.49 | | | | | | | | | | | #1008.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | (84) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3
% 142.81/21.49 | | | | | | | | | | & op(e0, e1) = e3)
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | BETA: splitting (84) gives:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (85) all_57_8 = e3 & op(e1, e1) = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (85) implies:
% 142.81/21.49 | | | | | | | | | | | (86) op(e1, e1) = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (23), (42), (46), (86) are inconsistent by
% 142.81/21.49 | | | | | | | | | | | sub-proof #1096.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (87) all_57_14 = e3 & op(e0, e1) = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (87) implies:
% 142.81/21.49 | | | | | | | | | | | (88) all_57_14 = e3
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | COMBINE_EQS: (76), (88) imply:
% 142.81/21.49 | | | | | | | | | | | (89) e3 = e0
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | COMBINE_EQS: (36), (89) imply:
% 142.81/21.49 | | | | | | | | | | | (90) all_57_0 = e0
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (9), (11), (22), (25), (26), (33), (37), (42),
% 142.81/21.49 | | | | | | | | | | | (48), (90) are inconsistent by sub-proof #1103.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | End of split
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | End of split
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | End of split
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | Case 2:
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | (91) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1,
% 142.81/21.49 | | | | | | e0) = e2)
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | REF_CLOSE: (5), (6), (8), (9), (11), (13), (17), (18), (22), (23),
% 142.81/21.49 | | | | | | (25), (26), (32), (33), (34), (35), (36), (37), (38),
% 142.81/21.49 | | | | | | (39), (40), (41), (42), (46), (48), (49), (52), (53),
% 142.81/21.49 | | | | | | (56), (57), (91) are inconsistent by sub-proof #908.
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | End of split
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | Case 2:
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | (92) all_57_7 = e3 & op(e1, e2) = e3
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | ALPHA: (92) implies:
% 142.81/21.49 | | | | | (93) all_57_7 = e3
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | BETA: splitting (39) gives:
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | | Case 1:
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | (94) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1,
% 142.81/21.49 | | | | | | e2) = e2)
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | BETA: splitting (94) gives:
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | Case 1:
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | (95) all_57_6 = e2 & op(e1, e3) = e2
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | ALPHA: (95) implies:
% 142.81/21.49 | | | | | | | (96) all_57_6 = e2
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | BETA: splitting (20) gives:
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | (97) (all_57_1 = e2 & op(e3, e2) = e2) | (all_57_3 = e2 &
% 142.81/21.49 | | | | | | | | op(e2, e2) = e2)
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | BETA: splitting (97) gives:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | (98) all_57_1 = e2 & op(e3, e2) = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | ALPHA: (98) implies:
% 142.81/21.49 | | | | | | | | | (99) all_57_1 = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | BETA: splitting (7) gives:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | (100) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2
% 142.81/21.49 | | | | | | | | | | & op(e2, e2) = e2)
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | BETA: splitting (100) gives:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (101) all_57_2 = e2 & op(e2, e3) = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (101) implies:
% 142.81/21.49 | | | | | | | | | | | (102) all_57_2 = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | BETA: splitting (29) gives:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | (103) (all_57_0 = e1 & op(e3, e3) = e1) | (all_57_1 = e1
% 142.81/21.49 | | | | | | | | | | | | & op(e3, e2) = e1)
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | BETA: splitting (103) gives:
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | (104) all_57_0 = e1 & op(e3, e3) = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | ALPHA: (104) implies:
% 142.81/21.49 | | | | | | | | | | | | | (105) all_57_0 = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | COMBINE_EQS: (36), (105) imply:
% 142.81/21.49 | | | | | | | | | | | | | (106) e3 = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | REF_CLOSE: (23), (35), (38), (42), (46), (52), (93), (96),
% 142.81/21.49 | | | | | | | | | | | | | (106) are inconsistent by sub-proof #907.
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | (107) all_57_1 = e1 & op(e3, e2) = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | REF_CLOSE: (7), (9), (10), (11), (13), (15), (16), (19),
% 142.81/21.49 | | | | | | | | | | | | | (21), (22), (23), (24), (25), (26), (27), (28),
% 142.81/21.49 | | | | | | | | | | | | | (30), (32), (33), (34), (35), (37), (38), (39),
% 142.81/21.49 | | | | | | | | | | | | | (40), (42), (44), (46), (47), (48), (49), (50),
% 142.81/21.49 | | | | | | | | | | | | | (51), (55), (96), (99), (102), (107) are
% 142.81/21.49 | | | | | | | | | | | | | inconsistent by sub-proof #906.
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | (108) (all_57_4 = e1 & op(e3, e1) = e1) | (all_57_9 = e1
% 142.81/21.49 | | | | | | | | | | | | & op(e3, e0) = e1)
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | BETA: splitting (108) gives:
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | (109) all_57_4 = e1 & op(e3, e1) = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | ALPHA: (109) implies:
% 142.81/21.49 | | | | | | | | | | | | | (110) all_57_4 = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (11), (13), (17), (18), (22), (23),
% 142.81/21.49 | | | | | | | | | | | | | (25), (26), (32), (33), (34), (35), (36), (37),
% 142.81/21.49 | | | | | | | | | | | | | (38), (39), (40), (41), (42), (46), (48), (49),
% 142.81/21.49 | | | | | | | | | | | | | (52), (53), (56), (57), (110) are inconsistent by
% 142.81/21.49 | | | | | | | | | | | | | sub-proof #909.
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | (111) all_57_9 = e1 & op(e3, e0) = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | ALPHA: (111) implies:
% 142.81/21.49 | | | | | | | | | | | | | (112) all_57_9 = e1
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | | REF_CLOSE: (32), (63), (112) are inconsistent by sub-proof
% 142.81/21.49 | | | | | | | | | | | | | #1079.
% 142.81/21.49 | | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (113) all_57_3 = e2 & op(e2, e2) = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (113) implies:
% 142.81/21.49 | | | | | | | | | | | (114) op(e2, e2) = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (34), (42), (49), (114) are inconsistent by
% 142.81/21.49 | | | | | | | | | | | sub-proof #1076.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | (115) (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2
% 142.81/21.49 | | | | | | | | | | & op(e2, e0) = e2)
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | BETA: splitting (115) gives:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (116) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (116) implies:
% 142.81/21.49 | | | | | | | | | | | (117) all_57_5 = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | COMBINE_EQS: (14), (117) imply:
% 142.81/21.49 | | | | | | | | | | | (118) e2 = e1
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | SIMP: (118) implies:
% 142.81/21.49 | | | | | | | | | | | (119) e2 = e1
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | COMBINE_EQS: (8), (119) imply:
% 142.81/21.49 | | | | | | | | | | | (120) all_57_4 = e1
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (5), (6), (9), (11), (13), (17), (18), (22), (23),
% 142.81/21.49 | | | | | | | | | | | (25), (26), (32), (33), (35), (36), (37), (38),
% 142.81/21.49 | | | | | | | | | | | (39), (40), (42), (46), (48), (49), (52), (53),
% 142.81/21.49 | | | | | | | | | | | (56), (57), (117), (120) are inconsistent by
% 142.81/21.49 | | | | | | | | | | | sub-proof #910.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | (121) all_57_10 = e2 & op(e2, e0) = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | ALPHA: (121) implies:
% 142.81/21.49 | | | | | | | | | | | (122) op(e2, e0) = e2
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | | REF_CLOSE: (42), (44), (55), (122) are inconsistent by
% 142.81/21.49 | | | | | | | | | | | sub-proof #1030.
% 142.81/21.49 | | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | (123) all_57_3 = e2 & op(e2, e2) = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | ALPHA: (123) implies:
% 142.81/21.49 | | | | | | | | | (124) op(e2, e2) = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | REF_CLOSE: (34), (42), (49), (124) are inconsistent by
% 142.81/21.49 | | | | | | | | | sub-proof #1076.
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | End of split
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | (125) (all_57_7 = e2 & op(e1, e2) = e2) | (all_57_13 = e2 &
% 142.81/21.49 | | | | | | | | op(e0, e2) = e2)
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | BETA: splitting (125) gives:
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | (126) all_57_7 = e2 & op(e1, e2) = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | REF_CLOSE: (35), (93), (126) are inconsistent by sub-proof
% 142.81/21.49 | | | | | | | | | #1084.
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | (127) all_57_13 = e2 & op(e0, e2) = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | ALPHA: (127) implies:
% 142.81/21.49 | | | | | | | | | (128) all_57_13 = e2
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | BETA: splitting (17) gives:
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | | Case 1:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | (129) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0
% 142.81/21.49 | | | | | | | | | | & op(e2, e1) = e0)
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | REF_CLOSE: (8), (34), (42), (53), (57), (129) are
% 142.81/21.49 | | | | | | | | | | inconsistent by sub-proof #914.
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | Case 2:
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | (130) (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0
% 142.81/21.49 | | | | | | | | | | & op(e0, e1) = e0)
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | | REF_CLOSE: (5), (13), (18), (22), (23), (32), (35), (40),
% 142.81/21.49 | | | | | | | | | | (42), (46), (128), (130) are inconsistent by
% 142.81/21.49 | | | | | | | | | | sub-proof #1063.
% 142.81/21.49 | | | | | | | | | |
% 142.81/21.49 | | | | | | | | | End of split
% 142.81/21.49 | | | | | | | | |
% 142.81/21.49 | | | | | | | | End of split
% 142.81/21.49 | | | | | | | |
% 142.81/21.49 | | | | | | | End of split
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | Case 2:
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | (131) all_57_7 = e2 & op(e1, e2) = e2
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | | REF_CLOSE: (35), (93), (131) are inconsistent by sub-proof #1084.
% 142.81/21.49 | | | | | | |
% 142.81/21.49 | | | | | | End of split
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | Case 2:
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | (132) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 &
% 142.81/21.49 | | | | | | op(e1, e0) = e2)
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | | REF_CLOSE: (5), (6), (8), (9), (11), (13), (17), (18), (22), (23),
% 142.81/21.49 | | | | | | (25), (26), (32), (33), (34), (35), (36), (37), (38),
% 142.81/21.49 | | | | | | (39), (40), (41), (42), (46), (48), (49), (52), (53),
% 142.81/21.49 | | | | | | (56), (57), (132) are inconsistent by sub-proof #908.
% 142.81/21.49 | | | | | |
% 142.81/21.49 | | | | | End of split
% 142.81/21.49 | | | | |
% 142.81/21.49 | | | | End of split
% 142.81/21.49 | | | |
% 142.81/21.49 | | | Case 2:
% 142.81/21.49 | | | |
% 142.81/21.49 | | | | (133) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1,
% 142.81/21.49 | | | | e0) = e3)
% 142.81/21.49 | | | |
% 142.81/21.49 | | | | REF_CLOSE: (23), (42), (46), (52), (133) are inconsistent by sub-proof
% 142.81/21.49 | | | | #911.
% 142.81/21.49 | | | |
% 142.81/21.49 | | | End of split
% 142.81/21.49 | | |
% 142.81/21.49 | | End of split
% 142.81/21.49 | |
% 142.81/21.49 | End of split
% 142.81/21.49 |
% 142.81/21.49 End of proof
% 142.81/21.49
% 142.81/21.49 Sub-proof #906 shows that the following formulas are inconsistent:
% 142.81/21.49 ----------------------------------------------------------------
% 142.81/21.49 (1) (all_57_2 = e2 & op(e2, e3) = e2) | (all_57_3 = e2 & op(e2, e2) = e2) |
% 142.81/21.49 (all_57_5 = e2 & op(e2, e1) = e2) | (all_57_10 = e2 & op(e2, e0) = e2)
% 142.81/21.49 (2) ~ (all_52_12 = e3)
% 142.81/21.49 (3) op(e1, e2) = all_52_6
% 142.81/21.49 (4) ~ (all_52_8 = e3)
% 142.81/21.49 (5) ~ (e2 = e1)
% 142.81/21.49 (6) ~ (all_52_7 = e0)
% 142.81/21.50 (7) (op(e3, e3) = all_56_9 & $i(all_56_9) & ((all_56_3 = e2 & op(e2, e3) =
% 142.81/21.50 e2) | ( ~ (all_56_11 = e3) & op(e2, e2) = all_56_11 &
% 142.81/21.50 $i(all_56_11))) & ((all_56_6 = e1 & op(e1, e3) = e1) | ( ~
% 142.81/21.50 (all_56_13 = e3) & op(e1, e1) = all_56_13 & $i(all_56_13))) &
% 142.81/21.50 ((all_56_10 = e0 & op(e0, e3) = e0) | ( ~ (all_56_15 = e3) & op(e0, e0)
% 142.81/21.50 = all_56_15 & $i(all_56_15))) & ((all_56_11 = e3 & op(e2, e2) = e3)
% 142.81/21.50 | ( ~ (all_56_3 = e2) & op(e2, e3) = all_56_3 & $i(all_56_3))) &
% 142.81/21.50 ((all_56_13 = e3 & op(e1, e1) = e3) | ( ~ (all_56_6 = e1) & op(e1, e3)
% 142.81/21.50 = all_56_6 & $i(all_56_6))) & ((all_56_15 = e3 & op(e0, e0) = e3) |
% 142.81/21.50 ( ~ (all_56_10 = e0) & op(e0, e3) = all_56_10 & $i(all_56_10)))) |
% 142.81/21.50 (op(e2, e2) = all_56_11 & $i(all_56_11) & ((all_56_0 = e3 & op(e3, e2) =
% 142.81/21.50 e3) | ( ~ (all_56_9 = e2) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.50 & ((all_56_7 = e1 & op(e1, e2) = e1) | ( ~ (all_56_13 = e2) & op(e1,
% 142.81/21.50 e1) = all_56_13 & $i(all_56_13))) & ((all_56_9 = e2 & op(e3, e3)
% 142.81/21.50 = e2) | ( ~ (all_56_0 = e3) & op(e3, e2) = all_56_0 &
% 142.81/21.50 $i(all_56_0))) & ((all_56_12 = e0 & op(e0, e2) = e0) | ( ~
% 142.81/21.50 (all_56_15 = e2) & op(e0, e0) = all_56_15 & $i(all_56_15))) &
% 142.81/21.50 ((all_56_13 = e2 & op(e1, e1) = e2) | ( ~ (all_56_7 = e1) & op(e1, e2)
% 142.81/21.50 = all_56_7 & $i(all_56_7))) & ((all_56_15 = e2 & op(e0, e0) = e2) |
% 142.81/21.50 ( ~ (all_56_12 = e0) & op(e0, e2) = all_56_12 & $i(all_56_12)))) |
% 142.81/21.50 (op(e1, e1) = all_56_13 & $i(all_56_13) & ((all_56_1 = e3 & op(e3, e1) =
% 142.81/21.50 e3) | ( ~ (all_56_9 = e1) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.50 & ((all_56_4 = e2 & op(e2, e1) = e2) | ( ~ (all_56_11 = e1) & op(e2,
% 142.81/21.50 e2) = all_56_11 & $i(all_56_11))) & ((all_56_9 = e1 & op(e3, e3)
% 142.81/21.50 = e1) | ( ~ (all_56_1 = e3) & op(e3, e1) = all_56_1 &
% 142.81/21.50 $i(all_56_1))) & ((all_56_11 = e1 & op(e2, e2) = e1) | ( ~
% 142.81/21.50 (all_56_4 = e2) & op(e2, e1) = all_56_4 & $i(all_56_4))) &
% 142.81/21.50 ((all_56_14 = e0 & op(e0, e1) = e0) | ( ~ (all_56_15 = e1) & op(e0, e0)
% 142.81/21.50 = all_56_15 & $i(all_56_15))) & ((all_56_15 = e1 & op(e0, e0) = e1)
% 142.81/21.50 | ( ~ (all_56_14 = e0) & op(e0, e1) = all_56_14 & $i(all_56_14)))) |
% 142.81/21.50 (op(e0, e0) = all_56_15 & $i(all_56_15) & ((all_56_2 = e3 & op(e3, e0) =
% 142.81/21.50 e3) | ( ~ (all_56_9 = e0) & op(e3, e3) = all_56_9 & $i(all_56_9)))
% 142.81/21.50 & ((all_56_5 = e2 & op(e2, e0) = e2) | ( ~ (all_56_11 = e0) & op(e2,
% 142.81/21.50 e2) = all_56_11 & $i(all_56_11))) & ((all_56_8 = e1 & op(e1, e0)
% 142.81/21.50 = e1) | ( ~ (all_56_13 = e0) & op(e1, e1) = all_56_13 &
% 142.81/21.50 $i(all_56_13))) & ((all_56_9 = e0 & op(e3, e3) = e0) | ( ~
% 142.81/21.50 (all_56_2 = e3) & op(e3, e0) = all_56_2 & $i(all_56_2))) &
% 142.81/21.50 ((all_56_11 = e0 & op(e2, e2) = e0) | ( ~ (all_56_5 = e2) & op(e2, e0)
% 142.81/21.50 = all_56_5 & $i(all_56_5))) & ((all_56_13 = e0 & op(e1, e1) = e0) |
% 142.81/21.50 ( ~ (all_56_8 = e1) & op(e1, e0) = all_56_8 & $i(all_56_8))))
% 142.81/21.50 (8) ~ (all_52_1 = e0)
% 142.81/21.50 (9) (all_57_0 = e0 & op(e3, e3) = e0) | (all_57_2 = e0 & op(e2, e3) = e0) |
% 142.81/21.50 (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_12 = e0 & op(e0, e3) = e0)
% 142.81/21.50 (10) ~ (e3 = e0)
% 142.81/21.50 (11) op(e1, e1) = e1
% 142.81/21.50 (12) op(e1, e1) = all_4_2
% 142.81/21.50 (13) ~ (all_52_4 = e3)
% 142.81/21.50 (14) op(e3, e1) = all_52_8
% 142.81/21.50 (15) (all_57_6 = e0 & op(e1, e3) = e0) | (all_57_7 = e0 & op(e1, e2) = e0) |
% 142.81/21.50 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_11 = e0 & op(e1, e0) = e0)
% 142.81/21.50 (16) op(e2, e3) = all_52_1
% 142.81/21.50 (17) ~ (all_4_2 = e3)
% 142.81/21.50 (18) ~ (e1 = e0)
% 142.81/21.50 (19) op(e3, e2) = all_52_4
% 142.81/21.50 (20) ~ (e2 = e0)
% 142.81/21.50 (21) all_57_6 = e2
% 142.81/21.50 (22) ~ (e3 = e2)
% 142.81/21.50 (23) op(e3, e0) = all_52_12
% 142.81/21.50 (24) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.50 (25) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.50 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.50 (26) op(e0, e0) = e2
% 142.81/21.50 (27) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (28) all_57_1 = e1 & op(e3, e2) = e1
% 142.81/21.50 (29) ~ (all_52_13 = e2)
% 142.81/21.50 (30) ~ (e3 = e1)
% 142.81/21.50 (31) op(e0, e2) = all_52_7
% 142.81/21.50 (32) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.50 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.50 (33) all_57_1 = e2
% 142.81/21.50 (34) op(e2, e2) = e0
% 142.81/21.50 (35) (all_56_9 = e2 & all_56_11 = e3 & ~ (all_56_0 = e3) & op(e3, e3) = e2 &
% 142.81/21.50 op(e3, e2) = all_56_0 & op(e2, e2) = e3 & $i(all_56_0)) | (all_56_9 =
% 142.81/21.50 e2 & all_56_11 = e3 & ~ (all_56_3 = e2) & op(e3, e3) = e2 & op(e2,
% 142.81/21.50 e3) = all_56_3 & op(e2, e2) = e3 & $i(all_56_3)) | (all_56_9 = e1 &
% 142.81/21.50 all_56_13 = e3 & ~ (all_56_1 = e3) & op(e3, e3) = e1 & op(e3, e1) =
% 142.81/21.50 all_56_1 & op(e1, e1) = e3 & $i(all_56_1)) | (all_56_9 = e1 &
% 142.81/21.50 all_56_13 = e3 & ~ (all_56_6 = e1) & op(e3, e3) = e1 & op(e1, e3) =
% 142.81/21.50 all_56_6 & op(e1, e1) = e3 & $i(all_56_6)) | (all_56_9 = e0 &
% 142.81/21.50 all_56_15 = e3 & ~ (all_56_2 = e3) & op(e3, e3) = e0 & op(e3, e0) =
% 142.81/21.50 all_56_2 & op(e0, e0) = e3 & $i(all_56_2)) | (all_56_11 = e1 &
% 142.81/21.50 all_56_13 = e2 & ~ (all_56_4 = e2) & op(e2, e2) = e1 & op(e2, e1) =
% 142.81/21.50 all_56_4 & op(e1, e1) = e2 & $i(all_56_4)) | (all_56_11 = e1 &
% 142.81/21.50 all_56_13 = e2 & ~ (all_56_7 = e1) & op(e2, e2) = e1 & op(e1, e2) =
% 142.81/21.50 all_56_7 & op(e1, e1) = e2 & $i(all_56_7)) | (all_56_11 = e0 &
% 142.81/21.50 all_56_15 = e2 & ~ (all_56_5 = e2) & op(e2, e2) = e0 & op(e2, e0) =
% 142.81/21.50 all_56_5 & op(e0, e0) = e2 & $i(all_56_5)) | (op(e0, e0) = all_56_15 &
% 142.81/21.50 $i(all_56_15) & ((all_56_9 = e0 & all_56_15 = e3 & ~ (all_56_10 = e0)
% 142.81/21.50 & op(e3, e3) = e0 & op(e0, e3) = all_56_10 & $i(all_56_10)) |
% 142.81/21.50 (all_56_11 = e0 & all_56_15 = e2 & ~ (all_56_12 = e0) & op(e2, e2)
% 142.81/21.50 = e0 & op(e0, e2) = all_56_12 & $i(all_56_12)) | (all_56_13 = e0 &
% 142.81/21.50 all_56_15 = e1 & ~ (all_56_8 = e1) & op(e1, e1) = e0 & op(e1, e0)
% 142.81/21.50 = all_56_8 & $i(all_56_8)) | (all_56_13 = e0 & all_56_15 = e1 & ~
% 142.81/21.50 (all_56_14 = e0) & op(e1, e1) = e0 & op(e0, e1) = all_56_14 &
% 142.81/21.50 $i(all_56_14))))
% 142.81/21.50 (36) ~ (all_52_6 = e0)
% 142.81/21.50 (37) all_57_2 = e2
% 142.81/21.50 (38) op(e2, e0) = all_52_13
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | ALPHA: (28) implies:
% 142.81/21.50 | (39) all_57_1 = e1
% 142.81/21.50 |
% 142.81/21.50 | COMBINE_EQS: (33), (39) imply:
% 142.81/21.50 | (40) e2 = e1
% 142.81/21.50 |
% 142.81/21.50 | COMBINE_EQS: (37), (40) imply:
% 142.81/21.50 | (41) all_57_2 = e1
% 142.81/21.50 |
% 142.81/21.50 | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.81/21.50 | (13), (14), (15), (16), (17), (18), (19), (20), (21), (22), (23),
% 142.81/21.50 | (24), (25), (26), (27), (29), (30), (31), (32), (34), (35), (36),
% 142.81/21.50 | (38), (41) are inconsistent by sub-proof #944.
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #907 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) op(e1, e1) = e1
% 142.81/21.50 (2) all_57_6 = e2
% 142.81/21.50 (3) ~ (e3 = e2)
% 142.81/21.50 (4) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.50 (5) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (6) ~ (e3 = e1)
% 142.81/21.50 (7) e3 = e1
% 142.81/21.50 (8) all_57_11 = e1
% 142.81/21.50 (9) all_57_7 = e3
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | COMBINE_EQS: (7), (9) imply:
% 142.81/21.50 | (10) all_57_7 = e1
% 142.81/21.50 |
% 142.81/21.50 | BETA: splitting (4) gives:
% 142.81/21.50 |
% 142.81/21.50 | Case 1:
% 142.81/21.50 | |
% 142.81/21.50 | | (11) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.81/21.50 | | e3)
% 142.81/21.50 | |
% 142.81/21.50 | | BETA: splitting (11) gives:
% 142.81/21.50 | |
% 142.81/21.50 | | Case 1:
% 142.81/21.50 | | |
% 142.81/21.50 | | | (12) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.50 | | |
% 142.81/21.50 | | | ALPHA: (12) implies:
% 142.81/21.50 | | | (13) all_57_6 = e3
% 142.81/21.50 | | |
% 142.81/21.50 | | | REF_CLOSE: (2), (3), (13) are inconsistent by sub-proof #1004.
% 142.81/21.50 | | |
% 142.81/21.50 | | Case 2:
% 142.81/21.50 | | |
% 142.81/21.50 | | | (14) all_57_7 = e3 & op(e1, e2) = e3
% 142.81/21.50 | | |
% 142.81/21.50 | | | REF_CLOSE: (6), (9), (10) are inconsistent by sub-proof #915.
% 142.81/21.50 | | |
% 142.81/21.50 | | End of split
% 142.81/21.50 | |
% 142.81/21.50 | Case 2:
% 142.81/21.50 | |
% 142.81/21.50 | | (15) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.81/21.50 | | e3)
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (1), (5), (6), (8), (15) are inconsistent by sub-proof #911.
% 142.81/21.50 | |
% 142.81/21.50 | End of split
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #908 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.50 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.50 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.50 (3) all_57_4 = e2
% 142.81/21.50 (4) ~ (all_52_12 = e3)
% 142.81/21.50 (5) ~ (all_52_8 = e3)
% 142.81/21.50 (6) ~ (e2 = e1)
% 142.81/21.50 (7) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.50 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.50 (8) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.50 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.50 (9) ~ (e3 = e0)
% 142.81/21.50 (10) op(e1, e1) = e1
% 142.81/21.50 (11) ~ (all_52_4 = e3)
% 142.81/21.50 (12) op(e3, e1) = all_52_8
% 142.81/21.50 (13) ~ (e1 = e0)
% 142.81/21.50 (14) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.50 (15) op(e3, e2) = all_52_4
% 142.81/21.50 (16) ~ (e2 = e0)
% 142.81/21.50 (17) ~ (e3 = e2)
% 142.81/21.50 (18) all_57_0 = e3
% 142.81/21.50 (19) op(e3, e0) = all_52_12
% 142.81/21.50 (20) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.50 (21) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.50 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.50 (22) op(e0, e0) = e2
% 142.81/21.50 (23) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.50 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.50 (24) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (25) ~ (e3 = e1)
% 142.81/21.50 (26) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.50 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.50 (27) op(e2, e2) = e0
% 142.81/21.50 (28) all_57_11 = e1
% 142.81/21.50 (29) op(e2, e1) = all_52_9
% 142.81/21.50 (30) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.50 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.50 (31) ~ (all_52_9 = e0)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | BETA: splitting (14) gives:
% 142.81/21.50 |
% 142.81/21.50 | Case 1:
% 142.81/21.50 | |
% 142.81/21.50 | | (32) all_57_8 = e2 & op(e1, e1) = e2
% 142.81/21.50 | |
% 142.81/21.50 | | ALPHA: (32) implies:
% 142.81/21.50 | | (33) op(e1, e1) = e2
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (6), (10), (24), (33) are inconsistent by sub-proof #1085.
% 142.81/21.50 | |
% 142.81/21.50 | Case 2:
% 142.81/21.50 | |
% 142.81/21.50 | | (34) all_57_11 = e2 & op(e1, e0) = e2
% 142.81/21.50 | |
% 142.81/21.50 | | ALPHA: (34) implies:
% 142.81/21.50 | | (35) all_57_11 = e2
% 142.81/21.50 | |
% 142.81/21.50 | | COMBINE_EQS: (28), (35) imply:
% 142.81/21.50 | | (36) e2 = e1
% 142.81/21.50 | |
% 142.81/21.50 | | COMBINE_EQS: (3), (36) imply:
% 142.81/21.50 | | (37) all_57_4 = e1
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (1), (2), (4), (5), (6), (7), (8), (9), (10), (11), (12), (13),
% 142.81/21.50 | | (15), (16), (17), (18), (19), (20), (21), (22), (23), (24), (25),
% 142.81/21.50 | | (26), (27), (28), (29), (30), (31), (37) are inconsistent by
% 142.81/21.50 | | sub-proof #909.
% 142.81/21.50 | |
% 142.81/21.50 | End of split
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #909 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.50 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.50 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.50 (3) ~ (all_52_12 = e3)
% 142.81/21.50 (4) ~ (all_52_8 = e3)
% 142.81/21.50 (5) ~ (e2 = e1)
% 142.81/21.50 (6) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.50 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.50 (7) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.50 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.50 (8) ~ (e3 = e0)
% 142.81/21.50 (9) op(e1, e1) = e1
% 142.81/21.50 (10) ~ (all_52_4 = e3)
% 142.81/21.50 (11) op(e3, e1) = all_52_8
% 142.81/21.50 (12) ~ (e1 = e0)
% 142.81/21.50 (13) op(e3, e2) = all_52_4
% 142.81/21.50 (14) ~ (e2 = e0)
% 142.81/21.50 (15) ~ (e3 = e2)
% 142.81/21.50 (16) all_57_0 = e3
% 142.81/21.50 (17) op(e3, e0) = all_52_12
% 142.81/21.50 (18) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.50 (19) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.50 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.50 (20) op(e0, e0) = e2
% 142.81/21.50 (21) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) = e2) |
% 142.81/21.50 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) = e2)
% 142.81/21.50 (22) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (23) all_57_4 = e1
% 142.81/21.50 (24) ~ (e3 = e1)
% 142.81/21.50 (25) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.50 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.50 (26) op(e2, e2) = e0
% 142.81/21.50 (27) all_57_11 = e1
% 142.81/21.50 (28) op(e2, e1) = all_52_9
% 142.81/21.50 (29) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.50 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.50 (30) ~ (all_52_9 = e0)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | BETA: splitting (21) gives:
% 142.81/21.50 |
% 142.81/21.50 | Case 1:
% 142.81/21.50 | |
% 142.81/21.50 | | (31) (all_57_4 = e2 & op(e3, e1) = e2) | (all_57_5 = e2 & op(e2, e1) =
% 142.81/21.50 | | e2)
% 142.81/21.50 | |
% 142.81/21.50 | | BETA: splitting (31) gives:
% 142.81/21.50 | |
% 142.81/21.50 | | Case 1:
% 142.81/21.50 | | |
% 142.81/21.50 | | | (32) all_57_4 = e2 & op(e3, e1) = e2
% 142.81/21.50 | | |
% 142.81/21.50 | | | REF_CLOSE: (5), (23), (32) are inconsistent by sub-proof #1109.
% 142.81/21.50 | | |
% 142.81/21.50 | | Case 2:
% 142.81/21.50 | | |
% 142.81/21.50 | | | (33) all_57_5 = e2 & op(e2, e1) = e2
% 142.81/21.50 | | |
% 142.81/21.50 | | | ALPHA: (33) implies:
% 142.81/21.50 | | | (34) all_57_5 = e2
% 142.81/21.50 | | |
% 142.81/21.50 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.81/21.50 | | | (13), (15), (16), (17), (18), (19), (20), (22), (23), (24),
% 142.81/21.50 | | | (25), (26), (27), (28), (29), (30), (34) are inconsistent by
% 142.81/21.50 | | | sub-proof #910.
% 142.81/21.50 | | |
% 142.81/21.50 | | End of split
% 142.81/21.50 | |
% 142.81/21.50 | Case 2:
% 142.81/21.50 | |
% 142.81/21.50 | | (35) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_14 = e2 & op(e0, e1) =
% 142.81/21.50 | | e2)
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (5), (6), (9), (12), (14), (22), (23), (28), (30), (35) are
% 142.81/21.50 | | inconsistent by sub-proof #918.
% 142.81/21.50 | |
% 142.81/21.50 | End of split
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #910 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) (all_57_12 = e3 & op(e0, e3) = e3) | (all_57_13 = e3 & op(e0, e2) = e3) |
% 142.81/21.50 (all_57_14 = e3 & op(e0, e1) = e3) | (all_57_15 = e3 & op(e0, e0) = e3)
% 142.81/21.50 (2) (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_5 = e3 & op(e2, e1) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_14 = e3 & op(e0, e1) = e3)
% 142.81/21.50 (3) ~ (all_52_12 = e3)
% 142.81/21.50 (4) ~ (all_52_8 = e3)
% 142.81/21.50 (5) ~ (e2 = e1)
% 142.81/21.50 (6) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0) |
% 142.81/21.50 (all_57_8 = e0 & op(e1, e1) = e0) | (all_57_14 = e0 & op(e0, e1) = e0)
% 142.81/21.50 (7) (all_57_12 = e1 & op(e0, e3) = e1) | (all_57_13 = e1 & op(e0, e2) = e1) |
% 142.81/21.50 (all_57_14 = e1 & op(e0, e1) = e1) | (all_57_15 = e1 & op(e0, e0) = e1)
% 142.81/21.50 (8) ~ (e3 = e0)
% 142.81/21.50 (9) op(e1, e1) = e1
% 142.81/21.50 (10) ~ (all_52_4 = e3)
% 142.81/21.50 (11) op(e3, e1) = all_52_8
% 142.81/21.50 (12) ~ (e1 = e0)
% 142.81/21.50 (13) op(e3, e2) = all_52_4
% 142.81/21.50 (14) ~ (e3 = e2)
% 142.81/21.50 (15) all_57_0 = e3
% 142.81/21.50 (16) op(e3, e0) = all_52_12
% 142.81/21.50 (17) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) = e3) |
% 142.81/21.50 (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.50 (18) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2) = e2) |
% 142.81/21.50 (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0) = e2)
% 142.81/21.50 (19) op(e0, e0) = e2
% 142.81/21.50 (20) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (21) all_57_5 = e2
% 142.81/21.50 (22) all_57_4 = e1
% 142.81/21.50 (23) ~ (e3 = e1)
% 142.81/21.50 (24) (all_57_0 = e3 & op(e3, e3) = e3) | (all_57_1 = e3 & op(e3, e2) = e3) |
% 142.81/21.50 (all_57_4 = e3 & op(e3, e1) = e3) | (all_57_9 = e3 & op(e3, e0) = e3)
% 142.81/21.50 (25) op(e2, e2) = e0
% 142.81/21.50 (26) all_57_11 = e1
% 142.81/21.50 (27) op(e2, e1) = all_52_9
% 142.81/21.50 (28) (all_57_1 = e3 & op(e3, e2) = e3) | (all_57_3 = e3 & op(e2, e2) = e3) |
% 142.81/21.50 (all_57_7 = e3 & op(e1, e2) = e3) | (all_57_13 = e3 & op(e0, e2) = e3)
% 142.81/21.50 (29) ~ (all_52_9 = e0)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | BETA: splitting (17) gives:
% 142.81/21.50 |
% 142.81/21.50 | Case 1:
% 142.81/21.50 | |
% 142.81/21.50 | | (30) (all_57_6 = e3 & op(e1, e3) = e3) | (all_57_7 = e3 & op(e1, e2) =
% 142.81/21.50 | | e3)
% 142.81/21.50 | |
% 142.81/21.50 | | BETA: splitting (30) gives:
% 142.81/21.50 | |
% 142.81/21.50 | | Case 1:
% 142.81/21.50 | | |
% 142.81/21.50 | | | (31) all_57_6 = e3 & op(e1, e3) = e3
% 142.81/21.50 | | |
% 142.81/21.50 | | | ALPHA: (31) implies:
% 142.81/21.50 | | | (32) all_57_6 = e3
% 142.81/21.50 | | |
% 142.81/21.50 | | | BETA: splitting (18) gives:
% 142.81/21.50 | | |
% 142.81/21.50 | | | Case 1:
% 142.81/21.50 | | | |
% 142.81/21.50 | | | | (33) (all_57_6 = e2 & op(e1, e3) = e2) | (all_57_7 = e2 & op(e1, e2)
% 142.81/21.50 | | | | = e2)
% 142.81/21.50 | | | |
% 142.81/21.50 | | | | BETA: splitting (33) gives:
% 142.81/21.50 | | | |
% 142.81/21.50 | | | | Case 1:
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | (34) all_57_6 = e2 & op(e1, e3) = e2
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | REF_CLOSE: (14), (32), (34) are inconsistent by sub-proof #998.
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | Case 2:
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | (35) all_57_7 = e2 & op(e1, e2) = e2
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | ALPHA: (35) implies:
% 142.81/21.50 | | | | | (36) all_57_7 = e2
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11),
% 142.81/21.50 | | | | | (12), (13), (14), (15), (16), (19), (20), (21), (22), (23),
% 142.81/21.50 | | | | | (24), (25), (27), (28), (29), (36) are inconsistent by
% 142.81/21.50 | | | | | sub-proof #923.
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | End of split
% 142.81/21.50 | | | |
% 142.81/21.50 | | | Case 2:
% 142.81/21.50 | | | |
% 142.81/21.50 | | | | (37) (all_57_8 = e2 & op(e1, e1) = e2) | (all_57_11 = e2 & op(e1, e0)
% 142.81/21.50 | | | | = e2)
% 142.81/21.50 | | | |
% 142.81/21.50 | | | | BETA: splitting (37) gives:
% 142.81/21.50 | | | |
% 142.81/21.50 | | | | Case 1:
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | (38) all_57_8 = e2 & op(e1, e1) = e2
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | ALPHA: (38) implies:
% 142.81/21.50 | | | | | (39) op(e1, e1) = e2
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | REF_CLOSE: (5), (9), (20), (39) are inconsistent by sub-proof #1085.
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | Case 2:
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | (40) all_57_11 = e2 & op(e1, e0) = e2
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | | REF_CLOSE: (5), (26), (40) are inconsistent by sub-proof #913.
% 142.81/21.50 | | | | |
% 142.81/21.50 | | | | End of split
% 142.81/21.50 | | | |
% 142.81/21.50 | | | End of split
% 142.81/21.50 | | |
% 142.81/21.50 | | Case 2:
% 142.81/21.50 | | |
% 142.81/21.50 | | | (41) all_57_7 = e3 & op(e1, e2) = e3
% 142.81/21.50 | | |
% 142.81/21.50 | | | REF_CLOSE: (1), (2), (3), (4), (5), (6), (7), (8), (9), (10), (11), (12),
% 142.81/21.50 | | | (13), (14), (15), (16), (19), (20), (21), (22), (23), (24),
% 142.81/21.50 | | | (25), (27), (28), (29), (41) are inconsistent by sub-proof
% 142.81/21.50 | | | #922.
% 142.81/21.50 | | |
% 142.81/21.50 | | End of split
% 142.81/21.50 | |
% 142.81/21.50 | Case 2:
% 142.81/21.50 | |
% 142.81/21.50 | | (42) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) =
% 142.81/21.50 | | e3)
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (9), (20), (23), (26), (42) are inconsistent by sub-proof #911.
% 142.81/21.50 | |
% 142.81/21.50 | End of split
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #911 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) (all_57_8 = e3 & op(e1, e1) = e3) | (all_57_11 = e3 & op(e1, e0) = e3)
% 142.81/21.50 (2) op(e1, e1) = e1
% 142.81/21.50 (3) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (4) ~ (e3 = e1)
% 142.81/21.50 (5) all_57_11 = e1
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | BETA: splitting (1) gives:
% 142.81/21.50 |
% 142.81/21.50 | Case 1:
% 142.81/21.50 | |
% 142.81/21.50 | | (6) all_57_8 = e3 & op(e1, e1) = e3
% 142.81/21.50 | |
% 142.81/21.50 | | ALPHA: (6) implies:
% 142.81/21.50 | | (7) op(e1, e1) = e3
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (2), (3), (4), (7) are inconsistent by sub-proof #1096.
% 142.81/21.50 | |
% 142.81/21.50 | Case 2:
% 142.81/21.50 | |
% 142.81/21.50 | | (8) all_57_11 = e3 & op(e1, e0) = e3
% 142.81/21.50 | |
% 142.81/21.50 | | ALPHA: (8) implies:
% 142.81/21.50 | | (9) all_57_11 = e3
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (4), (5), (9) are inconsistent by sub-proof #912.
% 142.81/21.50 | |
% 142.81/21.50 | End of split
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #912 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) all_57_11 = e3
% 142.81/21.50 (2) all_57_11 = e1
% 142.81/21.50 (3) ~ (e3 = e1)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.50 | (4) e3 = e1
% 142.81/21.50 |
% 142.81/21.50 | SIMP: (4) implies:
% 142.81/21.50 | (5) e3 = e1
% 142.81/21.50 |
% 142.81/21.50 | REDUCE: (3), (5) imply:
% 142.81/21.50 | (6) $false
% 142.81/21.50 |
% 142.81/21.50 | CLOSE: (6) is inconsistent.
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #913 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) all_57_11 = e2 & op(e1, e0) = e2
% 142.81/21.50 (2) all_57_11 = e1
% 142.81/21.50 (3) ~ (e2 = e1)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | ALPHA: (1) implies:
% 142.81/21.50 | (4) all_57_11 = e2
% 142.81/21.50 |
% 142.81/21.50 | COMBINE_EQS: (2), (4) imply:
% 142.81/21.50 | (5) e2 = e1
% 142.81/21.50 |
% 142.81/21.50 | REDUCE: (3), (5) imply:
% 142.81/21.50 | (6) $false
% 142.81/21.50 |
% 142.81/21.50 | CLOSE: (6) is inconsistent.
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #914 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) all_57_4 = e2
% 142.81/21.50 (2) (all_57_4 = e0 & op(e3, e1) = e0) | (all_57_5 = e0 & op(e2, e1) = e0)
% 142.81/21.50 (3) ~ (e2 = e0)
% 142.81/21.50 (4) ! [v0: $i] : ! [v1: $i] : ! [v2: $i] : ! [v3: $i] : (v1 = v0 | ~
% 142.81/21.50 (op(v3, v2) = v1) | ~ (op(v3, v2) = v0))
% 142.81/21.50 (5) op(e2, e1) = all_52_9
% 142.81/21.50 (6) ~ (all_52_9 = e0)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | BETA: splitting (2) gives:
% 142.81/21.50 |
% 142.81/21.50 | Case 1:
% 142.81/21.50 | |
% 142.81/21.50 | | (7) all_57_4 = e0 & op(e3, e1) = e0
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (1), (3), (7) are inconsistent by sub-proof #1013.
% 142.81/21.50 | |
% 142.81/21.50 | Case 2:
% 142.81/21.50 | |
% 142.81/21.50 | | (8) all_57_5 = e0 & op(e2, e1) = e0
% 142.81/21.50 | |
% 142.81/21.50 | | ALPHA: (8) implies:
% 142.81/21.50 | | (9) op(e2, e1) = e0
% 142.81/21.50 | |
% 142.81/21.50 | | REF_CLOSE: (4), (5), (6), (9) are inconsistent by sub-proof #1091.
% 142.81/21.50 | |
% 142.81/21.50 | End of split
% 142.81/21.50 |
% 142.81/21.50 End of proof
% 142.81/21.50
% 142.81/21.50 Sub-proof #915 shows that the following formulas are inconsistent:
% 142.81/21.50 ----------------------------------------------------------------
% 142.81/21.50 (1) all_57_7 = e3
% 142.81/21.50 (2) all_57_7 = e1
% 142.81/21.50 (3) ~ (e3 = e1)
% 142.81/21.50
% 142.81/21.50 Begin of proof
% 142.81/21.50 |
% 142.81/21.50 | COMBINE_EQS: (1), (2) imply:
% 142.81/21.50 | (4) e3 = e1
% 142.81/21.50 |
% 142.81/21.50 | SIMP: (4) implies:
% 142.81/21.50 | (5) e3 = e1
% 142.81/21.50 |
% 142.81/21.50 | REDUCE: (3), (5) imply:
% 142.81/21.50 | (6) $false
% 142.81/21.50 |
% 142.81/21.50 | CLOSE: (6) is